Sound

Physics 202Professor Lee

CarknerLecture 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) = sm cos (kx-t)

This is similar to the transverse wave equation but does not involve y

Pressure Wave

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 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

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)

Inverse Square Law

Source

r

2rA1=4r2

I1 = Ps/A1

A2=4(2r)2 = 16r2 = 4A1

I2 = Ps/A2 = ¼ I1

Next Time

Read: 17.5-17.10