Obtain an expression for the instantaneous displacement of a stationary wave.

Explanation

Let `y_(1)= A sin ( omega t -kr) `and `y_(2) = A sin ( omega t + kx ) ` represent two identical waves travelling in opposite directions and superpose with each other.
But `y = y _(1) + y_(2)` ( superposition theorem) .
i.e.,`y = A[sin (omega t - kx ) + sin ( omega t + kx ) ]`
ie., `y = A [2sin (cancel(2) omegat)/(cancel(2)) cos (( cancel(2)kx)/( cancel(2)))]`
i.e., y = ( 2A cos kx ) `sin omega t ` and the maximum displacement of the wave = 2A and `k = ( 2pi )/( lambda ) rad m^(-1)` .