What Is the Formula for Velocity of a Wave?

The wave equation applies to sound and light vibrations as well as water waves.
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Anyone who has watched the movement of waves on water can understand the wave equation, one of the most basic relationships in physics. The two parameters you need to calculate a wave's velocity are its frequency -- the number of wave crests that pass a given point per second -- and its wavelength, which is the distance between crests.

The Wave Equation

If you choose a point in a medium through which a wave is propagating, the period of the wave is the time it takes that point to oscillate back to its original position. Dividing this number into 1 yields the number of times the point oscillates each second, which is the frequency of the wave. Multiplying the wave's frequency by its wavelength, which is its physical length, yields the velocity of the wave. The relationship can be expressed as velocity equals frequency times wavelength.

Applications of the Wave Equation

Among the multiple uses of the wave equation in physics is the determination of the density of a medium. The procedure involves passing light or sound waves of known frequency and wavelength through the medium and recording variations in those parameters. Plugging the recorded values for frequency and wavelength into the wave equation tells you the speed at which the waves travel in the medium, and comparing that speed to the speed of the waves in a known medium, such as air, reveals the density of the medium.

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