Can random constructive interference with sound waves cause damage?

Any two sound waves have a random chance to constructively interfere with each other at a given spot and this will cause an increase or decrease in pressure. So is it possible that a large number of local noises in a loud environment could interfere perfectly at a single point, such as on a person or building, and cause damage? I'm not worried, just curious if this is a daily occurrence or if the probability of it is extremely low or if it can even happen.

• It depends on the sound waves and the medium . Have a look at mecheshier.hubpages.com/hub/… – anna v May 27 '13 at 4:16
• Given that sound is pressure waves, it can cause damage if the amplitude is high enough. See en.wikipedia.org/wiki/Cavitation. Interference isn't needed. It is possible that interference could make it worse. – mmesser314 Jul 22 '14 at 13:09

3 Answers

Let's say you have $n$ sources, each producing a sine wave of amplitude $A$, and they combine with random phases. In principle, the sum could be as large as $nA$, and if $n$ is very large we could imagine that this amplitude could be big enough to be destructive. However, because the terms being added are independent and identically distributed, with finite variance, the central limit theorem tells us that the probability distribution of the sum should be well approximated by a normal (Gaussian) distribution. Normal distributions have thin tails, so the probability of a very large sum is negligible.

To get extreme values ("black swans") of a random sum with high probability, you need to violate one of the hypotheses of the central limit theorem. E.g., in economics, many times the individual variables don't have finite variances, and instead of a normal distribution for the sum, you get a Levy-stable distribution, which has fat tails.

You're right that sound waves can interfere constructively or destructively leading to dead spots or live spots (which is an effective phenomenon to be considered when constructing large auditoriums) which can be harmful sometimes.

Your example of local noises in buildings fail for one reason you mention ...

So is it possible that a large number of local noises in a loud environment could interfere perfectly at a single point, such as on a person or building, and cause damage?

This weird occurrence seems unreasonable to me. I'd say it has the lowest possibility than anything and for such a phenomenon to occur...

• All those waves (low energy noises) shouldn't be absorbed, the reflected waves should be coherent with the other waves of similar pitch in order to undergo perfect constructive interference
• Finally, the resultant wave(s) should be focused on a person or building.

In theory, we can show that if these waves do interfere, they'd add up to some harmful high-pressure region traveling at speed of sound. But in reality, there's always some interruption for this to happen that make these to be the lowest probabilistic factors one can consider.

Two things against:

1. It's unlikely that the waves will actually all interfere constructively. In a realistic setting the sounds won't be constant, so points of constructive interference are very temporary and don't have time to do anything even if they could.
2. Each of the sound sources is putting out a certain amount of power as sound (in all directions), and this is the total power available for whatever destructive purposes you have in mind.

One source (http://engineering.mit.edu/ask/can-sound-be-converted-useful-energy) claims

What the human ear perceives as clanging cacophony—the roar of a train engine or the whine of a pneumatic drill—only translates to about a hundredth of a watt per square meter.

Constructive interference of several such sources (and their echoes) would deliver more power intensity than that, but as you can see the available power in sound isn't much to start with. It also doesn't transfer neatly to a single object. Most objects either reflect sound well, or else are flexible enough that absorbing sound doesn't damage them.

Sound is most commonly demonstrated to be destructive by matching a resonant frequency of some brittle object (such as a wine glass) and forcing the vibration of that object over a period of time until it breaks. That is, the target object stores some energy from the sound, in order to get over the fact that the power transferred from the sound wave is feeble.

This could in principle happen by chance given many loud sound sources. But we don't need to take special measures to prevent road-facing windows spontaneously shattering. Admittedly they're large, and their modes of vibration in the range of audible sound require far more energy than the wine glass. Even so I think it's fair to conclude that although I don't have a mathematical model to estimate the probability, a typical "noisy environment" such as a busy street doesn't do anything of the sort and so the probability must be tiny.