At $50\ \mathrm{kHz}$ \b[modes $n=1,2,3,4$ can propagate]. Their positive $k_x$ values are approximately $769.5,719.8,628.3,471.2\ \mathrm{m^{-1}}$. Mode $n=5$ is a <nonpropagating mode at waveguide cutoff>: $k_x=0$ and $v_g=0$, so it does not carry longitudinal <power> as a traveling mode. Higher modes are <evanescent>. The injected transverse profile determines which permitted modes are actually excited.

Solution

Past exam of the physics A course of the University of Cambridge / 2014 / Paper 2 / Section B / B7 / b / Solution

 Solution (source code)