Sound

Physics 202Professor 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) = sm 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 pressurep(x,t) = pm sin (kx - t)

Where pm is the pressure amplitude The pressure amplitude is related to the

displacement amplitude by:pm = (v) sm

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