## Proof of the Wave Equation

The wave equationrelates the speedfrequencyand wavelengthof a wave or vibration.

We can prove the wave equation starting with the formula distance = speed times time. Rewrite this as

Take the distance as equal to one wavelength, then the time becomes the time for one oscillation, T.

Sinceis the time for one oscillation,is the number of oscillations per second, the frequency