= Solution
If $c_0\ll\omega a$, then $x\gg1$. The sphere is acoustically large, and
$$
\langle K\rangle\sim\langle W\rangle,
\qquad
|\langle I_r\rangle|
\sim c_0\langle K+W\rangle.
$$
Pressure and velocity are nearly in phase, so the near-surface field behaves locally like a progressive radiating wave. The power approaches
$$
2\pi a^2\rho_0\omega^2\epsilon^2c_0.
$$
If $c_0\gg\omega a$, then $x\ll1$. The sphere is acoustically compact, and
$$
\frac{\langle W\rangle}{\langle K\rangle}\sim x^2\ll1,
\qquad
\frac{c_0\langle K+W\rangle}{|\langle I_r\rangle|}
\sim\frac1{2x^2}\gg1.
$$
The surface field is mainly reactive kinetic energy: pressure and velocity are nearly in quadrature, energy is stored and returned during each cycle, and only a small mean <acoustic energy flux> is radiated. The mean power scales as
$$
\boxed{\langle\mathcal P\rangle
\sim\frac{2\pi\rho_0\omega^4\epsilon^2a^4}{c_0}.}
$$
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