Acoustic dipole Mach-number scaling
= Acoustic dipole Mach-number scaling
{title2=$\rho'/\rho_0=O((l/r)M^3)$}
For a small body of size $l$ in flow of speed $u$, force of order $\rho_0u^2l^2$ varying on time $l/u$ produces an <acoustic dipole> density amplitude of the displayed order, where $M=u/c_0$ is the <Mach number>. Its sound power scales as $\rho_0u^6l^2/c_0^3$. The corresponding <compact acoustic quadrupole Mach-number scaling> has density amplitude of order $(l/r)M^4$ and power $\rho_0u^8l^2/c_0^5$.