Sound Physics 202 Professor Lee Carkner Lecture 9

Sound   More generally we can describe a sound wave as any longitudinal wave   Unlike waves on a string, a sound wave propagates outward in all 3 dimensions  Example: If a balloon pops you hear it no matter where you are, above, below, left, right, etc.

Sound Wavefronts

Traveling Through a Medium  How sound travels depends on the medium in is moving through (like any other wave)  For a wave on a string: v=(  ) ½   For sound what is the elastic property? What is the inertial property?

Sound Speed  For sound the velocity is: v = (B/  ) ½   The bulk modulus indicates how hard it is to compress a fluid and is given by B = -  p/(  V/V)   Example: Water is more dense than air, so why does sound travel faster in water?  It has a much larger B. Water is hard to compress

Wave Equations   The displacement of any element of air will also be in the x direction and is represented by: s(x,t) = s m cos (kx-  t)   This is similar to the transverse wave equation but does not involve y

Pressure Wave

Pressure  As the element of air moves it creates a change in pressure  p(x,t) =  p m sin (kx -  t)   The pressure amplitude is related to the displacement amplitude by:  p m = (v  ) s m   This is not an absolute pressure but rather a pressure change

Pressure Wave Equation

Pressure and Displacement  The pressure and the displacement variations are  /2 radians out of phase   When the displacement is zero the pressure is a maximum   It is pushed and pulled by high and low pressure

Pressure and Displacement

Max and Min Pressure  At max pressure the air is at its rest position   At min pressure the air is also at rest position   At zero pressure the air is at max displacement one way or another  There is a “squeeze” one way and a “stretch” the other, in between is normal

Interference   If an observer is an equal distance from each, the sound will be in phase   For a phase difference of 2  the path length difference is  L   L 

Combining Waves From 2 Sources

Constructive and Destructive   L=m   Fully destructive interference occurs when  is an integer multiple of , or:  L = (m+½)   You can also have intermediate interference making the sound louder or softer

Interference and You  Why don’t we notice interference much?   Each with a different  L   You hear a combination of many different L   Not all will have strong interference at your location  You move 

Next Time  Read:  Homework: Ch 17, P: 14, 26, 35, 36