A periodic wave repeats its pattern in both time and space. A simple sinusoidal travelling wave can be written as

$$y(x,t)=A\cos(kx-\omega t+\phi).$$

Each parameter describes a different feature of the wave.

Amplitude

The amplitude $A$ is the maximum magnitude of the disturbance from equilibrium.

Period and frequency

The period $T$ is the time for one complete oscillation. The frequency is the number of cycles per unit time:

$$f=\frac1T.$$

Angular frequency is

$$\omega=2\pi f.$$

Wavelength

The wavelength $\lambda$ is the spatial distance between equivalent points on successive cycles, such as neighboring crests.

The wave number is

$$k=\frac{2\pi}{\lambda}.$$

Phase

The phase tells where a point lies within the oscillation cycle. Two waves with the same frequency can be shifted relative to one another by a phase difference.

These quantities provide the language needed to compare wave shapes, propagation speeds and interference.