## Wave Equation for Travelling and Standing Waves

The fundamental wave equation is

\[v=f \lambda\]

, where\[v\]

is the wave speed\[f\]

is the frequency\[\lambda\]

is the wavelengthThis equation is true for both traveling waves and standing waves - waves on a stretched spring fixed between two points, or sound waves in a pipe. But standing waves don't travel, so how can the standing wave have a speed? You should think of wavelength and frequency for longitudinal and standing waves as in the table below.

Quantity\type | Frequency | Wavelength |

Standing | Number of complete up and down cycles per second | Twice the distance between successive nodes, or this distance between two points moving at thew same speed in the same direction (up and up, or down and down) |

Traveling | Number of complete wavelengths a particular wave moves per second - the above definition does not work because travelling waves do not move up and down. The whole waveform moves, like a train | Twice the distance between a peak and a trough - the above definition will no do because all points on a travelling wave are moving at the same speed in the same direction (horizontally for a water wave) |