Wave Speed Calculator
Wave speed is frequency multiplied by wavelength, written v = f times lambda. The arithmetic is trivial; the insight is that the two factors are locked together by the speed of the medium, so changing one forces the other to compensate.
Wave speed in metres per second
343.2
- Period in seconds per cycle
- 0.0023
- The same speed in kilometres per hour
- 1,235.52
- The same speed in miles per hour
- 767.7165
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
v = f x lambda
- v
- Wave speed — how fast the disturbance travels through the medium
- f
- Frequency in hertz — cycles passing a fixed point each second
- lambda
- Wavelength in metres — distance between two neighbouring crests
- T
- Period in seconds — the time for one complete cycle, equal to 1/f
How to check the result by hand
- 1
Establish the frequency and the wavelength in matching SI units
Frequency belongs in hertz and wavelength in metres, so the product comes out in metres per second with no hidden factor. Write both quantities down with their units before touching the numbers. If the wavelength is given in centimetres or millimetres, convert it to metres first, because multiplying a frequency in hertz by a wavelength in centimetres gives an answer that is wrong by a factor of one hundred and still looks plausible.
- 2
Multiply the frequency by the wavelength
440 Hz times 0.78 m is 440 times 0.78, which is 343.2 metres per second. This single multiplication is the whole of the wave-speed formula, so carry full precision and resist rounding until the end. The result inherits the units of the two inputs, hertz and metres, which combine to metres per second.
- 3
Take the reciprocal of the frequency to get the period
The period is 1 divided by f, so 1 divided by 440 is 0.0022727272727272726 seconds per cycle. This step answers a different question from the speed: not how far the wave travels each second, but how long one cycle lasts. Keeping the two straight avoids the common error of reporting the period where the speed was asked for.
- 4
Sanity-check the inverse relationship
Confirm that the frequency and wavelength really do multiply to the speed of the medium. In 20 degrees Celsius air the product must be 343.2, so a 1000 Hz tone has to pair with a wavelength of 0.343 metres. If your pair of numbers does not multiply to a sensible speed for the medium, one of the two inputs has been copied wrongly.
- 5
Convert to kilometres per hour or miles per hour if the context asks
Multiply metres per second by 3.6 for kilometres per hour, giving 1235.52 for the sound in air, or by 2.2369362920544 for miles per hour, giving 767.71653543307. These conversions change only the reporting scale, never the underlying physics. Finish by rounding once to a precision the weakest input can justify.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Wave Speed page.