Sympathetic resonance

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Sympathetic resonance is a harmonic phenomenon wherein a frequency or note will start resonating in 'sympathy' with another, not due to any external agency. Refer sympathetic strings as a specific case in point. Sympathetic resonance is overtone harmonics by any other name. Overtone singing of the Himalaya is another example. The effect is most often heard in strings when the fundamental frequency is in unison or an octave lower or higher than the catalyst note or frequency, although it can occur for other intervals such as a perfect fifth with less effect.

Lewcock et. al.(2006) states that:

The property of sympathetic vibration is encountered in its direct form in room acoustics in the rattling of window panes, light shades and movable panels in the presence of very loud sounds, such as may occasionally be produced by a full organ. As these things rattle (or even if they do not audibly rattle) sound energy is being converted into mechanical energy, and so the sound is absorbed. Wood panelling and anything else that is lightweight and relatively unrestrained have the same effect. Absorptivity is at its highest at the resonant frequency, usually near or below 100 Hz. (NB: original quotation not meta-enhanced.)

Arden Wilken on his website provides a significant example of the power of sympathetic resonance:

The power of resonance can be seen dramatically in what occurred in 1940 to the Tacoma Road Bridge in the State of Washington, USA. The wind created a tone as it blew across the valley, which happened to be the natural frequency of the bridge itself. This resonance created by the wind led to the total collapse of the bridge.

A film of the bridge in the process of collapsing showed it undulating wildly in a continuous wave, appearing to be made out of ribbon instead of concrete and steel. The wind and the bridge sang together in sympathetic resonance. In this case, unfortunately, it was the destruction of the bridge because it could not incorporate the vibration. (NB: original quotaiton not meta-enhanced.)

According to Grove Music Online (2007) article on Duplex Scaling, Steinway progressed a system of Aliquot scaling to provide sympathetic resonance with the intention of enriching the treble register of the pianoforte. In the 'octave duplex' piano by Hoerr of Toronto, each note had four strings, of which two, three or four could potentially be struck by the hammer depending on the depression of one of four pedals. Steinway’s duplex scale was precipitated a half century earlier by an experiment conducted by the German piano maker Wilhelm Leberecht Petzoldt, in which a small bridge was placed behind the standard larger one with the intention of maximizing the potential additional resonance of a sympathetically vibrating additional length of string.

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