Sound Physics 202 Professor Lee Carkner Lecture 9

PAL # 8 Standing Waves  Longest and shortest wavelength that produces resonance on a 2 m string   For n=1, = 4m (longest)   For n=1 case and f = 8 Hz, what is  ?    = mg = (2)(9.8) = 19.6 N    =  /v 2 = (19.6)/(32) 2 = kg/m

PAL # 8 Standing Waves (cont.)  Starting with n = 1 case, which changes will still give you resonance?   Double hanging mass   Double frequency  2f, ½, resonance  Quarter mass ¼¼  Quadruple mass  4m, 4 , 2v, 2, no resonance

Sound  What we think of as sound is a longitudinal wave transmitted through the air at frequencies that our ears are sensitive to   Packets of air move back and forth along the direction of propagation   Example: If a balloon pops you hear it no matter where you are, above, below, left, right, etc.

Sound Wavefronts

Traveling Through a Medium   For a wave on a string:  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   The bulk modulus indicates how hard it is to compress a fluid and is given by  Where p is the pressure and V is the volume   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:    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    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   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  Consider two sources of sound a certain distance apart    For a phase difference of 2  the path length difference is   L 

Combining Waves From 2 Sources

Constructive and Destructive  Fully constructive interference occurs when  is an integer multiple of 2 , or:    Fully destructive interference occurs when  is an integer multiple of , or:    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   Sound reflects   Most sound is a combination of many frequencies   You move 