Solving Wave Interference: A Study of Frequency & Amplitude

[JuanYsimura]

Homework Statement

Write a wave in one space dimension as ARe(ei(kx-wt-d))where A is the
amplitude of the wave. Find a second wave of the same frequency such that
the sum of the two vanishes at x = 0 and x = L. Assuming the wave velocity
c = w/|k| is fixed, for what frequencies ! is this possible?

The Attempt at a Solution

My attempt: I Let x1 = ARe(ei(kx-wt+d)) be wave 1 and x2 = A'Re(ei(kx-wt+d')) be wave 2.
since they vanish at x=0,L, I obtained the following equations:
ARe(ei(-wt+d))+A'Re(ei(-wt+d)) = 0 and ARe(ei(Lk-wt+d))+A'Re(ei(Lk-wt+d)) = 0.
My question is: should I solve this equations and find the frequencies that satisfy this equation ?? Am I in the right path to solve the problems? Id Like to hear different opinions and different approaches.

Thanks,

Juan

 

[Spinnor]

Don't we want a standing wave where at least one pair of nodes is at 0 and L?

See,