Speed of Sound
The velocity of sound is (gamma* R* T/M)^.5. So is it independent of
pressure? Then what about sound travel in a gas at very low pressure?
Also at night the air temp usually goes down and it gets more dense but
then the velocity of sound should go down because the T goes down while it
should go up because density goes up. Which is true?
The velocity of sound is not independent of pressure. Pressure varies with
temperature. Density varies inversely with pressure. It is the ratio,
pressure divided by density, that turns out to be important. This ratio
happens to be proportional to temperature. Instead of including both
pressure and density in the formula, which would make the formula more
complex, scientists just use temperature. Another advantage of using
temperature is that it's much easier to measure than pressure or density.
If both pressure and density increase, the effect on temperature and the
speed of sound depends on which increases more. If pressure increases 10%
and density increases 5%, temperature and sound speed must also increase.
If pressure increases by only 5% while density increases by 10%, temperature
and sound speed must decrease.
Math, Science, Engineering
Illinois Central College
The equation you cite is based on the kinetic theory of an ideal gas --
which is pretty good at atmospheric pressure, but it does have its limits.
As the pressure is reduced the speed of sound does decrease, as for example,
with altitude. At approx. atm. pressure the pressure does cancel out
however. Another small effect is the "gamma" is not strictly a constant -- it
varies a little with temperature. You will find the site:
very interesting. It gives you a lot of info on the atmosphere, including a
"calculator" to find all the properties of air as a function of altitude. It
is a lot of fun to play with. The reference to the "1976 Standard
Atmosphere" is a kind of average behavior of the atmosphere over the U.S.
that is used in design calculations and other applications involving the
atmosphere so that scientists and engineers are "plugging in" the same
numbers into their calculations.
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Update: June 2012