Free · Waves and acoustics calculators 🔊

Wave Speed, Frequency, Wavelength & Wavenumber

Relate wave speed and frequency to wavelength and reciprocal wavelength, with medium presets and custom speed.

  • 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 wave travelling at 343 m/s with frequency 686 Hz has wavelength 0.5 m and spectroscopic wavenumber 2 m⁻¹.

Wavelength = phase speed / frequency; spectroscopic wavenumber = 1 / wavelength

Worked example

Enter these known values and leave the other values blank.

Medium preset or custom speed
Sound in air at 20 °C
Wave frequency
686 Hz
Wave phase speed
343 m/s
Wavelength
0.5 m
Spectroscopic wavenumber (cycles per length)
2 1/ m

Assumptions and limitations

  • Speed, frequency, wavelength and wavenumber are positive. Use phase speed at the frequency and conditions of interest.
  • The wavenumber here is 1/wavelength, in cycles per unit length. Angular wavenumber is 2π/wavelength and has a different numerical value.
  • Medium presets are fixed illustrative speeds. Real values depend on temperature, composition, wave type and frequency; Custom allows a suitable measured or modeled value. Vacuum light speed is exactly 299,792,458 m/s.

Common questions

What does the reciprocal unit selector mean?

Selecting centimeters for wavenumber means inverse centimeters, not centimeters. For example, a wavelength of 1 cm has wavenumber 1 cm⁻¹.

Can I use group velocity for wavelength?

Use phase velocity in wavelength = velocity/frequency. Group velocity can differ in a dispersive medium.

References

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

Explore waves and acoustics calculators 🔊 or browse all physics calculators.