 Solution

ID: past-exam-of-the-fluids-and-waves-course-of-the-university-of-oxford/2023/1/c/i/solution

p (R, t) = 0

0 = \frac{1}{R} (R^{2} \ddot{R} + 2 R \dot{R}^{2}) - \frac{1}{2} \dot{R}^{2} + \frac{p _{\infty}}{ρ} .

R \ddot{R} + \frac{3}{2} \dot{R}^{2} = - \frac{p _{\infty}}{ρ}, R (0) = a, \dot{R} (0) = 0 .

For

p_{\infty} > 0

, initially

\ddot{R} (0) = - p_{\infty} / (ρ a) < 0

, so the physically relevant branch describes Rayleigh collapse of a spherical cavity.

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