Question

Question #c6006

Answer 1

In classical physics, a wave is a periodic disturbance propagating through space.

Therefore, the wave varies as a function of both position and time.

Such a wave may be represented by, `phi (x,t)` in 1D or `phi (x,y,z,t)` in 3D.

Considering for simplicity the 1D case of `phi = phi (x,t)`. It satisfies the wave equation of D'Alembert as given by,

`(del^2phi)/(delx^2) = 1/v^2(del^2phi)/(del t^2)`

Where `v` is the wave velocity.

The equation stated above is the 1D wave equation and is known to have solutions of the form,

`phi (x,t) = f(kx - omegat) + g(kx + omegat)` where `f` and `g` are functions.

`omega` is the angular frequency and `k` is the wave vector related as,

`omega = kv`

Similarly for the 3D case, the wave equation looks like,

`nabla^2phi = 1/v^2 (del^2phi)/(delt^2)`

Where `nabla` is vector Differential del operator.