Free · Acoustic waves calculators 🔊

Ordinary & Angular Wavenumber from Wavelength

Relate wavelength, cycles per length and radians per length, with optional phase-speed presets.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A wavelength of 2 m corresponds to ordinary wavenumber 0.5 m⁻¹ and angular wavenumber π rad/m. At 10 m/s, its frequency is 5 Hz.

Ordinary wavenumber = 1/λ; angular wavenumber = 2π/λ; phase speed = frequency × wavelength

Worked example

Enter these known values and leave the other values blank.

Reference medium or custom phase speed
custom
Phase speed
10 m/s
Wavelength
2 m
Ordinary wavenumber (cycles per length)
0.5 1/ m
Angular wavenumber (radians per length)
3.1416 radian/ m
Wave frequency
5 Hz

Assumptions and limitations

  • All wave quantities here are positive magnitudes. Speed means phase speed, not particle speed or necessarily group velocity.
  • Use quantities for the same periodic wave in the same medium. Dispersion and changes in the medium are not modeled.
  • The vacuum-light preset uses exactly 299,792,458 m/s. Other presets are representative fixed speeds and do not adjust for temperature, pressure, composition or wave polarization.
  • Select custom speed to supply a value appropriate to the wave and conditions. A selected material preset holds its speed fixed.
  • The inverse-length selectors apply to both wavenumbers. Radians are dimensionless in SI; the angular label distinguishes radians per length from cycles per length.

Common questions

Why can an inverse calculation stay blank after locking and clearing fields?

A lock can constrain the available calculation order. Reset and enter only the known values without locks, or unlock phase speed, clear the old wavelength, then clear and re-enter wavenumber. Do not use a result while a conflict is shown.

Does wavenumber mean 1/λ or 2π/λ?

Both conventions appear in scientific work. The ordinary wavenumber here is 1/λ, in cycles per length. Angular wavenumber is 2π/λ, in radians per length. Always check the convention used by your formula.

Can I enter ordinary wavenumber instead of wavelength?

Yes. A positive ordinary wavenumber determines wavelength through its reciprocal. Frequency also requires a phase speed.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

Explore acoustic waves calculators 🔊 or browse all physics calculators.