Sound Physics 202 Professor Vogel (Professor Carkner’s notes, ed) Lecture 7

Sound  What we think of as sound is a longitudinal wave transmitted through the air at frequencies that our ears are sensitive to  More generally we can describe a sound wave as any longitudinal wave  Packets of air move back and forth along the direction of propagation  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  The linear density tells you how hard it is to move the string from rest, the tension tells you how much the string wants to snap back into place  For sound what is the elastic property? What is the inertial property?

Sound Speed  For sound the velocity is: v = (B/  ) ½  Where  is the density and B is the bulk modulus  The bulk modulus indicates how hard it is to compress a fluid and is given by B = -  p/(  V/V)  Where p is the pressure and V is the volume  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  Consider a sound wave moving through a tube along the x-axis  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)  s tells you how far from the equilibrium position the element of air a distance x along the tube is at time 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)  Where  p m is the pressure amplitude  The pressure amplitude is related to the displacement amplitude by:  p m = (v  ) s m  The pressure acts on your eardrum enabling you to hear  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 a maximum the pressure is zero  When the displacement is zero the pressure is a maximum  The motion of the fluid element is affected by the pressures of the near-by regions  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  The air ahead of it is at negative displacement and the the air behind is at positive, “squeezing” the element  At min pressure the air is also at rest position  The air ahead is at positive displacement and the air behind is at negative, “stretching” the element  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  Consider two sources of sound a certain distance apart  If an observer is an equal distance from each, the sound will be in phase  If not, the phase difference depends on the path length difference  L  For a phase difference of 2  the path length difference is  L   L 

Combining Waves From 2 Sources

Constructive and Destructive  Fully constructive interference occurs when  is an integer multiple of 2 , or:  L=m  The sound will be at max amplitude (louder than an individual source)  Fully destructive interference occurs when  is an integer multiple of , or:  L = (m+½)  The two sources will cancel out (you hear nothing)  You can also have intermediate interference making the sound louder or softer

Interference and You  Why don’t we notice interference much?  You have two ears  Each with a different  L  Sound reflects  You hear a combination of many different L  Most sound is a combination of many frequencies  Not all will have strong interference at your location  You move  You don’t hold perfectly still at the spot with maximum interference