deletions | additions       diff --git a/subsection_bf_Wave_Leakage_Time__.tex b/subsection_bf_Wave_Leakage_Time__.tex  index 23e0436..35b8135 100644  --- a/subsection_bf_Wave_Leakage_Time__.tex  +++ b/subsection_bf_Wave_Leakage_Time__.tex 
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After solving the wave equations, we compute the leakage time of the wave energy contained within the acoustic cavity at radii $r_2 < r < R$. The wave energy contained within the acoustic cavity is simply  \begin{equation}  \label{eqn:ecav}  E_{\rm ac} = \int^{R}_{r_2} dr \,  \rho r^2 \omega^2  \bigg( | \xi_r |^2 + \ell(\ell+1) | \xi_\perp |^2 \bigg) \, . \end{equation}   
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