Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 40C / b / iii / Solution

At $r=a$,
$$
\frac{c_0\langle K+W\rangle}{|\langle I_r\rangle|}
=1+\frac{c_0^2}{2\omega^2a^2}.
$$
For $\omega a/c_0\gg1$, kinetic and compressional energies are equal and the field is locally radiative. For $\omega a/c_0\ll1$, reactive kinetic energy dominates and the mean radiated flux is small.


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 Incoming links: Surface acoustic energy-to-flux ratio of a pulsating sphere