From: AAFEG@ASUACAD.BITNET
Newsgroups: alt.folklore.urban
Subject: Re: Falling Bullets and tuning musical instruments
Date: 16 Apr 92 03:21:45 GMT
Article-I.D.: ASUACAD.92106.202145AAFEG
 <1992Apr16.014024.5899@hpcvaac.cv.hp.com>
Organization: Arizona State University

You guys have had the answer under your nose for the last few postings.
The speed of sound in a gas is equal to the sqrt(gamma*R*T) where gamma is
the ratio of specific heats of the gas, R is the gas constant of the gas in
question and T is the temperature of the gas.  This equation is true assuming
that the gas is a perfect gas.  For good ole' air, gamma is 1.4 and the gas
constant is 287.05 N m/(kg K). Substitutin these quatities into the perfect
law we get that the speed of sound in air is 20.047*sqrt(T) m/s with the
measured in degrees Kelvin.

Therefore the speed of sound is heavily a function of the temperature of the
air.  A good example of this in nature is to look at the assumed standard
atmosphere.  The density decreases with altitude in an exponential manner, the
temperature decreases until you get to about 11,000 m when it becomes nearly
constant (this altitude is known as the tropopause).  The speed of sound above
11,000 m (36,000 ft) is basically constant (because the temperature is constant
) while the density is steadily decreasing.  Once again, this means that the
speed of sound in air is mainly a function of temperature.  Two good references
on this subject are "Aerodynamics for Engineers" by Bertin and Smith, and
"Aircraft Performance, Selection and Design" by Francis Hale.  Here's what is
confusing you, the density is a function of three things.  The equation for
the density of a perfect gas is density = pressure / (R*T).  The R and T are
the same gas constant and temperature as mentioned above.  Therefore, the
the density of the gas is also a function of temperature, but it is also a
function of the pressure and the type of gas being considered.  For example,
the reason the density decreases in the atmosphere is the pressure is changing.

Please note that the reason that your professor could change the speed of sound
in the pipes was that he was changing the gas in the pipes and therefore he was
changing the gas constant and gamma.  The pressure and temperature were the
same, therefore he was also changing the density.  However, the reason the
speed of sound changed was because he had changed the gas constant and specific
heat ratio of the fluid in the pipe.  But, if he were to increase the pressure
he would increase the density but the speed of sound would be the same.

Here is an example of the speed of sound, temperature and density in the
standard atmosphere:

            altitude(m)    density (kg/m3)   temp (K)    speed of sound (m/s)

                0              1.2225          288.15        340.294
              5000             .7364           255.68        320.55
             10000             .4135           223.252       299.53
             11000             .3648           216.65        295.15
             15000             .1948           216.65        295.07
             20000             .0889           216.65        295.07
             30000             .0184           226.51        301.71

Note the correspondence of the temperature and the speed of sound.  The speed
of sound actually goes up as the density is decreasing at high altitudes, as
shown, because the temperature increases slightly.

Frederick E. Garrett, Jr. PhD
Assistant Professor of Mechanical and Aerospace Engineering
Arizona State University
Tempe, Arizona  85287
ethernet: garrett@enuxha.eas.asu.edu

My opinions are mine, mine alone and I like it that way.