Introduction to Acoustics

438 Part D Hearing and Signal Processing
Part D 12.2
a)
100
µV
10 5
10 3
10 1
1 mm
b) Sensitivity (mm/Pa)
4 7 10 20
Frequency (kHz)
c) Velocity (mm/s)
10 4
10 3
10 2
10 1
2 kHz
10 dB SPL
50 dB
100 dB
10 kHz
1 2 3 0.5 kHz
45
0.15 kHz
0 20 40 60 80 100 120
Sound pressure level (dB)
closely to log than to linear frequency. The logarithmic
frequency organization corresponds to a number
of phenomena in the perception of sound, such as the
fact that musical notes are spaced logarithmically in
frequency.
The basilar-membrane responses in Fig. 12.7a illustrate
the property of tuning, in that the displacement
in response to a tone is confined to a region of the
membrane centered on a place of maximal displacement.
Tuning can be further understood by plotting
basilar-membrane displacement as in Fig. 12.7b. This
8
2
11
16
Fig. 12.7 (a) An estimate of the instantaneous displacement
of the basilar membrane in the guinea-pig cochlea for a
2 kHz tone (solid lines) and estimates of the envelope of the
displacement for two lower-frequency tones (dashed lines).
Distance along the basilar membrane runs from left (base)
to right (apex) and the displacement of the membrane is
plotted vertically. The estimates were obtained by measuring
the cochlear microphonic at three sites, indicated by
the three vertical lines, and then interpolating or extrapolating
to other locations using an informal method [12.35];
this method can be expected to produce only qualitatively
correct results. The 2 kHz estimates are shown at 0.1msintervals.
Waveforms at successive times are identified with
the numbers “1” through “5”. Thedashed curves were
drawn through the maximum displacements of similar data
for 0.5 and 0.15 kHz tones, which were scaled to have
the same maximum displacement as the 2 kHz data. The
cochlear microphonic is produced by hair cells, mainly
OHCs, and is roughly proportional to basilar-membrane
displacement. The ordinate scale has been left as microvolts
of cochlear microphonic. The scale markers at lower left
show distance from the origin. (b) Measurements of the gain
of the basilar membrane (root mean square displacement
divided by pressure at the eardrum) for two data sets. In
each case, basilar-membrane displacement at one place was
measured with an interferometer. Both frequency (abscissa)
and sound level (symbols) were varied. The curves peaking
near 9–10 kHz are from the chinchilla cochlea [12.36]
and the curves peaking near 20 kHz are from the guinea
pig cochlea [12.37] (After [12.34]). (c) Basilar-membrane
input–output curves, showing the velocity of membrane displacement
(ordinate) versus sound intensity (abscissa), at
various frequencies, marked on the plots (kHz). The dashed
line at right shows the linear growth of basilar-membrane
motion (velocity proportional to sound pressure). The curve
for 10 kHz is extrapolated to low sound levels (dashed line
at left) under the assumption of linear growth at low sound
levels (Fig. 12.7a after [12.35], Fig. 12.7b after [12.34], and
Fig. 12.7c after [12.36])
plot shows the displacement plotted against frequency
at a fixed location, thus providing a direct measure of
the frequency sensitivity of a place on the membrane.
Data are shown at two locations from separate experiments
(in different species). The ordinate actually shows
basilar-membrane gain, defined as membrane displacement
divided by sound pressure at the eardrum. At low
sound levels (20 dB, plotted with empty circles), the gain
peaks at a particular best frequency (BF) and decreases at
adjacent frequencies. If such measurements could be repeated
at multiple locations along the basilar membrane