School · Physics · Intermediate

Wave speed calculator

Wave speed, frequency and wavelength are locked together by one equation. Leave the one you want blank and this solves it, showing the rearrangement and the period as well.

Picking one fills in the wave speed. Your data sheet may round these differently, so use its values if they differ.
Leave exactly one blank. Frequency is in hertz, which just means waves per second.

Why v = fλ makes sense

Frequency is how many complete waves pass a point each second. Wavelength is how long one complete wave is. Multiply them and you get how far the wave travels in a second, which is its speed.

If 440 waves go past every second and each one is 0.78 m long, the wave front must have moved 440 × 0.78 = 343 m in that second. That is all the equation is saying.

The part that catches people out: for a given medium the wave speed is fixed by the medium itself, not by the source. So if you raise the frequency, the wavelength must shrink to compensate. A high note and a low note both travel through air at the same 343 m/s; only their wavelengths differ.

Period, and how it relates to frequency

The period T is the time for one complete wave to pass, measured in seconds. It is simply the reciprocal of frequency: T = 1 ÷ f. A 440 Hz note has a period of about 0.00227 s, because 440 waves fit into each second.

That also gives an alternative form of the wave equation, v = λ ÷ T, which some syllabuses prefer. It says the same thing: one wavelength travelled in one period.

QuantitySymbolUnit
Wave speedvmetres per second (m/s)
Frequencyfhertz (Hz)
Wavelengthλ (lambda)metres (m)
PeriodTseconds (s)

Common questions

Does changing the frequency change the wave speed?
Not in a given medium. The speed is set by the material the wave travels through. Change the frequency and the wavelength adjusts instead, keeping the product the same.
Why does sound travel faster in solids than in air?
Because the particles are closer together and more strongly bonded, so a disturbance passes from one to the next more quickly. Sound moves at roughly 343 m/s in air, 1480 m/s in water, and around 5100 m/s in steel.
What happens when a wave crosses into a different material?
The frequency stays the same, because it is set by the source, but the speed changes, so the wavelength must change with it. That is what causes refraction, the bending of light entering glass or water.
Is this the same equation for light and sound?
Yes. v = fλ applies to all waves. Only the speed differs: sound needs a medium, while light travels through a vacuum at 299,792,458 m/s, usually written as 3.00 × 10⁸ m/s in school work.