# Engineering Acoustics/Sonar

The use of navigation instruments was always of great importance to those who depend on the sea. Methods to find the position on earth according to the stars were available since long ago, but the first apparatus that track what is underwater are relatively recent. One of these instruments, which improved the safety of navigation is the fathometer. It has the simple concept of measuring how much time a sound wave generated at the ship takes to reach the bottom and return. If one knows the speed of sound in the medium, the depth could be easily determined. Another mechanism consists of underwater bells on lightships or lighthouses and hydrophones on ships that are to find the distance between them. These could be considered the forerunners of the SONAR (SOund Navigation And Ranging).

There are a lot of animals that also take advantage of underwater sound propagation to communicate.

# Speed of Sound

In 1841, Jean-Daniel Colladon [1] was able to measure the speed of sound in water for the first time.

The equation for speed of sound(m/s) in water developed by Del Grosso,[1] applicable in Neptunian[2] waters, depends on the Temperature(T) in Celsius, Salinity(S) in ppt(part per thousand) and gauge Pressure(P) in atmospheres.:

${\displaystyle c(T,S,P)=1449.08+4.57Te^{-(T/86.9+(T/360)^{2})}+1.33(S-35)e^{-T/120}+0.1522Pe^{T/1200+(S-35)/400}+1.4610^{-5}P^{2}e^{-T/20+(S-35)/10}}$

where the pressure is a function of depth[Km] and the Latitude, given by:

${\displaystyle P=99.5(1-0.00263cos2\phi )Z+0.239Z^{2}}$

The speed of sound is very sensible to the temperature, which changes considerably in the thermocline [2]. After 1000m meters deep, the pressure governs the equation, increasing slowly the speed with depth. The salinity has very low effect on the equation unless in very specific situations, such as heavy rain or the encounter between a river and the sea.

## References

1. Del Grosso (1974), J. Acoust. Soc. Am.,56,1084(1974)., p. 56,1084
2. Leroy (1969), J. Acoust. Soc. Am.,56,1084(1974)., p. 46,216