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Normal Frequencies Of A String Vibrating At Large Amplitudes

Student Name: Ripplinger, David
Advisor Name: Anderson, Brian E.
Approval Date: 8/1/2009
Report Type: Senior Thesis
Title: Normal Frequencies Of A String Vibrating At Large Amplitudes
Abstract: Large displacement amplitudes in a freely vibrating string require that one consider the dynamic tension of the string to determine the normal frequencies instead of the commonly used equilibrium tension approximation. Large amplitudes can cause these frequencies to be significantly sharper. A theoretical model is presented to provide a more accurate approximation of the tension, which includes a correction term that is proportional to the total energy in the string. Experiments have been performed using a repeatable plucking mechanism on a monochord string apparatus. The motion of the plucked string was recorded for both vertical and horizontal displacements using a high speed camera. The instantaneous total energy in the string was then calculated as the string’s motion decayed, using the instantaneous frequency method and a narrow band-pass Bessel filter. A comparison is made between the model and the experimental results of the total energy in the string as a function of time. The data show that when a string is plucked at large displacement amplitudes the partial frequencies can be as much as 83 cents sharp relative to their stable frequency values.
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