= Normal-incidence acoustic velocity reflection coefficient
{title2=$r_u=(Z_1-Z_2)/(Z_1+Z_2)$}
Fix a positive normal from medium 1 toward medium 2, and define all <velocity> amplitudes in that coordinate. A right-going linear <sound wave> satisfies $p'=Zu'$ and a left-going wave satisfies $p'=-Zu'$, with <acoustic impedance> $Z=\rho c_s$. Continuity gives $u_i+u_r=u_t$ and $Z_1(u_i-u_r)=Z_2u_t$. Eliminating $u_t$ gives the displayed reflected-to-incident velocity ratio. The pressure reflection coefficient is its negative. A surface mass, surface restoring force or oblique incidence changes the boundary calculation.
Back to article page
