Solution
= Solution
At $5\ \mathrm{kHz}$ every transverse mode is below cutoff. There is \b[no propagating guided mode] in an infinite uniform guide; excitation produces only <evanescent> penetration. For the slowest-decaying mode write $\psi\propto e^{-\kappa x}$, so $k_x=-i\kappa$ under the preceding convention, with $\kappa=\sqrt{(\pi/b)^2-(2\pi f/v_m)^2}=136.0\ \mathrm{m^{-1}}$, giving a penetration length about $7.35\ \mathrm{mm}$.