Wave Speed
Speed of a wave from frequency and wavelength.
Formula
Variables
How it works
Wave speed tells you how fast a wave pattern moves through a medium. In one complete cycle, the wave advances by one wavelength \(\lambda\), and if it completes \(f\) cycles each second, then the distance travelled per second is \(f\lambda\), which is why \(v = f\lambda\). This relationship applies to many waves, including sound, light, and water waves, as long as the frequency and wavelength describe the same wave.
When to use it
Use this formula when you know a wave’s frequency and wavelength and need its speed, or when you want to find wavelength or frequency from the other two quantities. It is especially useful in physics problems about sound waves, electromagnetic waves, and ripple tanks.
Worked example, step by step
A water wave has a frequency of 3.0 Hz and a wavelength of 2.5 m. Use v = f\lambda v = 3.0 \times 2.5 v = 7.5 m/s So the wave speed is 7.5 m/s.
Common mistakes to avoid
- using frequency in kHz or MHz without converting to Hz when needed
- mixing up wavelength and amplitude, which are not the same thing
- forgetting to include units, or giving the speed in m/s when the wavelength was in cm without converting first
Did You Know?
Light travels about a million times faster than sound, which is why you see lightning well before you hear thunder.
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