The Greenwood Function
By summing the experimentally derived critical bandwidths over the length of the human cochlea, Greenwood developed the following function that describes the relationship between the frequency of a pure tone and the position of the hair cells measured as the fraction of the total length of the cochlear spiral in which it resides:
- f is the characteristic frequency of the sound in hertz
- A is a scaling constant between the characteristic frequency and the upper frequency limit of the species
- a is the slope of the straight-line portion of the frequency-position curve, which has shown to be conserved throughout all investigated species after scaling the length of the cochlea
- x is the length in millimeters from the apical end of the cochlea to the region of interest normalized by the total length in millimeters of the cochlear spiral
- K is a constant of integration that represents the divergence from the log nature of the curve and is determined by the lower frequency audible limit in the species.
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