Wave Speed Calculator

The formula

v = fλ; k = 2π/λ; ω = 2πf

One equation, and what it does not say

Speed equals frequency times wavelength for every wave there is — sound, light, water, seismic. The relation is definitional: a wave passing at f cycles a second, each λ long, advances fλ metres a second.

What the equation does not tell you is which quantity is fixed. That depends on the physics of the situation, and getting it the wrong way round is the usual mistake. When a wave crosses into a new medium its frequency is unchanged — the source is still oscillating at the same rate — so the speed change shows up entirely as a change in wavelength. Light entering glass slows and its wavelength shortens, while its colour, set by frequency, does not change.

Note that the wave speed and the speed of the medium are different things. A water wave can travel at metres per second while the water itself only bobs up and down slowly — the maximum transverse speed above is the latter, and it depends on amplitude, which the wave speed does not.