Past exam of the physics A course of the University of Cambridge / 2010 / Paper 1 / Section B / B7 / a / Solution

At5kHz every transverse mode is below cutoff, so no propagating guided mode exists. A driven boundary can produce an evanescent near field. For n=1 the decay coefficient is $\sqrt{(20\pi {)}^2-(10\pi {)}^2}=10\pi \sqrt{3}=54.4{\mathrm{m}}^{-1}$, an e-folding distance of18.4mm. This is decay along the guide, not attenuation of an otherwise propagating lossless wave.