# Speed of Sound in Salt Water

## Main Question or Discussion Point

I've preformed an experiment about the speed of sound waves in water and I found that sound travelled faster in hot water than cold water (distilled water), but it travelled still faster in salt water. So, how can I explain why the speed of sound increases with salinity?

We have the equation:

$c= \sqrt{\frac{B}{\rho}}$

Clearly since hot water is less dense, the velocity of sound is greater in hot water. But salt water is denser than fresh water, so shouldn't sound travel slower in salt water?

I have repeated the experiment over and over, but the result is the same.

The only explanation I can think of is that compared to fresh water, sea water has a greater percentage of increase in bulk modulus than in density increase. That's why sound travels faster in salt (25°C) water than hot fresh water (40-50°C). Is that right?

But isn't bulk modulus really a measure of compressibility? But salt water is harder to compress than fresh water so it has a greater B...

I appreciate it if anyone could help me understand this in a more mathematical way.

## Answers and Replies

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Bobbywhy
Gold Member
“For a liquid the speed of sound decreases with increasing density but increases with increasing bulk modulus. For salt water (compared to fresh water) the percent increase in bulk modulus is greater than the percent increase in density so the sound velocity increases with salinity.

The problem is that the bulk modulus and the density are not constants. They each depend upon temperature, pressure, the salinity of the water, as well as the frequency of the sound. So one needs to be cautious about making comparisons and over-interpreting comparisons.”
http://en.wikipedia.org/wiki/Speed_of_sound

“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.”
This site also has a built-in sound speed calculator
http://www.akin.ru/spravka_eng/s_i_svel_e.htm