Describing Waves

Wave — a disturbance that transfers energy from one place to another without transferring matter. The water in a ripple tank moves up and down; it does not travel across the tank. Only the energy does.

Amplitude — the maximum displacement of a point from its undisturbed position, measured in metres. It is measured from the middle to a crest, not from a crest to a trough. Halving that distance is the usual error.

Wavelength (λ) — the distance between two corresponding points on adjacent waves, such as crest to crest or trough to trough, measured in metres.

Frequency (f) — the number of complete waves passing a point each second, measured in hertz (Hz). One hertz is one wave per second.

Period (T) — the time for one complete wave to pass a point, in seconds. Frequency and period are reciprocals:

T = 1 / f

A wave of frequency 50 Hz has a period of 1/50 = 0.02 s.

The wave equation relates all three:

v = f λ

with speed in m/s, frequency in Hz and wavelength in m. This is the single most used equation in the whole section.

Wavefronts — lines drawn along the crests of a wave, at right angles to the direction of travel. The distance between adjacent wavefronts is one wavelength. They are a convenient way of drawing a wave from above, which is how a ripple tank is photographed.

What changes and what does not. When a wave passes from one material into another, its frequency stays the same — the source is still producing the same number of waves per second. The speed changes, and so the wavelength must change to keep v = f λ true. Saying the frequency changes on refraction is a guaranteed lost mark.

Example: a wave of wavelength 0.25 m has a frequency of 12 Hz. Its speed is v = fλ = 12 × 0.25 = 3.0 m/s. If it then moves into deeper water and speeds up to 4.5 m/s, the frequency is still 12 Hz, so the wavelength has become 4.5 ÷ 12 = 0.375 m.