Resonant strings are thin auxiliary strings found on many (Asian) Indian musical instruments, as well as some Western Renaissance-era instruments. They are typically not played directly by the performer (except occasionally as an effect) but instead resonate along with the main strings played on an instrument. The musician retunes the resonant (often referred to as "sympathetic") strings for each mode or raga, so that when the corresponding note (or one an octave below it) is played on the main strings of the instrument, the resonant strings vibrate sympathetically, providing a sound analogous to our modern echo chamber, and aiding in the instrument's projection.
The same effect can be performed on a modern piano, by softly striking a key in the lower register of the piano and immediately striking that note in a higher octave.
This is the string's fundamental resonant pattern, or frequency.
Each resonant pattern is a multiple of the fundamental frequency: The fundamental is half of a complete wave, the second harmonic is a complete wave, the third harmonic is one and a half waves, and the fourth harmonic is two waves.
Although the fundamental string shown above is depicted as a two-dimensional object, the strings in string theory are one-dimensional.
In an electrical circuit, resonance occurs at a particular frequency when the inductive reactance and the capacitive reactance are of equal magnitude, causing electrical energy to oscillate between the magnetic field of the inductor and the electric field of the capacitor.
Resonance is an important consideration for instrument builders as most acoustic instruments use resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of a drum membrane.
A sharp resonance is a resonance with a sharp peak in the S-matrix (which corresponds to a long lifetime compared to the reciprocal of its mass) while a broad resonance is a resonance with a spread out peak (which corresponds to a short lifetime relative to the reciprocal of its mass).
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