Waves and Sound notes

Here is a skeleton outline of the notes from the past few classes.

Waves - a periodic disturbance, typically oscillating with sinusoidal behavior. Imagine a simple harmonic oscillator moving through space.

Types of waves (in general):

mechanical - require medium
electromagnetic - do not require a medium, and travel at the speed of light (in a vacuum)
c = 3 x 10^8 m/s

Types of wave (by geometry):

transverse - disturbance is perpendicular to wave speed
longitudinal - disturbance is parallel to wave speed

Wave speed, v = frequency x wavelength

Standing waves on a string:

There are harmonics - "standing" waves which occur at points where the energy maximizes the displacement of the string. A string can typically vibrate at any frequency, but some are dramatically better than others. These frequencies are called harmonics.

wavelength = 2L / n

This is an expression for the wavelength of given harmonic (with harmonic number n)

To find the frequency (or speed), use the wave speed expression above.


For organ pipes open at both ends, the mathematical treatment is very similar. The waves, however, are NOT transverse - they are longitudinal. That is, the sound jiggles back and forth, NOT up and down. However, we can represent the motion of the particles (in terms of particle density inside the tube) as a sine function with anti-nodes on both ends. This gives rise to the pictures we saw in class (and on the applets posted earlier).

If the tube is capped at one end, the wavelengths are given by 4L/n. Furthermore, due to this geometry, the tube can only generate ODD numbered harmonics.


The Doppler Effect

The changed in perceived/detected frequency, due to relative motion between source and observer. See previously posted applets.

f' = f [(v +/- vd) / (v -/+ vs)]

where v is the speed of sound, vd is the speed of the detector, and vs is the speed of the source.