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Banjo Break Angle Tension Modulation as Parametric Oscillation

Politzer, David (2020) Banjo Break Angle Tension Modulation as Parametric Oscillation. , Pasadena, CA. (Unpublished)

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The motion of the floating bridge of the banjo, in conjunction with the break angle of the strings over that bridge, produces string tension modulation that is first order in the amplitude of the string motion. This note refines a previous suggestion regarding the impact on the frequencies of the strings’ and bridge’s motion. For a given mode frequency pair of string and bridge, the resulting tension modulation produces a new, additional motion characterized by the sum and difference of the original ones.Strictly speaking, this corresponds to canonical “frequency modulation” only in the limit of modulation slow compared to the string frequency. The more general result is precisely an example of what is known as “parametric oscillation,” first analyzed by Rayleigh. The qualitative impact of tension modulation on banjo timbre remains as suggested previously. It is only the precise math and physics that warrants this correction.

Item Type:Report or Paper (Discussion Paper)
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Politzer, David0000-0002-4983-6621
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Record Number:CaltechAUTHORS:20200115-154856194
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100744
Deposited By: H. Politzer
Deposited On:16 Jan 2020 17:52
Last Modified:16 Jan 2020 17:52

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