Audio compression - The MPEG - page 108

is driven by it except at very low frequencies where the fluid flows through the helicotrema, decoupling the basilar
membrane.
Figure 4.10: (a) The cochlea is a tapering spiral cavity. (b) The cross-section of the cavity is divided by Reissner's
membrane and the basilar membrane.
Figure 4.11: The basilar membrane tapers so its resonant frequency changes along its length.
To assist in its frequency domain operation, the basilar membrane is not uniform. Figure 4.11 shows that it tapers
in width and varies in thickness in the opposite sense to the taper of the cochlea. The part of the basilar membrane
which resonates as a result of an applied sound is a function of the frequency. High frequencies cause resonance
near to the oval window, whereas low frequencies cause resonances further away. More precisely the distance
from the apex where the maximum resonance occurs is a logarithmic function of the frequency. Consequently
tones spaced apart in octave steps will excite evenly spaced resonances in the basilar membrane. The prediction
of resonance at a particular location on the membrane is called place theory . Among other things, the basilar
membrane is a mechanical frequency analyser. A knowledge of the way it operates is essential to an
understanding of musical phenomena such as pitch discrimination, timbre, consonance and dissonance and to
auditory phenomena such as critical bands, masking and the precedence effect.
The vibration of the basilar membrane is sensed by the organ of Corti which runs along the centre of the cochlea.
The organ of Corti is active in that it contains elements which can generate vibration as well as sense it. These are
connected in a regenerative fashion so that the Q factor, or frequency selectivity, of the ear is higher than it would
otherwise be. The deflection of hair cells in the organ of Corti triggers nerve firings and these signals are conducted
to the brain by the auditory nerve.
Nerve firings are not a perfect analog of the basilar membrane motion. A nerve firing appears to occur at a constant
phase relationship to the basilar vibration, a phenomenon called phase locking, but firings do not necessarily occur
on every cycle. At higher frequencies firings are intermittent, yet each is in the same phase relationship.
The resonant behaviour of the basilar membrane is not observed at the lowest audible frequencies below 50 Hz.
The pattern of vibration does not appear to change with frequency and it is possible that the frequency is low
enough to be measured directly from the rate of nerve firings.
4.6 Level and loudness
At its best, the HAS can detect a sound pressure variation of only 2 x 10 -5 Pascals rms and so this figure is used as
the reference against which sound pressure level (SPL) is measured. The sensation of loudness is a logarithmic
function of SPL hence the use of the deciBel explained in section 4.2 . The dynamic range of the HAS exceeds 130
dB, but at the extremes of this range, the ear is either straining to hear or is in pain.
The frequency response of the HAS is not at all uniform and it also changes with SPL. The subjective response to
level is called loudness and is measured in phons . The phon scale and the SPL scale coincide at 1 kHz., but at
other frequencies the phon scale deviates because it displays the actual SPLs judged by a human subject to be
equally loud as a given level at 1 kHz. Figure 4.12 shows the so-called equal loudness contours which were
originally measured by Fletcher and Munson and subsequently by Robinson and Dadson. Note the irregularities
caused by resonances in the meatus at about 4 kHz and 13 kHz.