Speed of Sound

Air is a gas, and a very important
property
of any gas is the speed of sound through the gas. Why
are we interested in the speed of sound? The speed of “sound”
is actually the speed of transmission of a small disturbance through
a medium. Sound itself is a sensation created in the human
brain in response to sensory inputs from the inner ear.
(We won’t comment on the old
“tree falling in a forest” discussion!)

Disturbances are transmitted through a gas as a result of
collisions
between the randomly moving molecules in the gas.
The transmission of a small disturbance through a gas is an
isentropic process. The conditions in the
gas are the same before and after the disturbance passes through.
Because the speed of transmission depends on molecular collisions,
the speed of sound depends on the state
of the gas. The speed of sound is a constant within a given gas
and the value of the constant depends on the type of gas (air, pure oxygen,
carbon dioxide, etc.) and the temperature of the gas. An
analysis
based on conservation of
mass
and
momentum
shows that the speed of sound a is equal to the square root of the
ratio of
specific heatsg times the gas constant R times the
temperature T.

a = sqrt [g * R * T]

Notice that the
temperature
must be specified on an absolute scale (Kelvin
or Rankine). The dependence on the type of gas is included in the
gas constant R. which equals the universal gas constant divided by the
molecular weight of the gas, and the ratio of specific heats.

The speed of sound in air depends on the type of gas and
the temperature of the gas. On
Earth, the atmosphere is composed of
mostly diatomic nitrogen and oxygen, and the temperature
depends on the altitude in a rather complex way.
Scientists and engineers have created a
mathematical model of the atmosphere to help
them account for the changing effects of temperature with altitude.
Mars also has an atmosphere composed of
mostly carbon dioxide. There is a similar
mathematical model of the Martian atmosphere.
We have created an
atmospheric calculator
to let you study the variation of sound speed with planet and
altitude.

Here’s another Java program to calculate speed of sound and
Mach number
for different planets, altitudes, and speed. You can use this calculator
to determine the Mach number of a rocket at a given speed and altitude
on Earth or Mars.

To change input values, click on the input box (black on white),
backspace over the input value, type in your new value, and
hit the Enter key on the keyboard (this sends your new value to the program).
You will see the output boxes (yellow on black)
change value. You can use either English or Metric units and you can input either the Mach number
or the speed by using the menu buttons. Just click on the menu button and click
on your
selection. There is a
sleek version
of this program for experienced users who do not need these instructions.

You can also download your own copy of this program to run off-line by clicking
on this button:

As an object moves through the atmosphere, the air is disturbed
and the disturbances are
transmitted through the air at the speed of sound.
You can study how the disturbances are transmitted with an
interactive
sound wave simulator.
If we consider the atmosphere on a
standard day
at sea level static conditions, the speed of sound is about
761 mph, or 1100 feet/second.
We can use this knowledge to approximately
determine
how far away a lightning strike has occurred.

The speed of sound in the atmosphere is a constant that depends on
the altitude, but an aircraft can move through the air at any desired
speed. The ratio of the aircraft’s speed to the speed of sound
affects the forces on the aircraft.
Aeronautical engineers call the ratio of the aircraft’s speed to
the speed of sound the
Mach number, M.
If the aircraft moves much slower than the speed of sound,
conditions are said to be
subsonic, 0 < M << 1,
and compressibility
effects are small and can be neglected.
If the aircraft moves near the speed of sound,
conditions are said to be
transonic, M ~ 1,
and compressibility effects like
flow choking
become very important.
For aircraft speeds greater than the speed of sound,
conditions are said to be
supersonic, 1 < M < 3,
and compressibility effects are important.
Depending on the specific shape and speed of the aircraft,
shock waves
may be produced in the supersonic flow of a gas. For
high supersonic speeds, 3 < M < 5,
aerodynamic heating becomes very important.
If the aircraft moves more than five times the speed of sound,
conditions are said to be
hypersonic, M > 5,
and the high energy involved under these
conditions has significant effects on the air itself.
The Space Shuttle re-enters the atmosphere at
high hypersonic speeds, M ~ 25.
Under these conditions, the heated air becomes an ionized plasma
of gas and the spacecraft must be insulated from the high temperatures.