Every wave obeys the same simple rule: speed equals frequency multiplied by wavelength. This wave velocity calculator takes the frequency and the wavelength and returns the wave speed, the period, and how the result compares with the speed of sound in air. It also works in reverse, so you can find the wavelength or the frequency from the other two values.
What Is the Wave Velocity Calculator?
Wave speed is how fast a disturbance travels through a medium, and it is always the product of the number of cycles per second and the distance covered by each cycle. Change either one and the other must change to keep the speed the same.
This calculator works in all three directions, so you can start with a frequency and a wavelength to get the speed, start with a speed and a frequency to get the wavelength, or start with a speed and a wavelength to get the frequency.
How the Wave Formula Works
v = f × λ, where f is the frequency in hertz and λ is the wavelength in metres
The period, which is the time for one complete cycle, is simply the reciprocal of the frequency, so a 440 hertz tone has a period of about 2.27 milliseconds. The number of complete waves that fit into a kilometre is the inverse of the wavelength and is a useful figure for antenna and spacing calculations.
The comparison with the speed of sound in air, roughly 343 metres per second, gives a quick sense of scale. Anything at that speed or below is in the audible range for sound, while radio waves run at roughly 300,000 times faster.
What Sets the Speed of a Wave
The speed depends on the medium and the type of wave, not on the frequency or the wavelength. Sound travels about 343 metres per second in air at room temperature, 1,480 metres per second in seawater and about 5,100 metres per second in steel.
For light in a vacuum the speed is fixed at roughly 299,792 kilometres per second, and it slows slightly when it passes through glass or water. This is why a refractive index is defined as the speed of light in a vacuum divided by its speed in the material.
Frequency, Wavelength and Pitch
For sound, frequency is what you perceive as pitch. A 440 hertz wave has a longer wavelength than a 880 hertz wave of the same speed, which is why the lower note travels further and diffracts around obstacles more readily.
That relationship is also the reason a small speaker cannot reproduce a bass note efficiently. The cone would have to move far too far at a low frequency for the required wavelength to fit in a small enclosure.
Frequently Asked Questions
What is the formula for wave speed?
Wave speed equals frequency multiplied by wavelength. With frequency in hertz and wavelength in metres, the result is in metres per second.
What is the speed of sound in air?
About 343 metres per second at 20 degrees Celsius, which is roughly 1,235 kilometres per hour. It increases by about 0.6 metres per second for every degree of temperature increase.
What is the relationship between frequency and wavelength?
They are inversely proportional when the wave speed is fixed. Doubling the frequency halves the wavelength, so a 440 hertz tone and an 880 hertz tone of the same speed occupy 0.78 metres and 0.39 metres respectively.
Does the frequency affect the speed of sound?
No. The speed is set by the medium and remains essentially constant across the audible range, which is why a tuning fork at 256 hertz and one at 512 hertz travel through air at the same speed.
What does the period of a wave tell me?
The period is the time for one complete cycle and is the reciprocal of the frequency. It matters for pulsed systems, since a pulse must last at least one period to be recognised as a wave rather than a single disturbance.