Wave Equation for Travelling and Standing Waves

The fundamental wave equation is

\[v=f \lambda\]
, where
is the wave speed
is the frequency
is the wavelength
This 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)


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