Wave Speed Calculator
Find wave speed from frequency and wavelength.
Results update as you type.
How it works
The wave equation links the three fundamental properties of any wave, and this calculator uses it to find wave speed from frequency and wavelength. You enter the frequency, the number of cycles per second in hertz, and the wavelength, the distance between successive crests, and it returns the speed at which the wave travels. The relationship, speed equals frequency times wavelength, applies to every kind of wave: sound, light, water ripples, seismic waves, and waves on a string. A key insight is that in a uniform medium the wave speed is constant, set by the medium's properties, so frequency and wavelength trade off inversely: a higher-pitched sound has a shorter wavelength but travels at the same speed as a lower note in the same air. This is why light of different colours travels at the same speed in a vacuum despite having different frequencies and wavelengths. Physics students use the equation constantly, and it is essential in acoustics, optics, telecommunications, and music, where tuning, antenna design, and instrument dimensions all depend on it. You can rearrange it to find any one of the three quantities from the other two. Enter the frequency and wavelength to compute the wave speed.
v = f · λ
The wave equation states that a wave's speed equals its frequency multiplied by its wavelength. Frequency is how many wave cycles pass a point each second, and wavelength is the distance between successive crests, so their product is the distance the wave travels per second. In a given medium the speed is fixed, meaning higher frequency waves have proportionally shorter wavelengths and vice versa.
Source:Physics (wave equation)
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Worked example
How to use this calculator
- 1
Enter your values
Enter frequency (f) and wavelength (λ).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Wave speed updates instantly as you type — no button to press.
Frequently asked questions
What is the wave equation?
The wave equation states that a wave's speed equals its frequency multiplied by its wavelength. It connects how often the wave oscillates with how long each wave is to give how fast it moves. This simple relationship applies universally to all waves, from sound and light to water and seismic waves, and can be rearranged to find any of the three quantities.
What is the difference between frequency and wavelength?
Frequency is how many complete wave cycles pass a fixed point each second, measured in hertz, while wavelength is the physical distance between two successive crests, measured in metres. Frequency describes the wave in time, wavelength in space. Their product gives the wave's speed, and in a fixed medium they vary inversely, so raising one lowers the other.
Does wave speed depend on frequency?
In a uniform, non-dispersive medium, no. The speed is set by the medium's properties, so all frequencies travel at the same speed and frequency and wavelength adjust inversely. In dispersive media, however, speed can vary slightly with frequency, which is why a prism separates white light into colours. For most introductory problems the speed is treated as constant.
What is the speed of sound and light?
Sound travels at about 343 metres per second in air at room temperature and faster in water and solids. Light travels at about 300 million metres per second in a vacuum, the fastest speed possible. You can use the calculator with either by entering a wave's frequency and wavelength, and the result should match the known speed for that medium.
Can I find frequency or wavelength instead?
Yes, by rearranging the equation. If you know the wave speed and wavelength, divide speed by wavelength to get frequency; if you know speed and frequency, divide speed by frequency to get wavelength. This calculator solves for speed from frequency and wavelength, but the same relationship lets you find whichever quantity you are missing from the other two.