Free · Acoustic waves calculators 🔊

Wave Frequency & Period by Medium Speed

Calculate cycles per second and time per cycle from wavelength and a custom or preset phase speed.

Formula & worked example
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Calculator inputs

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How to use this calculator

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

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Formula and method

At phase speed 1,500 m/s and wavelength 3 m, frequency is 500 Hz and period is 0.002 s, or 2 ms.

Frequency = phase speed ÷ wavelength; period = 1/frequency

Worked example

Enter these known values and leave the other values blank.

Reference medium or custom phase speed: Set a custom wave velocity
Phase speed: 1500 m/s
Wavelength: 3 m

Time per cycle: 0.002 sec
Cycles per second: 500 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.
Frequency here is ordinary frequency in hertz, not angular frequency in radians per second. Angular frequency would be 2π times the hertz value.

Common questions

Can I find frequency from the period alone?

Yes. The reciprocal of a positive period in seconds is frequency in hertz. Determining wavelength additionally requires phase speed.

Does higher frequency always imply shorter wavelength?

Only when phase speed is held constant. A dispersive medium can have a phase speed that changes with frequency.

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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