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On my acoustic guitar, whenever I strum my high E string my A string starts vibrating. This only happens with my high E string. When my A string vibrates it creates an echoing sound that won't stop unless I put my finger on the string. It is so annoying but I don't know what is wrong with it.

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Could you post a recording of the sound? – Archundia Dec 26 '13 at 18:46
You say acoustic, but might it be electo-acoustic plugged in to an amp? – Tim Dec 26 '13 at 19:39

Sounds like a sympathetic vibration to me, also known as string resonance. From Wikipedia:

String resonance occurs on string instruments. Strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded. For example, an A string at 440 Hz will cause an E string at 330 Hz to resonate, because they share an overtone of 1320 Hz (3rd overtone of A and 4th overtone of E).

I get this on my acoustic guitars as well -- it's a natural part of acoustic instruments. I believe the specific strings/frequencies that vibrate depend on a variety of factors, such as how the top of your guitar is tuned (yes, the top of your guitar is likely "tuned," if it was built by a reasonably good luthier!), the bridge and which string/fret you play.

If you'd like to tone this vibration down a bit and you have room behind your bridge (e.g., for an archtop guitar or a Selmer-style gypsy-jazz guitar), you can wind some cloth in the strings behind the bridge. If you're playing a dreadnought, I'm not sure what you can do (sorry!).

Long story short, this vibration is a natural thing -- part of playing an acoustic instrument. Embrace it!

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The A string shouldn't be resonating to the E string. At least not if they are tuned to A and E and both are being played openly (which I'm assuming). – Archundia Dec 26 '13 at 21:51
@JCP: Since the third partial of A is the tone E it's actually very natural for the A string to start ringing (with the frequency of the higher E) when the high E string is strum. You can equally try it on a piano by slowly (in order to not hit the string with the hammer but releasing the damper on that string) pressing down any key and then quickly hit and release the key an octave and a fifth above. You will then hear the high fifth ringing on the undamped string. – Ulf Åkerstedt Dec 29 '13 at 1:16
@UlfÅkerstedt That's correct, I poorly worded my comment. What I meant is that on a guitar the A string shouldn't be resonating like in the description. The resonance induced by the third harmonic of A is very small and decays fast, it shouldn't be noticeable to that extent (if at all in most scenarios). I don't think resonance between the A and E strings are causing this. – Archundia Dec 29 '13 at 6:39

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