Date post: | 31-Dec-2015 |
Category: |
Documents |
Upload: | hermione-mendez |
View: | 45 times |
Download: | 2 times |
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) = sm cos (kx-t)
This is similar to the transverse wave equation but does not involve y
Pressure
p(x,t) = pm sin (kx - t) Where pm is the pressure amplitude
pm = (v) sm
This is not an absolute pressure but rather a pressure change
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
LL
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/m2
I = ½v2sm
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 = Ps/(4r2) Sounds get fainter as you get further away
because the energy is spread out over a larger area I falls off as 1/r2 (inverse square law)