The physical nature of sound waves

• Sound waves can travel through liquid, solid or gaseous media
• The speed of a sound wave is given by the square root of the ration of bulk modulus to density
• One may describe sound waves by the displacement of individual molecules as a function of space and time
• One may also describe sound waves by the pressure in the medium as a function of space and time
• The intensity of a wave is the power it transmits through some area
• Intensity is proportional to the SQUARE of the amplitude of a wave

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  Let's look at the human hearing mechanism for a moment. It has a very wide dynamic range:

  
     maximum for safe detection, without damage to ear
  
            delta-Pressure  P   ~   2.8 x 10^(+1)  Pascals
  
     minimum for detection   
  
            delta-Pressure  P   ~   2.8 x 10^(-5)  Pascals
  
  

  Can you figure out the amplitudes of motion of the air molecules in the following two sounds?

  1. Jane whispers very softly in Jack's ear, so that he can barely detect her voice. Her voice has a frequency of about 1000 Hz.
  2. Andy asks his mother to pass the salt in an ordinary manner. His voice produces pressure waves which are about 1000 times larger in amplitude than Jane's waves. His voice has a frequency of about 300 Hz.

  The typical human eardrum has a diameter of about 8 mm. In ordinary conversation, the pressure fluctuations on the membrane of the drum have an amplitude of about 0.028 Pascals.

  
  
      Q:  What is the magnitude of the fluctuations
          in the FORCE exerted on the eardrum
          in ordinary conversation?
  
  
      Q:  Suppose we make a model of the eardrum
          by stretching a piece of plastic over
          the mouth of a bottle.  In order to
          exert a similar force on this plastic,
          we place an object on the plastic,
          so its weight presses down.
         
          What is the mass of an object which
          will exert the proper force?
  
  

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Fred's little brother Bobby is a real pain in the neck. He is always talking -- about baseball, comic books, Egyptian antiquities, flavors of ice cream -- he just won't be quiet. Fred decides to make the best of a bad situation: he builds a device to harness the power of Bobby's voice. A very thin panel 1 meter on a side converts the energy of the sound waves coming out of Bobby's mouth into electricity.

     Q:  Assume that Bobby talks at an ordinary
         volume, so the sound waves have a pressure
         amplitude of 2.5 x 10^(-2) pascals. 
         Estimate the power this device will
         produce.  

  
     Q:  Could it light an ordinary bulb?


     Q:  Fred builds a solar panel which is also
         1 meter on a side and places it outside
         on a sunny day.  Roughly how much 
         power does this panel produce?