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How sound propagates

Supplement for chapter 1

Sound files:

From Auditory Demonstrations CD:

The Decibel Scale

Impedance and impedance matching are key concepts. Roughly, impedance Z is "force divided by velocity" i.e.Z= F/v . If you apply a force, but the system in question does not move much, it has high impedance, because the velocity v is small and Z=F/v is large. If two objects have the same impedance Z, energy flows freely between them. That happens with adjacent parcels of air if the air is the same temperature, pressure, and composition in both parcels; thus sound propagates freely in uniform air, but some reflection occurs when sound in air meets a flame, for example. An important point is that impedance depends on the frequency of the force, that is applied sinusoidally. This point is a bit premature in chapter 1, since we get around to sinusoidal motion in chapter 3.

An excellent web reference showing the effect of impedance changes on wave reflection (and many other wave and acoustical phenomena) is Penn State Prof. Daniel Russell's,

This site has some of the best dynamic illustrations of acoustical phenomena on the web.

For the wave reflection and impedance, see here scroll down to "Reflection from an Impedance Discontinuity."


Speed of sound

Push and push-back

can be seen in this Wikimedia commons animation.

Even though the source of the sound below is a nuclear explosion, (1950's era) and the initial disturbance propagated at many times the speed of sound in air, it has slowed down and is propagating at the speed of sound long before the time the shock wave reaches the soldiers. Its rate of travel can be seen by the dust kicked up on the desert floor.

A shock wave might lead to an extra pressure of 1/10 of one atmosphere at a building some distance away. An atmosphere is a pressure of 14 pounds of force per square inch, so the "overpressure" from the shock wave is about 1.4 pounds per square inch. One side of a building might be 100 ft by 300 ft, or 30,000 sq. ft., i.e. 4,320,000 square inches. Thus, the net overpressure amounts to about 6.5 million pounds of force on the building.


Waves at Boundaries

Reflections of a wave on a string at various types of boundary: hard wall (fixd end), "soft" wall (free end), and impedance mismatch (going up or going down): another set of Dan Russells' excellent animated gifs.

Suggestion for an experiment in Ripple.

Even though sound propagates through your body, you reflect a lot of the sound impinging on you, since your body's impedance is very different than that of the surrounding air.

In the Harvard modified Ripple you can draw various shapes like rectangles and circles filled with a medium, whose impedance (adjustable from lower to higher than the surrounding medium, with a slider labeled Medium, seen after Mouse=Draw Medium is selected). Then waves can be sent at the object you have drawn. Note that the wave both penetrates the object in blue and reflects from it (see the figure below). Medium was set to 191 in this case, but if Medium is set near 0, the nominal value of the surrounding medium, the impedance mismatch is small and very little reflection takes place (also the blue tint will be barely visible).

It helps to send a short burst of wave energy toward the object, so you can see the reflected waves free of the stronger incident wave. There are several ways of doing this, including turning off the Source or "Src" and drawing a small ball of wave energy somewhere with Draw Wave, or quickly turning on and off a source so that a burst of waves is created, as was done for the figure below. The source was a point at the top middle sending out an oscillating wave; the wave emerged as a circular band from there and collided with the blue circular "lens". The weaker reflected wave off the surface of the lensis seen heading back toward the top, a consequence of the impedance mismatch inside vs. outside the blue lens. A refracted wave is seen inside the lens, traveling slower. Setting Medium to say 75 instead of 191 results in significantly less reflection.

Picture of atomic gaseous collisions

An excellent demonstration of gaseous molecular motion with many user controls and good real time animations was developed at Northwestern University

Another good demonstration of the wild chaos of colliding particles, and the so-called Brownian motion of a much larger particle suspended in the smaller ones, can be found at

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