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I need assistance please. Not possessing one (never mind two!) pianos myself, I wonder if someone could test this experiment for me? (Or has someone already noticed this phenomenon?)

I am presently conducting a research project on quantum mechanics and the results of this experiment would prove very significant for me. Any assistance would be much appreciated so thank you in advance.

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Any musical instrument can cause any other nearby musical instrument to resonate, as long as the other musical instrument has something that can resonate that is free to vibrate and is tuned to frequencies sympathetic with the source notes or chords being played by the first instrument. The degree of resonance will vary with the loudness of the source instrument. A soft sound may not cause enough resonance to be heard, but a louder sound will work. Basic physics. –  Wheat Williams Sep 4 '13 at 19:46
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Out of curiosity, in what way are you applying this to your quantum mechanics research? I know sympathetic responses are easily explained by classical physics (as @NReilingh stated in his answer). –  Basstickler Sep 4 '13 at 22:24
    
@Basstickler Hi, I'm both a musician and a physicist. Here's one example from quantum mech: lasers. The basic principle behind the Einstein equations is that a photon will stimulate "resonant" emission or absorption of photons of exactly the same wavelength as electrons change orbital levels (whose energy differences are equal to the photon energy). So, oddly enough, There is a sort-of similarity to resonant pianos. It's more conceptual than physical, since you'd have a hard time "storing energy" in a piano string (ooh! String Theory!) for release when stimulated. –  Carl Witthoft Sep 5 '13 at 12:00
    
@CarlWitthoft Totally wrote a piece called "String Theory" about causing sympathetic resonance within a piano when I was in college. :-D –  NReilingh Sep 5 '13 at 15:34
    
@CarlWitthoft Very interesting! I imagine you could describe the tension of the string as stored energy, which I think is classically called potential energy? For some reason your talk of lasers reminded me of this ted.com/talks/woody_norris_invents_amazing_things.html maybe because the lasers emit unidirectional light. –  Basstickler Sep 5 '13 at 22:22
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Yes, but this phenomenon is easily explained by classical physics.

If you hold down the sustain pedal on a piano (thus releasing the strings to vibrate freely), any instrument nearby playing a tone that is matched by one of the piano strings will cause that string to vibrate in sympathy.

The tone provided by the voice, trombone, second piano, violin, etc. is causing sound waves (periodic waves of air compression) to emanate from the instrument towards the piano string. Force from these waves of air compression is imparted to the piano string. Because the resonant frequency of the piano string is the same as the frequency of the air compression waves, the piano string responds by absorbing this kinetic energy and amplifying its own vibration.

Other strings on the piano that occur at perfect intervals (or harmonics) of the sound will also vibrate in sympathy, but with less intensity.

See also:

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I'd also like to add that this is also true for other instruments as well - anything that can vibrate in a given room will vibrate in that room at the appropriate frequency - snare drums, light fixtures, chairs, etc. Some instruments, such as the Sitar depend on sympathetic vibrations for the instrument to function. I should also add that the pianos would have to be fairly close together and you would have to strike one of them loudly. Also, the results would be more pronounced if two grand pianos were used. –  jjmusicnotes Sep 4 '13 at 17:56
    
Lorries passing by can and do have the same effect on ,for example, fittings in the house - like badly fitting windows. Low frequency seems to be more successful in this phenomenon.The 'opera singer breaking the wineglass' syndrome is also relevant, and while I've never experienced it, believe it can happen. Yes, snare drums seem to have a greater propensity to vibrate sympathetically - wonder why? –  Tim Sep 4 '13 at 18:29
    
I believe the snare drum just seems like it has a higher propensity because it is louder when this happens. I think this is due to the snares touching the bottom head while it (and to some extent the snares) is vibrating. You will notice that if the snares are turned off the drum will not have the same volume in its sympathetic resonance (drummers typically turn their snares off when not playing for an extended part of a song). Different drums will be tuned differently which will also effect the resonance. –  Basstickler Sep 4 '13 at 22:13
    
Also, rooms have a resonant frequency. That frequency will propagate and be louder than others. This means that the room's resonant frequency would be the easiest to frequency to stimulate as a sympathetic response. In an amplified setting that frequency would be most likely to create feedback as well. –  Basstickler Sep 4 '13 at 22:21
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Drums respond to a larger range of frequencies for two reasons: they all have a membrane which vibrates in two dimensions as opposed to one, and the 2-dimensional surface area absorbs MUCH more energy from sounds in the air than a string, so the pitch doesn't have to match exactly. –  NReilingh Sep 4 '13 at 23:31
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A nice little demo of this is one I use with pupils: rest a piece of folded paper, about a quarter of a postage stamp size, on, say, the top string of a guitar. The middle of the string on an acoustic is good. Play notes on another guitar (or other instrument) and see what happens when that same top E is played.

It also works, but not so markedly, with other notes which have that top E as a harmonic.

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I have a guitar with very light strings, and if one plays the fifth string ("A") it will cause the first string (upper "E") string to sound; that string will continue to sound even if the "A" is damped. –  supercat Sep 12 '13 at 23:38
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