Solution
= Solution
At25kHz, \b[the n=1 and n=2 modes can propagate], with
$$
\boxed{k_{x,1}=10\pi\sqrt{21}=144\,\mathrm{m^{-1}},\qquad k_{x,2}=30\pi=94.2\,\mathrm{m^{-1}}.}
$$
They have different phase and group speeds, so a launch exciting both produces multimode propagation and possible beating. Actual mode amplitudes depend on the transverse launch profile; their existence does not guarantee both are excited. Modes n≥3 remain evanescent.