Grafiek van de golffunctie

Consider a sinusoidal wave traveling in the x-direction.

As its wave equation is the function of displacement and time, a particle's motion in the medium can be graphically represented by displacement-position and displacement-time graphs.

At a fixed time, the particle's displacement varies as a function of the position.

This represents the displacement of the particle from its equilibrium position. The wavelength can then be deduced from this graph.

Considering the case of a transverse wave on a string, the graph represents the actual shape of the string at a particular instant of time.

When a specific coordinate is chosen, graphing the wave equation results in a displacement-time graph.

Using this graph, the period—the time required for the wave to travel one wavelength—is deduced.

In the wave equation, the argument of the cosine function is called the phase of the wave.

The phase velocity is the speed at which the wave moves, keeping the phase constant.

Taking a derivative with respect to time, an expression for the phase velocity is obtained.