Sympathetic resonance or sympathetic vibration is a

harmonic A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...

phenomenon wherein a passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. The classic example is demonstrated with two similarly-tuned

tuning forks A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against ...

. When one fork is struck and held near the other, vibrations are induced in the unstruck fork, even though there is no physical contact between them. In similar fashion,

string String or strings may refer to: *String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian anim ...

s will respond to the vibrations of a tuning fork when sufficient harmonic relations exist between them. The effect is most noticeable when the two bodies are tuned in unison or an octave apart (corresponding to the first and second harmonics, integer multiples of the inducing frequency), as there is the greatest similarity in vibrational frequency. Sympathetic resonance is an example of injection locking occurring between

coupled oscillator Oscillation is the repetitive or Periodic function, periodic variation, typically in time, of some measure about a central value (often a point of Mechanical equilibrium, equilibrium) or between two or more different states. Familiar examples o ...

s, in this case coupled through vibrating air. In musical instruments, sympathetic resonance can produce both desirable and undesirable effects. According to '' The New Grove Dictionary of Music and Musicians'': This is the online edition of '' The New Grove Dictionary of Music and Musicians'', Second Edition, with newer revisions.

Sympathetic resonance in music instruments

Sympathetic resonance has been applied to musical instruments from many cultures and time periods, and to

string instrument String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when a performer plays or sounds the strings in some manner. Musicians play some string instruments by plucking the ...

s in particular. In instruments with undamped strings (e.g.

harp The harp is a stringed musical instrument that has a number of individual strings running at an angle to its soundboard; the strings are plucked with the fingers. Harps can be made and played in various ways, standing or sitting, and in orche ...

s, guitars and kotos), strings will resonate at their fundamental or overtone frequencies when other nearby 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 (the third harmonic of A and fourth harmonic of E). Sympathetic resonance is a factor in the timbre of a string instrument. Tailed bridge guitars like the

Fender Jaguar The Fender Jaguar is an electric guitar by Fender Musical Instruments characterized by an offset-waist body, a relatively unusual switching system with two separate circuits for lead and rhythm, and a short-scale 24" neck. Owing some roots to th ...

differ in timbre from guitars with short bridges, due to the resonance that occurs in their extended floating bridge. Certain instruments are built with sympathetic strings, auxiliary strings which are not directly played but sympathetically produce sound in response to tones played on the main strings. Sympathetic strings can be found on Indian musical instruments such as the sitar, Western Baroque instruments such as the viola d'amore and folk instruments such as the hurdy-gurdy. Some pianos are built with sympathetic strings, a practice known as aliquot stringing. Sympathetic resonance is sometimes an unwanted effect that must be mitigated when designing an instrument. For example, to dampen resonance in the headstock, some electric guitars use string trees near their tuning pegs. Similarly, the string length behind the bridge must be made as short as possible to dampen resonance.

References

{{Acoustics Acoustics Resonance