= Quality factor from ringdown
{title2=$Q=\omega\tau_E=\omega\tau_A/2$}
For an isolated weakly damped <resonator> mode, $Q=\omega E/P_{\rm loss}$. If $E(t)=E(0)e^{-t/\tau_E}$, differentiating gives $P_{\rm loss}=E/\tau_E$, so $Q=\omega\tau_E$. Since <energy> is quadratic in <wave amplitude>, the <wave amplitude> <exponential relaxation time> is $\tau_A=2\tau_E$. A decay by an <energy> factor $D$ in a measured interval $t_d$ gives $Q=\omega t_d/\ln D$. For a conventional <reverberation time>, $Q=2\pi fT_{60}/[6\ln(10)]$ under this exponential single-rate approximation.
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