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The speed of sound in sea water depends on its temperature, as well as on the salinity and hydrostatic pressure. For calculation of the speed of sound, Wilson's empirical formula offered in 1960 is of common use. (Wilson W. D. Equation for the speed of sound in sea water.- J. Acoust. Soc. Amer., 1960, vol.32, N 10, p. 1357).
Wilson's formula is accepted by the National Oceanographic Data Center (NODC) USA for computer processing of hydrological information.
Also, this formula formed the basis for hydroacoustical calñulations in the USSR (see the "Tables for calculation of the speed of sound in sea water".- L.: UGS VMF, 1965).
Wilson's formula looks as follows:
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c(S,T,P) = c0 + D
cT + D
cS + D
cP + D
cSTP, |
| c0 = 1449.14, |
| D
cT = 4.5721T - 4.4532·10-2T2 - 2.6045·10-4T3 + 7.9851·10-6T4,
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| D
cS = 1.39799(S-35) - 1.69202·10-3(S-35)2,
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| D
cP = 1.63432P - 1.06768·10-3P2 +
3.73403·10-6P3 -
3.6332·10-8P4,
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| D
cSTP = (S-35)(-1.1244·10-2T +
7.7711·10-7T2 +
7.85344·10-4P -
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- 1.3458·10-5P2 +
3.2203·10-7PT +
1.6101·10-8T2P) +
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+ P(-1.8974·10-3T +
7.6287·10-5T2 +
4.6176·10-7T3) +
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+
P2(-2.6301·10-5T +
1.9302·10-7T2) +
P3(-2.0831·10-7T),
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where c(S,T,P) - speed of sound, m/s; T - temperature, °C; S - salinity, per mille; P - hydrostatic pressure, MPa.
Wilson's formula is valid for the following ranges of temperature, salinity, and hydrostatic pressure:
- temperature from -4° to 30°;
- salinity from 0 to 37 per mille;
- hydrostatic pressure from 0.1 MPa to 100 MPa.
The mean-square error of calculation of the speed of sound via this formula with regard to Wilson's experimental data is 0.22 m/s.
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