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Name: Joh
Status: student
Age: 17
Location: N/A
Country: N/A
Date: 7/20/2004


Question:
Hi, 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?


Replies:
John,

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.

Ken Mellendorf
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: http://www.aerospaceweb.org/question/atmosphere/q0059.shtml 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.

Vince Calder



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