5.2 Describing Waves

Since waves are periodic, the representation of an entire wave can be drawn by simply drawing the activity of one wave component only. One kind of waveform graph is that of the displacement of a single oscillator, or wave component, against time. This can be used for both transverse and longitudinal waves, even though the displacement of each of their components is in different directions. Here is a graph of one such wave.

The amount of time it takes the oscillator to complete one whole cycle is called the time period of a wave, T, and is measured in seconds. Conversely, the reciprocal of this number gives the number of waves that will pass per second. This is called the frequency of a wave, f, and is measured in Hertz, Hz (cycles per second). Finally, the wave’s amplitude, a, is its maximum displacement from its equilibrium position, and is measured in meters.

A wave can also be graphed by taking into account the displacement of all the oscillators in the system at an instance in time. This can be shown on a displacement-distance(from the source) graph, from which we can derive more information about the wave. On this graph, the distance between two similar points on a graph - one cycle- yields new information. In this case, it is called the wavelength, l , and is measured in meters. The product of wavelength and frequency gives the velocity of the wave itself, in meters per second:

Waves that arrive at their crests and troughs at the same time, regardless of any difference in amplitude, are said to be in phase. This term can also be applied to points of a wave that also have this property. Points that are separated by integer multiples of T, or l , are in phase.