Interesting thing I noticed just now playing my ukulele.
For those who don't know how a ukulele works, it has four strings: a high G followed by a lower C, E, and A. Holding down frets causes the strings to play progressively higher-pitched notes. Now, it is possible for two or more strings to play the same note. I've noticed that when this happens, playing one string will cause the others of the same pitch to vibrate, even without actually playing them. However, it's only when they are exactly the same note. If it's not the same note, it doesn't vibrate (at least not perceptibly). Why? If it's caused by the vibration from the string spreading outward, why would it matter what pitch the strings are relative to each other?
Perhaps it's a property of the nylon in the strings? After noticing this, I checked on my steel-stringed acoustic guitar, which definitely does not (perceptibly) do this.