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Answer 1 · 2017-09-14T12:09:59

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.