This guide provides current information and equations for calculating the speed of sound in pure water as a function of temperature, and in the case of Begol’skii and Sekoyan’s equation, pressure.

To use the calculator below, enter the values of water temperature, and if you wish to use the Belogol’skii and Sekovan equation you will need to enter pressure. The six alternatives are derived using equations from the sources specified.

 Temperature (Celsius), T Pressure (MPa) P (Necessary for Belogol’skii and Sekoyan equation only) Bilaniuk and Wong - 36 Point Bilaniuk and Wong - 112 Point Bilaniuk and Wong - 148 Point Marczak Equation Lubbers and Graaff’s Simplified (A) (B) Belogol’skii and Sekoyan’s Equation

#### Range of Validity

 Equation Temperature (Celsius), T Pressure (MPa), P Bilaniuk and Wong 0 - 100 Atmospheric Only Marczak 0 - 95 Atmospheric Only Lubbers and Graaff 10 - 40 Atmospheric Only Belogol’skii and Sekovan 0 - 40 0.1 - 60

A list of references can be found on the page Underlying Physics.

#### Equations of state of water and steam

It is possible to calculate sound speeds from the thermodynamic equations for state for water and steam. For more information, please refer to the International Association for the Properties of Water and Steam (1995) and Saul and Wagner (1989). However, some acousticians may agree with Marczak (1997) that:

“the speed of sound in water can be calculated using the equation of state proposed by the International Association for the Properties of Steam (IAPS); the procedure, however, is labor consuming and leads to results of insufficient accuracy.”

#### Lakes: pure water and sea water

Chen and Millero (1977) point out that lake water is by no means pure water, especially when precise pressure, volume and temperature properties are considered. They argue that the properties of lake water can be determined from the equation of state for sea water provided that the total mass fraction of dissolved salts in sea water and lake water are equated.

It is also important to recognise that water may vary in density owing to variations in its isotopic composition. Marczak (1997) quoting Kell (1977) argues that an increase of 1.5 p.p.m in density (caused by the presence of deuterium oxide) results in an increase of 1 p.p.m in the speed of sound. Variations in density due to variations in isotopic composition of water can reach 20 p.p.m - leading to sound speed variations of up to 13 p.p.m.

#### Dispersion

Most of the experimental results for sound speed in pure water which have been reported in the literature have been acquired at MHz frequencies only. All the empirical equations which are listed in this technical guide are based on this high-frequency data. There is little information on sound speed at much lower frequencies. For further discussion on dispersion and the Kramers-Kronig relationship between phase velocity and attenuation, please refer to O'Donnell, Jaynes and Miller (1981).