# Wave Equation – with derivation

In this post, we will discuss the Wave Equation and derive this equation in easy steps.

Although the speed of a wave can vary, there is a relationship between the speed of a wave and other significant wave characteristics.

Speed is given by:

v =distance traveled/time taken= d/Δt

This can be rewritten in terms of the distance of one wavelength, λ, in one period, T, which will be:

speed v =λ/T………… [1]

and frequency f = 1 /T …………..[2]

So from equations [1] and [2], the relationship becomes:

v = fλ

This is known as thewave equationand applies to both longitudinal and transverse mechanical waves.