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Pops, Shocks, Impulses

January 8, 2014 — 1 Comment

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Take a balloon, blow it up, and quickly stick a needle through the rubber. What do you hear? You wouldn’t be surprised to hear a loud “pop” immediately after piercing the once-inflated balloon. Try it again with a few balloons of different radii. What do you hear now? Chances are that you will notice a slight change in frequency. Additionally, depending upon the room in which you pop the balloons, you may notice additional reverberation.

What is happening here? Why do different balloons sound slightly different? What is the reverberation, and is it useful?

First, why does a balloon make a loud popping sound? When a balloon pops, the rubber suddenly contracts. This leaves a discontinuity in the air pressure. Pressure outside the balloon is equal to the atmospheric pressure, but the balloon’s internal pressure is often a couple hundred Pascals higher than that of the surrounding air. Upon retraction of the rubber, this high pressure region meets the lower pressure of the atmosphere. This newly-formed pressure wave spreads outward from the center of the late balloon’s location as a weak shock wave. This abrupt change in pressure, as it spreads outward, acts like an impulse in the air, a point we will return to later. The balloon’s weak shock wave is similar to the strong shock wave from a jet plane, though the equations that govern the two differ.

As the peak in pressure propagates outward, something more fascinating is unveiled. Air is accelerated outward due to the sudden difference in pressure, and it will overshoot due to inertia. This leaves a region of low pressure behind the high pressure wave. Air will then accelerate inward in response and will once again overshoot, but this time it will do so in the opposite direction. The process continues, creating an oscillation in the air with a characteristic frequency. The frequency of this oscillation depends upon the radius of the former balloon. Thus, smaller balloons will have a more “shallow” sound, and larger balloons will sound “deeper.”

The question becomes far more interesting when considering that initial weak shock wave. As mentioned previously, this discontinuity acts like an impulse in the air. Impulses are powerful tools in that they contain all frequency information. If one wished to find the resonant frequency of a room, one could play sounds at various frequencies and find those which reflected most loudly off the walls of the room. However, this is a time-consuming process and is by all means impractical. An impulse, however, contains all frequencies. If an acoustical engineer were to supply an impulse at different locations in a room and place a microphone somewhere else, that engineer could calculate which frequencies are best reflected/selected by that room’s architecture. This could be done by firing a starter pistol or by clapping one’s hands (try it out). One could also pop a balloon. The balloon’s pop provides an impulse. The room (unless it is anechoic) will respond at particular frequencies. What this means is quite fascinating. The sound of the balloon’s pop is the sound of a recording studio, the sound of a theater, the sound of a living room, and the sound of a cafeteria.

The pop is the sound of the room itself.