WAVES II

I. Sound waves are longitudinal, mechanical waves

    1. Propagated in solids, liquids, and gases
    2. Audible range - 20 Hz to 20kHz
    3. Infrasonic - below 20 Hz
    4. Ultrasonic - above 20 kHz

II. Sound is composed of successive compressions and rarefactions

    1. Displacement is measured along the direction of propagation
    2.  

      y = ymaxsin(kx-w t)

       

    3. Displacement wave is 90° out of phase with the pressure wave

 

p = Pcos(kx-w t)

 

III. Pipes (columns of air) have different natural frequencies of vibration depending on whether the ends are open or closed.

    1. A closed end is a displacement node (pressure antinode)
    2. An open end is a displacement antinode (pressure node)
    3. For a pipe open at one end and closed at the other the natural frequencies are:
    4. fcl = n(v/4L)

      where v is the speed of sound in air, L is the length of the pipe, and n is an odd integer

    5. For a pipe open at both ends the natural frequencies are:
    6. fop = n(v/2L)

      where v is the speed of sound in air, L is the length of the pipe, and n is an integer.

    7. What are the fundamental, harmonics, and overtones for a pipe?

IV. Two sound sources with a small frequency difference of D f, will exhibit a beat frequency when heard together.

    1. There will be D f beats per second.

V. The Doppler Effect

    1. Change in frequency observed when source and/or observer are in motion.
    2. My sign convention: The positive direction will always be from the LISTENER to the SOURCE.
    3. If fL is the frequency heard by listener, f is natural frequency of the source, v is the VELOCITY of sound, vL is the VELOCITY of the listener, and vS is the VELOCITY of the source, then

 

fL/(v + vL) = fS/(v + vS)

 

VI. Intensity

A. For a point source of sound waves : Intensity = (Power)/4p R2

    1. Intensity of the faintest detectable sound wave: I0= 10-16 watts/m2
    2. Used as the reference on the decibel scale:

 

b = 10log(I/I0)