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# Waveform

The **waveform** is the shape of a wave as it travels. There are many different waveforms. They are usually a shape which is repeated over and over (a "periodic waveform"). A common waveform is the sine wave. It is normally not possible to see a waveform without some device.

## Root mean square

The amplitude of a waveform may change a lot. Even though it changes, the waveform has a **root mean square** (rms) value. For example: in the UK, the AC mains supply is a sine wave and has a voltage of 240 V. This is an rms voltage. The actual voltage varies:

- [math]V_{\text{peak}} = \sqrt 2 \times V_{\text{rms}} = \sqrt 2 \times 240 = \pm 339.411255\dots V[/math]

The amplitude of the sine wave keeps changing from -339.4 V to +339.4 V.

Root mean square is important. It lets us work out many useful things, like power and heating in a wire.

This table has information about working out the rms for some waveforms.

Wave type | rms amplitude |
---|---|

Sine wave | [math]A_{\text{rms}} = \frac{A_{\text{peak}}}{\sqrt 2}[/math] |

Square wave | [math]A_{\text{rms}} = A_{\text{peak}}[/math] |

Triangular wave | [math]A_{\text{rms}} = \frac{A_{\text{peak}}}{\sqrt 3}[/math] |