How to Calculate Sound Velocity in Seawater
The speed of sound in seawater is dependent largely on three factors: pressure, temperature, and salinity. Pressure increases with depth, so the speed of sound does too. In general, an increase of temperature of 1oC increases sound speed by 4 m/s and an increase in salinity of 1% increases sound's speed by 1 m/s. Several researchers have developed simple formulas for determining the speed of sound in seawater.
One commonly used formula is Wilson's formula, developed in 1960. The formula is as follows:
c(S,T,P) = c0+DcT+DcS+DcP+DcSTP
DcSTP=(S-35)(-1.1244*10-2+7.7711*10-7T2+7.85344*10-4P-1.3458*10-5P2+3.2203*10-7PT+1.6101*10-8T2P)+ P(-1.8974·10-3T+ 7.6287·10-5T2 + 4.6176·10-7T3) + P2(-2.6301·10-5T + 1.9302·10-7T2) + P3(-2.0831·10-7T)
c is speed of sound
T is temperature (in Celcius)
S is salinity (per mille)
P is hydrostatic pressure (MPa).
This formula is applicable within the following bounds:
- temperatures between -4° and 30°C,
- salinity between 0 and 37 per mille,
- hydrostatic pressure between 0.1 MPa and 100 MPa.
It is an empirical theory, meaning that it's based on data rather than theory. The formula has a mean square error of .22 m/s. There are several more complicated theories that take into account other variables, such as the Del Grosso Equation. Click here for more formulas. If you just want a calculator for the speed of sound in seawater, click here.