 Solution

The power linewidth is $\Delta f=f_0/Q\simeq 0.044\mathrm{Hz}$. Fourier frequency resolution is of order $1/T_{\mathrm{obs}}$, so $T_{\mathrm{obs}}\gtrsim Q/f_0\simeq 23\mathrm{s}$, and preferably longer to distinguish the intrinsic linewidth from the observation-window width. zero padding does not improve this physical resolution. A freely decaying signal also needs sufficient microphone dynamic range.