Sound Physics 202 Professor Lee Carkner Lecture 8

Sound   More generally: sound = longitudinal wave   Unlike waves on a string, a sound wave propagates outward in all 3 dimensions  Example:  String wave 1D, sound wave 3D

Sound Speed  For sound the velocity is: v = (B/  ) ½   Bulk modulus is like tension (how “springy” the fluid is)  Density is like linear density  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   p(x,t) =  p m sin (kx -  t)  Where  p m is the pressure amplitude   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   and away from where pressure is low

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 

Constructive and Destructive   L=m  The sound will be at max amplitude (louder than an individual source)   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 don’t hold perfectly still at the spot with maximum interference

Intensity of Sound  I = P/A  The units of intensity are W/m 2  I = ½  v  2 s m 2  Compare to expression for power in a transverse wave   Depends on the square of the amplitude and the frequency (wave properties)

Intensity and Distance   As you get further away from the source the intensity decreases because the area over which the power is distributed increases  I = P/A = P s /(4  r 2 )  Sounds get fainter as you get further away because the energy is spread out over a larger area  I falls off as 1/r 2 (inverse square law)

Inverse Square Law Source r 2r A 1 =4  r 2 I 1 = P s /A 1 A 2 =4  (2r) 2 = 16  r 2 = 4A 1 I 2 = P s /A 2 = ¼ I 1

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