Sound Pressure in Water from Source in Air and Vice Versa

Abstract

Sound pressure level Lp at a depth d, in water, due to a point source in air at a distance h above the water surface, may be calculated from Lp = [Ls −7 + 20 log (cosθ)] −20 log(r/rs), where Ls, the source level, is the SPL in air at distance ra from the source; r is the straight-line distance to the receiving hydrophone from a virtual sound source situated under the actual source at height h′ = (c1/c2) × h above the surface; c1 and c2 are the respective speeds of sound in air and water; θ is the angle between the vertical and the line of length r. Comparisons with various published results obtained by more sophisticated ray-theory show agreement within 1 dB, except at shallow depths and far sidewise from the sound source; agreement within 2 dB is found for new experimental data here presented for sound bursts of frequency 500, 1000, and 2000 Hz, and h = 3.5 m. For sound originating in water at depth d below the surface, the SPL received in air is to be calculated from Lp = Ls −52 + 40 log(cosθ) −20 log(r/rs), where Ls is the source level, at rs;, in the water. Experimental data obtained with a sound source in the water at depth d = 5.6 m, and frequency 500, 1000, or 2000 Hz, are in agreement with this equation, mostly within 2 dB, for receiving positions in air 1 or 2 m above the water and offsets as great as 3 m.