Archives For acoustics

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.

A Musician on Mars

December 11, 2013 — 1 Comment

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Welcome to Mars. As one of the first colonists on the fourth planet from the Sun, you endeavor to make it your new home. On Earth, you filled your time in numerous ways, but your real passion was music. Luckily, the Indian Space Research Organisation (ISRO) allowed you to bring your prized possession: a Steinway grand piano. Excited to play for the first time in months, you squeeze into your ISRO-issued space suit and wheel the piano onto the Martian surface. It’s noon near the equator. The temperature is around 25ºC (77ºF). You stretch out your arms, relax, and strike your first key. The sound is… quiet and out of tune. Assuming the piano needs to be retuned, you wheel it back into your pressurized vessel, take off your suit, and tune it yourself. Satisfied, you wheel the piano onto the surface again. The Martian surface is quiet, and you notice the colors of the sky are a lot redder than you had seen in NASA photographs. Again, you begin to play. It again sounds too quiet.

What is happening here? Why might a piano sound different when played on the Martian surface? This is a fairly involved question. Luckily, we are considering an instrument with taut strings rather than something that depends more upon atmospheric conditions than, say, a trombone or pipe organ. Furthermore, the equatorial temperature is Earth-like. Why, then, might a piano sound different on Mars?

When tuning and subsequently playing a piano, the frequency you perceive (or pitch) depends upon the tension, length, and mass of the strings within the piano. Since the temperature is about the same as before, and since you did not physically exchange the strings, these properties remain fairly constant. However, the fluid on the strings does play a role. Like any oscillator, the fluid in which it is immersed provides a load which will subsequently alter the frequency at which the oscillator resonates and by how much. On Mars, the atmosphere is more rarified, with a mean pressure of 600 Pa at the surface. Compare this with a pressure of over 100,000 Pa at sea level on Earth. This reduced loading by air results in a bias to slightly higher frequencies (or a higher pitch). If you retuned the piano in a pressurized cabin and then played the newly tuned piano on the Martian surface once again, it would still sound out of tune. A simple solution is to retune the piano while on the surface.

However, this is not the only problem with playing music on the Martian surface. Remember that Mars has a lower-pressure atmosphere. Sound, as you may recall, propagates as an oscillation of pressure in some medium (like air). If the mean pressure is lower, this presumably changes the ability of sound to propagate over longer distances. Without going into too many details here, what happens is that sound will not propagate very far on Mars, and there is an effect such that high frequencies are heavily attenuated. Before, the pitch was shifted slightly higher. Here, on the other hand, higher frequencies will sound softer than lower frequencies, and all frequencies will sound quieter. This means that not only does the piano sound out of tune, but it also sounds muted. The question of sound propagation is so interesting that an acoustics researcher simulated sound on Earth, Mars, and Titan. She found that a scream which may travel over one kilometer on Earth would only carry 14 meters on Mars!

Your out-of-tune, muted piano, probably wouldn’t be audible to a nearby audience on the Martian surface.