Sensation of the superposition of two tones
Note that the eardrum will follow the oscillation prescribed by the heavy curve ( the sum of y1 and y2). It does not "know" that this pattern is the result of two others.
This more complicated but single vibration pattern (the summation tone) arrives at the oval window and gives rise to two groups of travelling waves in the cochlear fluid, one for each of the component tones!! If the frequency difference f between the two component tones is large enough, the corresponding resonance regions of the basilar membrane are sufficiently separated from each other for each of these regions to oscillate with a frequency corresponding to a component tone and we thus hear two separate tones of constant loudness with pitches corresponding to each of the original tones.
This property of the cochlea disentangling a complex vibration pattern into original tone components is called frequency discrimination. It is a mechanical process, controlled by the hydrodynamic and elastic properties of the inner ear constituents.
If however, the frequency difference f is smaller than a certain amount, the resonance regions of the basilar membrane overlap and we hear only one tone of intermediate pitch with modulated or beating loudness. In this case the overlapping region of the basilar membrane follows a vibration pattern essentially identical to that of the eardrum. The amplitude modulation of the perceived pattern (broken curve) causes the perceived loudness modulation. This is called first order beats.
The frequency of the resulting vibration pattern, fr is equal to the average value:
The time interval Trafter which the resulting amplitude attains the initial value is called the beat period. The beat frequency fB = 1/TB turns out to be given by the absolute value of the difference in the two frequencies:
fB = <<f2+ f1<< = f
The closer together the frequencies f1 and f2 are the "slower" the beats will be.
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