A vibration produced in one material by the vibrations of the same frequency, or a harmonic multiple of that frequency, from a sound wave in contact with the object, by means of the air or an intervening material.
A common example of sympathetic vibration is to sound a tuning fork and bring it close to, but not touching, another fork of the same frequency. The second fork will then begin to vibrate sympathetically. If the forks are mounted on resonating boxes, the effect will be stronger and thus heard better. The same effect can be observed by shouting or singing near a set of undamped (sustain pedal down) piano strings.
In physics, vibration is commonly referred to as an oscillation – a movement, first in one direction and then back again in the opposite direction. You can observe this, for example, by striking the prongs of a tuning fork, or by plucking the string of a musical instrument. Sound is produced by the vibrations of a body that are transmitted through material media (air, for example) in waves of varying pressure. When a sound wave of one frequency strikes a surface (a wall, for example) that will vibrate naturally at the same frequency, that vibration is called sympathetic vibration. Any reinforcement (increase) of sound resulting from the sympathetic vibration is called resonance.
Most construction materials have low resonant frequencies, so low frequency sounds can easily cause sympathetic vibrations in such structures. This is commonly experienced when bass notes of music penetrate walls and ceilings. At the other end of the frequency spectrum is the classically trained singer who is able to smash a wine glass, by finding its resonant frequency and attacking that pitch at full volume.