How to Calculate Wave Speed from Frequency and Wavelength

Calculates wave speed as v = frequency × wavelength. Frequency is in hertz, wavelength in metres, and speed in m/s.

Explanation

The speed of a wave is its frequency times its wavelength. Each second the source sends out $f$ complete waves, each one $\lambda$ long, so the wave advances $f \lambda$ metres in that second.

v = f \lambda

$v$ is the wave speed, in m/s
$f$ is the frequency, in hertz (Hz), the number of oscillations per second
$\lambda$ (lambda) is the wavelength, the length of one wave, in metres (m)

The calculator also gives the period, the time for a single oscillation, which is $T = \frac{1}{f}$ , in seconds.

Example

The defaults are a frequency of 440 Hz and a wavelength of 0.78 m.

v = 440 \times 0.78 = 343.2\,\mathrm{m/s}

The speed is 343.2 m/s and the period is $\frac{1}{440} \approx 0.00227$ s. 440 Hz is concert A, the note an orchestra tunes to, and 343 m/s is close to the speed of sound in air at 20 °C.

Notes

The speed of a wave is set by the medium it travels through, not by the source. In air at a fixed temperature, sound travels at a fixed speed, so raising the frequency simply shortens the wavelength: $f$ and $\lambda$ are inversely proportional.

The speed of sound in air depends on temperature, roughly 331.5 + 0.6 × the temperature in °C. That gives about 331.5 m/s at 0 °C and about 343.5 m/s at 20 °C.

The frequency must be greater than zero. Zero or a negative value gives an error.

Light and radio waves obey $v = f \lambda$ too, travelling at about $3.0 \times 10^8$ m/s in a vacuum.