Physical Basis of Interference Effects in Hearing
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To capture faint sounds, the ear uses an active system of amplification. We and our colleagues have put forward the idea that the amplifier comprises a set of ‘self-tuned critical oscillators’: each hair cell contains a force-generating dynamical system which is maintained at the threshold of an oscillatory instability, or Hopf bifurcation. The active response to a pure tone is perfectly suited to the ear’s needs, since it provides frequency selectivity, exquisite sensitivity and wide dynamic range. However, the intrinsic nonlinearity of the mechanism causes tones of different frequency to interfere with one another in the cochlea. In order to provide a framework for understanding how the ear processes the more complex sounds of speech and music, we have examined the response of a critical Hopf oscillator to two tones. Our calculations indicate how the response to one tone is suppressed by the presence of a second tone of similar frequency. They also show how a characteristic spectrum of distortion products is generated. The results are in accord with experimental observations of basilar membrane motion. Given the complexity of the nonlinear response, how does the ear distinguish the frequency components of a sound source? We propose a simple model of pitch extraction based on the timings of neural spikes, and investigate to what extent psychophysical phenomena such as the sensation of dissonance and auditory illusions can be attributed to the physical nature of the peripheral detection apparatus.
KeywordsHair Cell Hopf Bifurcation Hair Bundle Oscillatory Instability Distortion Product
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