# Graphical representation of waves

Wave motion can be represented by graphs. The axes can include x-displacement, y-displacement, velocity, acceleration and time. However, take care to realise that a graph is not a picture of a wave.

Since there is no energy transfer, a pendulum wave isn't really a wave... but it looks impressive!

Key Concepts

A wave is made of a series of out of phase oscillations.

Essentials

Transverse waves

A transverse wave can be represented by graphs of:

• displacement-time
• displacement-position

Longitudinal waves

A longitudinal wave doesn't look like a sinousoidal wave because the oscillations are parallel to the direction of wave propagtation. However if graphs are drawn, the sinusoidal nature is revealed.

It is difficult to plot the displacement of the points on a longitudinal wave, but easy to represent them with a displacement-position graph.

Summary

The generic wave equation is as follows:

$$y=a\sin (2\pi ft-{2\pi x \over \lambda})$$

Test Yourself

Use quizzes to practise application of theory.