What causes the vibration of one guitar string

[spec138]

My friend brought up this concept somehow and I know the answer, I just CANT remember what it's called. Sounds silly, I know. But anyways perhaps someone here can help me. What causes the vibration of one guitar string to be the same frequency of another one that has been plucked on that guitar?
Or another example, a piano string vibrating at the same frequency as a singer's voice. Any help? Thanks.

 

[actionintegral]

sympathetic vibration?

 

[FredGarvin]

If they are mechanically connected in some way it could simply be forced vibration. The vibration from one object induces the vibration in another.

What you are probably thinking of is resonance, which isn't necessarily happening. This would mean that the initial excited object had to be vibrating at the same frequency as one of the other object's natural frequencies.

 

[HallsofIvy]

What causes the vibration of one guitar string to be the same frequency of another one that has been plucked on that guitar?
Or another example, a piano string vibrating at the same frequency as a singer's voice.

FredGarvin: I see no reason to think they might be "mechanically connected".

Either "resonance" or "sympathetic vibration" are good here. The first is perhaps more general than the second.

 

[FredGarvin]

When I say mechanically connected, I mean that they could terminate at the same object, i.e. the strings in a guitar share the same bridge piece.

 

[spec138]

THANK YOU! Resonance is the word I was looking for, you rock :P.

 

[Danger]

Aha! A legitimate excuse to share one of my favourite stories. On a trip to Edmonton 20+ years ago, I got trapped in an underpass due to construction delays. There was a VW bug (original type) in the lane beside me. It was shaking like crazy, and it was obvious from the driver's expression that he didn't know what was causing it. After a few minutes, I kicked the throttle up a notch to check the alternator, and the bug stopped shaking. When I dropped back to my normal 750rpm idle, it started again. That was my 446ci Roadrunner pumping through a pair of Baby Thrush (straight-through) mufflers bolted directly to the headers with no tail pipes. The exhaust pulses at idle exactly matched the natural resonance frequency of the bug body. I spent the next 10 or 15 minutes playing with it, and the poor guy never did figure out what was going on.