# Can a thing resonate whilst exposed to white noise?

Imagine some thing put in the presence of loud pure white noise, say at a level that might come from a teenager's HI-FI set to annoying. And the thing is like a champagne glass, sheet metal box or other thin walled vessel. I'm not considering anything like a cannon ball or anvil.

I can foresee two scenarios:-

1. The thing vibrates at it's natural self resonant frequency, but only with limited amplitude as the power content of white noise at a specific frequency is relatively small.
2. The thing does nothing whatsoever as all the various frequencies present in the white noise induce vibrations that cancel each other out.

Which is it, or might there be a third possibility?

• Please explain how a stereo/hifi is going to generate significant white noise -- or are you simply assuming a decent shot noise generator followed with a high-gain amp? Jul 12, 2017 at 14:54
• @CarlWitthoft Just use your imagination and assume that it produces pure white noise. It's the resonance bit that I'm after... Jul 13, 2017 at 1:07
• Have you evaluated how much power is produced by a teenager's Hi-Fi set? Show us what you have done so far, so we don't repeat good work. Jul 13, 2017 at 5:33

## 2 Answers

You won't get much resonance because the phase the thing is being driven with keeps changing.

The resonant thing will act like a notch filter, so you are left with the frequencies near its resonance. However, for resonant energy to build up, the system has to get pumped for a while. While a short segment of the filtered white noise could resonate the object, the next segment could just as well be out of phase and reduce the energy stored in the resonance. In the long run, the total power at a particular phase is 0, so no resonance.

White noise is random, so sometimes there can be long enough sequences of the right frequency that happen to be with a predominant phase to get a little resonance going. However, later sequences will always cancel that in the long run. The question is then is how long "long" is, and how long it takes for the object to build up enough resonant energy to do something interesting.

So it comes down to probability. It is very very unlikely that "white noise" from something like a boombox next to a wine glass can get enough resonance going for the glass to break. Put another way, the mean time to breaking is likely a lot longer than you're willing and able to wait.

The thing will vibrate at all frequencies. It will vibrate more (be amplified) at frequencies that are close to a natural frequency. Effectively, the system will act as a band pass filter (NOT a band notch filter)

I did a very similar experiment in graduate school many times. It wasn't a teenagers hi fi set or a wine class, but it was a random input to a vibratory system.