This page is intended for college, high school, or middle school students.
For younger students, a simpler explanation of the information on this page is
available on the
Interactive Sound Waves
With this software you can investigate how sound waves travel through the
When you become experienced with this simulator and the physical principles
behind the program, you can use a
which loads faster on-line and does not include these instructions.
You can also download your own copy of this simulator for use off-line
by clicking this button:
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As any object moves through the air, the air near the object is disturbed.
Small disturbances are
transmitted through the air at a distinct speed called
the speed of sound.
Sound is just a sensation created in the human
brain in response to small pressure fluctuations in the air.
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.
In our simulation,
a bug is creating a sound which moves through the air as a series of waves. When
the waves pass our microphone, the sound is detected. The distance between any two
waves is called the wavelength and the time interval between waves
passing is called the period. The inverse of the period is the
frequency of the wave. which is measured in cycles/second.
The brain associates a certain
musical pitch with each frequency; the higher the frequency, the
higher the pitch. Likewise, shorter wavelengths produce higher pitches since
more waves pass through a point every second.
The speed of transmission of the sound remains a constant regardless of
the frequency or the wavelength since the speed only depends on the
state of the air not on the characteristics of the generating
While the speed of sound does not change, the speed of the source of the
sound is arbitrary.
You can change the speed of the bug by using the slider at
the bottom. You can start or stop the motion of the bug by using the appropriate
buttons. If the source is stopped, you can advance or retreat by a single
time increment by using the "Step Forward" and "Step Back" buttons. And you
can "Resume" the animation by pushing that button. Notice how the frequency
of the sound changes when the source is moving and notice how the waves
collect into a
when the object moves faster than Mach 1.0, the speed of sound.
Here are some of the interesting physics problems which you will observe
with this simulator.
If the source
moves slower than the speed of sound, conditions are said to be
subsonic. As the source moves it continues to generate sound waves
which move at the speed of sound. Since the source is moving slower than
the speed of sound, the waves move out away from the source. Upstream (in
the direction of the motion), the waves bunch up and the wavelength
decreases. Downstream, the waves spread out and the wavelength increases. The
sound that our microphone detects will change in pitch as the object passes.
This change in pitch is called a
If the source moves at or near
the speed of sound conditions are said to be sonic or transonic.
In this case, the waves again bunch up upstream and spread out downstream.
But because the source speed is nearly the sound speed, the upstream wavelength
becomes nearly zero and the individual waves collect into a single
If the source moves higher than the speed of sound conditions are said to be
supersonic. The Mach wave now becomes conical and the
of the cone depends on the ratio of the speed of sound to the speed
of the object; the faster the speed of the object the sharper (smaller)
the cone angle. The ratio of the object speed to the speed of sound is the
of the flow, which explains the name "Mach wave".
We must be very careful not to confuse the Mach waves which appear in this
that occur in supersonic flows. In this simulation, we have only considered
the isentropic transmission of the sound generated by the bug. We haven't
looked at how the flow gets around the bug itself. The motion of the gas
around the bug generates shock waves which are not isentropic. Shock waves
in the flow are not inclined at the Mach angle but at a different angle
which depends on the shape and speed of the bug. The Mach angle is
determined by conditions in the flow.