THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

15.6 Parametric Variation of Absorption in Seawater 41915.6 Parametric Variation of Absorption in SeawaterFrom actual measurements [Wilson and Leonard (1954) among others] it becameevident that the absorption of sound in seawater was unexpectedly higher thanthat of pure water and it could not be attributable to scattering, refraction, or othereffects of propagation in the natural environment. For example, the absorption inseawater in the frequency range 5–50 kHz was found to be approximately 30 timesthat in distilled water. Liebermann (1949) suggested that this excess absorption isattributable to the sort of chemical reaction that evolves under the influence of asound wave and one of the dissolved salts in the sea.The absorption of sound in seawater depends on three effects: one is the presenceof shear viscosity, a classical effect studied by Lord Rayleigh, who derived thefollowing expression for the absorption coefficient:α = 16π 2 μ sf 2 (15.3)3ρc 3whereα = intensity absorption coefficient (cm −1 )μ s = shear viscosity, poises (approximately 0.01 for water)ρ = density, cg/cm 3 (1 for water)c = sound propagation speed (approximately 15,0000 m/s)f = frequency (Hz).According to Equation (15.3) the value of α is 6.7 × 10 –11 f 2 dB/kyd, but thisamounts to only about one-third of the absorption actually measured in distilledwater. The additional viscosity in pure water, besides that due to shear viscosity, isattributed to another type of viscosity called volume or bulk viscosity, which is theresult of a time lag for water molecules to “flow” in an expansive/compressive mannerin reacting to acoustic signals. This viscosity effect adds to the shear viscosity,so the absorption coefficient incorporating both types of viscosity becomesα = 16π 2 (μ3ρc 3 s + 3 )4 μ b f 2 (15.4)where μ b denotes the bulk viscosity. For water μ b = 2.81μ s .Below 100 kHz the predominant reason for absorption in seawater is due tothe phenomenon of ionic relaxation of the magnesium sulfate (MgSO 4 ) moleculespresent in the seawater. This association–dissociation process involves a relaxationtime, an interval during which the MgSO 4 ions in the seawater solution dissociateunder the impetus of the sound wave. Magnesium sulfate accounts for only 4.7%by weight of the total dissolved salts in seawater, but this particular salt was discoveredto be the dominant absorptive factor in seawater, rather than the principalconstituent NaCl (Leonard et al., 1949).The ionic relaxation mechanism causes a variation of the absorption with frequency,which is different from that in Equation (15.4). On the basis of more than