Question

A wave represented by the equation Y =a cos (kx-omega t) is superposed with another wave to form a stationary wave such that the point x =0 is a node.What is the equation of the Other wave? ........ ANS:-acos(kx+omega t)

Answer 1

Well,as due to superposition of the two propagating wave a stationary wave will be formed,we can say,that the other wave must be travelling on to the opposite direction.

So,its equation will be `y'= A cos (kx+omegat)`

Now,as it will be forming a note, at `x=0` so the wave should satisfy this thing as well `y+y'=0`

So,it must have a negative amplitude w.r.t the given wave,so its equation becomes `-acos(kx+omegat)`

Now,you write,

`y+y' = a cos (kx-omegat) +(-a cos (kx+omegat))`

or, `y+y'= -2a sin kx * sin 0 =0`

So,it is satisfying the given condition.