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