Frequency Calculator

The frequency calculator lets you quickly find the frequency, given either its period or its wavelength and velocity.

Clear
Frequency439.7436 Hz0.00227405 s per cycle
Wavelength780 mm
Wave speed343 m/s
Period2.2741 ms
Angular frequency ω2,762.990462 rad/s
Wave number k8.055366 rad/m2π/λ — radians of phase per metre
Check: ω/k343 m/sequals the wave speed, by definition
Maximum transverse speed27.629905ωA — the speed of the medium, not of the wave
Maximum transverse acceleration76,341.162931
As a sound wave in air780 mmwavelength at 343 m/s
As an electromagnetic wave681.7438 kmwavelength in vacuum at this frequency

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.