Free · Acoustic waves calculators 🔊

Wave Phase Speed & Medium Comparison

Use custom phase speed or fixed medium presets to relate frequency, wavelength and ordinary wavenumber.

  • Formula & worked example
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Calculator inputs

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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 500 Hz wave with wavelength 3 m has phase speed 1,500 m/s. Its ordinary wavenumber is one third of a cycle per meter.

Phase speed = frequency × wavelength; ordinary wavenumber = 1/wavelength

Worked example

Enter these known values and leave the other values blank.

Reference medium or custom phase speed
custom wave velocity
Wave frequency
500 Hz
Wavelength
3 m
Ordinary wavenumber (cycles per length)
0.3333 1 / m
Phase speed
1500 m/s

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.
  • This scalar calculator gives a positive propagation speed. It does not determine a travel direction or the motion of particles in the medium.

Common questions

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 speed be calculated while a material preset is selected?

A preset supplies a fixed speed. Select custom phase speed to calculate it from frequency and wavelength or enter your own speed.

References

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

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