sound physics 202 professor lee carkner lecture 9
Post on 18-Dec-2015
218 views
TRANSCRIPT
Sound
Physics 202Professor Lee
CarknerLecture 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 = /v2 = (19.6)/(32)2 = 0.0191 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
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) = sm 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 pressurep(x,t) = pm 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