Transmission/Reflection Across Fluid Boundaries

Transmission/Reflection Across Fluid Boundaries

Straight from Kinsler et. al. "Fundamentals of Acoustics", 4th ed.

A normally-incident wave hitting a plane boundary between two fluids with acoustic impendances r_1 and r_2 has reflection coefficient of

    ( r_2/r_1 - 1 ) ^ 2
R = | ----------- |
    ( r_2/r_1 + 1 )
and a transmission coefficient of
       4 * r_2/r_1 
T =  --------------- 
     (r_2/r_1 + 1)^2
In the case of a wave generated in water, where r_1 = rho * c = 998 kg/m^3 * 1482 m/s = 1.480e^6 and hitting the water/air boundary so r_2 = rho * c = 1.210 kg/m^3 * 343 m/s = 415.0. That means the ratio r_2/r_1 = 2.804e-4 and so R = 0.9989 and T = 0.001121.

So a normally incident wave in water will transmit about 0.1% of its amplitude into the air.