Speed of Sound and Medium Density
I am currently teaching a unit on sound. According
to the Prentice-Hall textbook, sound waves travel faster in
materials that are LESS dense, so long as you are comparing liquid
to liquid or solid to solid, etc.
As my class and I were talking about fresh water versus salt water,
we decided that since salt water has a greater density than fresh
water, that sound should travel faster in fresh water. However,
right beside the paragraph on how density affects sound waves in our
book is a table that states that sound waves actually travel faster
in salt water than fresh water. WHY?
In saltwater, sound travels at about 1500 m/s and in freshwater 1435 m/s.
The speed of sound in sea water depends on salinity.
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.
This is both simple and complex......we know that sound waves in the
oceans travel great distances......ie the wales and the basis of the
submarine service....stealth but good ears....
Part of this has to do with the fact that we are pushing various
molecules causing a domino effect in the ocean. The elemental mack
up is greatly different between the two fresh/salt aprt from the basics.
Hope this helps.
The "simple" equation for the speed of sound in a liquid is speed =
(K/rho)^1/2 where K is the bulk modulus and rho is the density (all
in a consistent set of units). The problem is that the bulk modulus
(strictly speaking the adiabatic 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. The two web sites below illustrate how these factors,
which start off being "simple" suddenly become rather involved when
you look into the details.
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Update: June 2012