INTERFACES DA MATEMÁTICA COM A FÍSICA OSCILAÇÕES E ONDAS - VI

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Interfaces da
Matemática com a Física:
Oscilações e Ondas
Material Teórico
Responsável pelo Conteúdo:
Prof. Dr. Jaime Sandro da Veiga
Ondas sonoras
• Introdução
• Velocidade do Som em um Gás
• Fatos Curiosos a Saber sobre o Som
• As Qualidades do Som
• O Efeito Doppler
• A Utilização de Ultrassons em Testes
 · Adquirir conhecimentos sobre ondas sonoras, nos quais serão 
explorados os conceitos de interferência, intensidade e nível sonoro, 
fontes e sons musicais e o estudo do efeito Doppler. 
 · Introduzir conceitos didáticos que venham a colaborar com a futura 
prática docente dos alunos, compreenderem fenômenos, expressando 
com clareza e precisão. 
 · Articular os conceitos e desenvolver a capacidade de raciocínio 
lógico para identificar, formular e resolver problemas.
OBJETIVO DE APRENDIZADO
Ondas sonoras
Orientações de estudo
Para que o conteúdo desta Disciplina seja bem 
aproveitado e haja uma maior aplicabilidade na sua 
formação acadêmica e atuação profissional, siga 
algumas recomendações básicas: 
Assim:
Organize seus estudos de maneira que passem a fazer parte 
da sua rotina. Por exemplo, você poderá determinar um dia e 
horário fixos como o seu “momento do estudo”.
Procure se alimentar e se hidratar quando for estudar, lembre-se de que uma 
alimentação saudável pode proporcionar melhor aproveitamento do estudo.
No material de cada Unidade, há leituras indicadas. Entre elas: artigos científicos, livros, vídeos e 
sites para aprofundar os conhecimentos adquiridos ao longo da Unidade. Além disso, você também 
encontrará sugestões de conteúdo extra no item Material Complementar, que ampliarão sua 
interpretação e auxiliarão no pleno entendimento dos temas abordados.
Após o contato com o conteúdo proposto, participe dos debates mediados em fóruns de discussão, 
pois irão auxiliar a verificar o quanto você absorveu de conhecimento, além de propiciar o contato 
com seus colegas e tutores, o que se apresenta como rico espaço de troca de ideias e aprendizagem.
Organize seus estudos de maneira que passem a fazer parte 
Mantenha o foco! 
Evite se distrair com 
as redes sociais.
Mantenha o foco! 
Evite se distrair com 
as redes sociais.
Determine um 
horário fixo 
para estudar.
Aproveite as 
indicações 
de Material 
Complementar.
Procure se alimentar e se hidratar quando for estudar, lembre-se de que uma 
Não se esqueça 
de se alimentar 
e se manter 
hidratado.
Aproveite as 
Conserve seu 
material e local de 
estudos sempre 
organizados.
Procure manter 
contato com seus 
colegas e tutores 
para trocar ideias! 
Isso amplia a 
aprendizagem.
Seja original! 
Nunca plagie 
trabalhos.
UNIDADE Ondas sonoras
         
 
      
 
      
           
     
  
       
      
 
 
            
   
          
          
           
             
   
               
           
          
          
            
          
           
    

8
9
         
 
      
 
      
           
     
  
       
      
 
 
            
   
          
          
           
             
   
               
           
          
          
            
          
           
    

             
                 
            
          
             
             
        
          
             
              
             
              
           
             
           
     
             
               
                
             
           
           
            
         
        
            
          
    
    

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UNIDADE Ondas sonoras
          
           
            
           
             
           
      
  
 
               
  
             
                
            
       
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          
           
            
           
             
           
      
  

 
               
  
             
                
            
       

          
             
             
    
   

            
       
          
            

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UNIDADE Ondas sonoras
   


        
             
            
          
     
 

              
           
           
         
            
             
            
             
         
             
              

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   


        
             
            
          
     
 

              
           
           
         
            
             
            
             
         
             
              

            
          
           
          
            
               
           
          
            
              
          
     
     
      


           
            
           
          
          
            
              

             
             
            
           
            
              
             
             
           
              
        
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UNIDADE Ondas sonoras
          
             
            
        
      
              
              
            
           
            
            
            
             
 
           
         


      
                        
          
      
       
   
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          
             
            
        
      
              
              
            
           
            
            
            
             
 
           
         


      
           
             
          
      
       
   
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                  
              
              
     
         
 




                  
              
                
             
 
          
 





 



         
         
               
           
           
               
            
            
            
           
           
              
               
              
              
           
          
              
           
     
         
            
               

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UNIDADE Ondas sonoras
       
 



            
            
           
  
       
                
          
             
             
             
             
                
            
            
          
            
             
           
           
              
           
             
          
            
              
           
             
             
            
             
            
             
              
              
            
            
             
   
     

16
17
       
 



            
            
           
  
       
                
          
             
             
             
             
                
            
                      
            
             
           
           
              
           
             
          
            
              
           
             
             
            
             
            
             
              
              
            
            
             
   
     

             
          
  
       
         
       
            
        
  
              
            
             
            
            

    
    
               
           
     


  

    
           
        
 






 


 

 
   
           
                 
      
           
    
          
          
            
            
          
           
          

17
UNIDADE Ondas sonoras
         
    
             
      
 


 
             
           
            
           
              
          
            
           
           
              
            
          
            
           
          
            
             
         
             
            
              
      
   
         


 



         
 



              
             
                
           
 







18
19
         
    
             
      
 


 
             
           
            
           
              
          
            
           
           
              
            
          
            
           
          
            
             
         
             
            
              
     
   
         


 



         
 



              
             
                
           
 







            
          
   
  
 



            
   
 
 









 
           
           
             
              
   
          
           
           
             
           
      

  

     
        
   
       
    
         

19
UNIDADE Ondas sonoras
              
                
            
               
              
              
              
        
            
             
               
               
       

       
            
             
             
              
      
             
             
             
    

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              
                
            
               
              
              
              
        
            
             
               
               
       

       
            
             
             
              
      
             
             
             
    

    
 
   
   
 
 
 
 
 
       
       

 
              
             
             
         
           
       
            
        

21
UNIDADE Ondas sonoras
             
              
             
           
                
            
           
 




            
  
            
           
            
          
           
           
             
           
           
         
           
          
             
          
            
          
           

         
             
          
            
              
                
                
                
             
              
            
              
            

22
23
             
              
             
           
                
            
           
 




            
  
            
           
            
          
           
           
             
           
           
         
           
          
             
          
            
          
           

         
             
           
            
              
                
                
                
             
              
            
              
            

            
             
         
            
            
             
            
 
 
   
  


           
             
           
             
             
           
   

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UNIDADE Ondas sonoras
        

 

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        

 

 
              
          
              
          
            
           
           
             
           
         
           
             
        
               
             
              
            
          
 
     
            
            
           
            
            
            
            
           
                
              
             
               


25
UNIDADE Ondas sonoras
        
     
  
          
         
          
          

             
            
           
            
              
                
       
            
  



                  
             
          
       

26
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        
     
  
          
         
          
          

              
            
           
            
              
                
       
            
  



                  
             
          
       

   
  
  
    
  

            
             
              
            
             
             
          
            
             
            
            
          
    
            
            
           
          

27
UNIDADE Ondas sonoras
    

 
              
             
               
          
             
             
              
            
               
                
            
           
           
            
           
              
           
               
       

28
29
    

 
              
             
               
          
             
             
              
            
               
                
            
           
           
            
           
              
           
               
       

 
            
    
           
                
         
           
             
            
            
            
             
             
        
     
   
  
    
  
   
   
 
   
   
  
  
   
  

29
UNIDADE Ondas sonoras
 
             
             
             
    
            
              
            
           
           
           
              
          
            
     
   

             
            
           
             
             
  
        
              
           
          
           
          
 

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 
             
             
              
    
            
              
            
           
           
           
              
          
            
     
   

             
            
           
             
             
  
        
              
           
          
           
          
 

       

      
   

   
    
     

            
            
           
            
           
           
           
          
            
              
             
         
            
          
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UNIDADE Ondas sonoras
          
           
           
            
        
   
           
  
            
            
           
            
         
              
             
           
           
           
           
              
           
   
             
           
          
             
            
            
          
              
           
   
      
             
 
     
             
 
    
     
   

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          
           
           
            
        
              
  
            
            
           
            
         
              
             
           
           
           
           
              
           
   
             
           
          
             
            
            
          
              
           
   
      
             
 
     
             
 
    
     
   

   
   
             
   



            
            
             
            
           
            
            
       
          
            
         
          
              
               
           
            
             
            
          
              
            

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UNIDADE Ondas sonoras
              
              
            
           
               
           
        
   
          
           
           
           
            
         
            
             
        
           
           
              
               
              
      
            
            
          
            
           
          
   
           
           
           
           
              
            
           
             
   
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              
              
            
           
               
           
        
   
          
           
           
           
            
         
            
             
        
           
          
              
               
              
      
            
            
          
            
           
          
   
           
           
           
           
              
            
           
             
   

    
      
      

   
            
             
           
            
            
             

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UNIDADE Ondas sonoras
   
  


             
             
             
             
             
            
              
         
          
            
              
              
            
             
    
          
             
           
            
            
             
         
            
      
           
           
         
              
            
           

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   
  


             
             
             
             
             
            
              
         
          
            
              
              
            
             
    
          
             
           
            
            
             
         
            
      
           
           
         
              
            
           

             
                
    
 

 


 
           
        
 

 


 
         
  
               
              
            
   
           

 

  

  
               
          
             
            
    
        
             
 
 