 Compact acoustic quadrupole Mach-number scaling

For a low-Mach number source with stress $O({\rho }_0{U}^2)$ and advective time $\ell /U$, the three-dimensional compact acoustic quadrupole has density amplitude $O({\rho }_0{M}^4\ell /r)$, where $M=U/c_0$. The power depends on these source-time and stress hypotheses, not only on the quadrupole label.