Date of Award

5-2015

Document Type

Honors Thesis

Degree Name

Bachelor of Science

Department

Physics

Advisor/Committee Chair

Philip Goyal

Abstract

Hair cells, which detect and encode sound stimuli, have been shown to have a non-linear response and self sustaining oscillations. Here, we look at the Van der Pol oscillator, which has these properties, and numerically calculate its response to multiple driving frequencies. Any nonlinear system's response to multiple driving frequencies will have not just the driving frequencies present, but also combination tones, or heterodyne frequencies, which have order defined by the number of driving frequency combinations. This phenomenon has been experimentally confirmed in the human auditory response [1]. In the frequency specture of the Van der Pol steady state response to two frequencies that were significantly present were recorded. When the Van der Pol oscillator was driven at frequencies corresponding to the musical notes A4 and C#5, which form a major third, no first order heterodyne frequencies, all but one second order heterodyne frequency, and at least four frequencies not associated with any first or second order heterodyne frequencies were present. When the two driving frequencies formed a perfect fifth, A4 and E5, all first and second order heterodyne frequencies could be observed and at least two frequencies not associated with any first or second order heterodyne frequencies were present.

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