Speed of sound in liquids
In a fluid the only non-zero stiffness is to volumetric deformation (a fluid does not sustain shear forces). Hence the speed of sound in a fluid is given by where K is the bulk modulus of the fluid. This value typically decreases with temperature for non-polar fluids: the speed of sound in ultra-wave frequency range is inverse proportional to the cube of the volume of a fixed amount of the fluid. Water The speed of sound in water is of interest to anyone using underwater sound as a tool, whether in a laboratory, a lake or the ocean. Examples are sonar, acoustic communication and acoustical oceanography. See Discovery of Sound in the Sea for other examples of the uses of sound in the ocean (by both man and other animals). In fresh water, sound travels at about 1497 m/s at 25 °C. See Technical Guides - Speed of Sound in Pure Water for an online calculator. Seawater Sound speed as a function of depth at a position north of Hawaii in the Pacific Ocean derived from the 2005 World Ocean Atlas. The SOFAR channel is centered on the minimum in sound speed at ca. 750-m depth. In salt water that is free of air bubbles or suspended sediment, sound travels at about 1560 m/s. The speed of sound in seawater depends on pressure (hence depth), temperature (a change of 1 °C ~ 4 m/s), and salinity (a change of 1‰ ~ 1 m/s), and empirical equations have been derived to
accurately calculate sound speed from these variables. Other factors affecting sound speed are minor. Since temperature decreases with depth while pressure and generally salinity increase, the profile of sound speed with depth generally shows a characteristic curve which decreases to a minimum at a depth of several hundred meters, then increases again with increasing depth (right). For more information see Dushaw et al. A simple empirical equation for the speed of sound in sea water with reasonable accuracy for the world's oceans is due to Mackenzie: c(T, S, z) = a1 + a2T + a3T2 + a4T3 + a5(S - 35) + a6z + a7z2 + a8T(S - 35) + a9Tz3 where T, S, and z are temperature in degrees Celsius, salinity in parts per thousand and depth in meters, respectively. The constants a1, a2, ..., a9 are: a1 = 1448.96, a2 = 4.591, a3 = -5.304?10-2, a4 = 2.374?10-4, a5 = 1.340, a6 = 1.630?10-2, a7 = 1.675?10-7, a8 = -1.025?10-2, a9 = -7.139?10-13 with check value 1550.744 m/s for T=25 °C, S=35 parts per thousand, z=1000 m. This equation has a standard error of 0.070 m/s for salinity between 25 and 40 ppt. See Technical Guides - Speed of Sound in Sea-Water for an online calculator. Other equations for sound speed in sea water are accurate over a wide range of conditions, but are far more complicated, e.g., that by V. A. Del Grosso and the Chen-Millero-Li Equation.