Wave notes.

Wave properties

A wave is essentially a traveling disturbance - motion of "energy", NOT the motion of stuff. Fundamentally, there are two varieties of these - one that requires a medium (mechanical) and one that does not require a medium (electromagnetic). An electromagnetic wave can often travel through a medium, but it always travels fastest (at the speed of light, c) where nothing gets in the way.

Properties of a wave:

Wavelength - the distance between 2 successive crests, or 2 successive troughs, or any 2 points "in phase" with each other. Wavelength is represented by the Greek letter lambda (which unfortunately I can't show here). The unit for wavelength is generally the meter, but it could be any unit of length.

Frequency is the number of waves/oscillations per second. It is represented by the letter f. The unit is the "cycle per second", usually called the hertz (Hz).

The period (T) is the amount of time for one oscillation. It is the inverse of the frequency. That is, if you have 2 oscillations/waves per second, the time for each is 1/2 second. In equation form:

T = 1/f or f = 1/T

Amplitude - the distance from equilibrium (the horizontal line) to the peak/crest of the wave, or to the trough/valley of the wave. The amplitude is usually a representation of the volume/loudness (if it's a sound wave) or intensity/brightness (if a light wave).


The velocity/speed (v) of a wave is the rate at which the energy travels. Simply, v is given by:

v = d/T

Since the wavelength is the distance in question, and T = 1/f, the equation can be written more conveniently for a wave:

v = d/T = wavelength * 1/T = wavelength * f

So.....

v = wavelength * frequency

We can imagine waves that travel outward from the origin - maybe in one direction (like sending a pulse on a spring) or in 3 dimensions (like a sound wave).

However, often waves interfere with other waves - to produce NEW waves. Sometimes waves interfere with themselves. This is the case with "standing waves", or waves on a string. It will also be the case with music in tubes or organ pipes.

Consider this applet, where the fundamental (lowest) possible resonant frequency is 25 Hz. The resonant frequency is that frequency that generates the largest possible amplitude for the energy investment. Think of it as the "just right" rate at which you'd need to "pump" a swing to get it higher and higher. Too little and you go nowhere. Too much and you also go nowhere. There is a "just right" amount of frequency - that's the resonant frequency.

http://ngsir.netfirms.com/englishhtm/StatWave.htm

Note what happens when you move the frequency to multiples of the resonant frequency: 50 Hz, 75 Hz, etc. This same sort of thing happens routinely on stringed instruments, as we shall see in class.