Speed of sound vs altitude ?
Richard J. Edgar
>Unresolved issue... Is the speed of sound a constant with reference to
>elevation? Say from sea level to 100,000 feet.
>
>Be gentle
>Return to:
>
>Randa...@Verifone.com
The speed of sound in an (ideal) gas is given by a = sqrt(gamma*kT/mu)
where a = soundspeed, gamma is the ratio of specific heats (5/3 for a
monatomic gas, 7/5 for a diatomic gas; also known as the adiabatic
constant, it's the gamma in p*V^gamma = const.), T is the absolute
temperature, and mu is the mean molecular mass per molecule. k is
the Boltzmann constant.
So the soundspeed could change for 3 reasons: gamma, mu, and T. The
first two are related; at very high altitudes the oxygen dissociates and
the nitrogen concentration drops, so gamma goes from 7/5 -> 5/3, and
the mean molecular weight goes from the surface value of, lemme see...
about 29 grams/mole to about 16 at space shuttle orbit altitudes.
The temperature can also change with altitude.
I think all these effects are very small up to 100,000 feet, so the
short answer to your question is that it's pretty much constant with
altitude. According to "U.S. Standard Atmosphere, 1976" (NOAA-S/T
76-1562; NOAA, NASA, USAF publication), T has changed from 288 to 227
Kelvin. The molecular weight (and hence gamma) has changed hardly at all.
The same publication lists the soundspeed at sea level as 340.29 m/s,
and 302.03 m/s at an altitude of 100,000 ft.
Thumbrule time (10% accuracy): In atomic hydrogen with mu = 1 gram/mole,
the soundspeed is a ~= 0.1 km/s sqrt(gamma*T), with T in Kelvins.
All those ugly constants have been evaluated for you. Or you can
remember that a ~= 0.1 km/s sqrt(gamma*T/mu), with mu in atomic units.
=============================================================================
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Harvard-Smithsonian Center for Astrophysics | upon whether or not it depends
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John Bain
(Richard J. Edgar) wrote:
From an engineers approach, here are some decent models:
rho = rhos*Exp(-h/Br) density
p = ps*Exp(-h/Bp) pressure
T = p/rho*R Temperature (K)
a = Sqrt(gamma_air*R*T) speed of sound
Mach = v/a Mach number
Where,
h is altitude above sea-level
v is velocity (relative to the free stream)
rhos = .002377 slugs/ft^3
Br = 23,800 ft
ps = 2116.0 lbs/ft^2
Bp = 23,200 ft
R = 3089.7 ft lb/slug K ideal gas constant
Gamma_air = 1.4 ratio for specific heat
Nice units huh?? Make your own table.
John Bain
UCLA
Scott
>In article <1995Sep11....@sfov1.verifone.com> randa...@sfov1.verifone.com writes:
>>Unresolved issue... Is the speed of sound a constant with reference to
>>elevation? Say from sea level to 100,000 feet.
>>
>>Be gentle
>>Return to:
>>
>>Randa...@Verifone.com
The speed of sound changes with air pressure / temperature, so changes
with altitude.
This is one reason why we hear a lot more at night, than we do during
the day. Sound defracts like pushing a stick into the water. It will
head towards a denser atmosphere where it travels faster.
Michael Lammers
>
>The speed of sound changes with air pressure / temperature, so changes
>with altitude.
>
>This is one reason why we hear a lot more at night, than we do during
>the day. Sound defracts like pushing a stick into the water. It will
>head towards a denser atmosphere where it travels faster.
>
Whoa! As has been mentioned in a number of excellent posts so far,
the speed of sound is NOT a function of air pressure in an ideal
gas (which air is a very close approximation of). It is a function
only of temperature, as stated in the formula:
a=sqrt(gamma*R*T)
Where gamma and R are constants and a is the speed of sound.
There are very large chunks of altitude, such as from 11-25 km,
47-53 km, and 79-90 km, where the temperature, and therefore
the speed of sound, remain constant. For a fuller explanation,
I would refer you to the textbook "Fundamentals of Flight", by
John D. Anderson.
As far as hearing better at night is concerned, my
guess would be that less background noise and generally
calm winds is what allows us to hear better at night.
Mike
--
Michael Lammers Structures Guy
Aerospace Engineering IJEMS Project
Iowa State University STS-69
Klingener
>
>The speed of sound changes with air pressure / temperature, so changes
>with altitude.
>
>This is one reason why we hear a lot more at night, than we do during
>the day. Sound defracts like pushing a stick into the water. It will
>head towards a denser atmosphere where it travels faster.
Partly right. Inversions (temperature increase/density decrease with
altitude) refract ground-sourced sounds much like a lens and tend to focus
the acoustic image on a ground-level listener. Inversions are more likely
at night. This is why you can hear traffic miles away in Fairbanks on
winter nights.
cheers
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Fred Klingener
Brock Engineering PC, Roxbury CT
klin...@aol.com
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