Impedance Matching in Sound Production and Hearing: a Comparative Study
51
4.3 Coupling the Medium to the Primary Vibrating Structure
Ear drums tend to be thin and fragile and are often protected by an external tube or
cover. Such tubes or covers can be shaped as horns or reflectors to increase the
sound pressure reaching the ear drum approximately in the ratio of the relative
areas of the reflector and the ear drum.
The pinnae of therian mammals such as rabbits provide gains of from 20 to
nearly 30 dB (a 100- to 1000-fold increase in sensitivity) between 2 and 5kHz
(Lewis 1983, see also Shaw 197 4 ). These hom-shaped reflectors are frequency
sensitive and only start to be effective when their dimensions approach 1/3 A., as is
predicted from their specific acoustic resistance (Fig. 2C) or, with a typical rabbit
ear that is 100 mm long, above I kHz. Significant further gain may be provided by
the tapering external auditory meatus (Fig.4).
A hom-like tracheal sound collector is connected to the ears of tettigoniid bush
crickets. Hill and Oldfield (1981) measured the effective gain due to the tracheal
hom in two bush cricket species using a probe microphone inserted into the
trachea at the cut distal end of the fore femur. The effective gain was +15 to +20
dB between 15 and 20 kHz which was similar to the difference in auditory
sensitivity in the intact animal and after removal of the sound input via the
acoustic trachea and also correlated with the gain predicted from the dimensions of
the acoustic trachea. Diffraction by the side of the head or body also provides a
useful increase in sound pressure of ca. 6 dB on the side facing the sound source at
frequencies above one halfto one third (see Olson 1957).
4.4 Coupling the Primary Vibrating Structure to the Sensory
Cells
The major impedance mismatch in an auditory system is likely to be between the
light thin primary vibrating structure (e.g., an ear drum) and the sensory cells
because the specific acoustic resistances of the two structures differ so greatly
(Sect. 2.2, Table 1): ideally a 60-fold transformation of pressure is required for
optimal impedance matching. Pressure transformers are common in engineering
and typically use levers or hydraulic mechanisms. In the simple ear of noctuid
moths, two sensory cells are attached near the centre of a thin tympanic membrane:
the attachment site of these cells is only about III 0 the diameter of the tympanum
so their relative areas are about I to I 00 (measured from figures in Treat and
Roeder 1959). The coupling between the tympanum and the sensory cells in cicada
ears appears to involve a lever system (Daws 1996, Doolan and Young 1981 ).
Unfortunately, there are no data about the relative areas or lever ratios in these
systems.
51
4.3 Coupling the Medium to the Primary Vibrating Structure
Ear drums tend to be thin and fragile and are often protected by an external tube or
cover. Such tubes or covers can be shaped as horns or reflectors to increase the
sound pressure reaching the ear drum approximately in the ratio of the relative
areas of the reflector and the ear drum.
The pinnae of therian mammals such as rabbits provide gains of from 20 to
nearly 30 dB (a 100- to 1000-fold increase in sensitivity) between 2 and 5kHz
(Lewis 1983, see also Shaw 197 4 ). These hom-shaped reflectors are frequency
sensitive and only start to be effective when their dimensions approach 1/3 A., as is
predicted from their specific acoustic resistance (Fig. 2C) or, with a typical rabbit
ear that is 100 mm long, above I kHz. Significant further gain may be provided by
the tapering external auditory meatus (Fig.4).
A hom-like tracheal sound collector is connected to the ears of tettigoniid bush
crickets. Hill and Oldfield (1981) measured the effective gain due to the tracheal
hom in two bush cricket species using a probe microphone inserted into the
trachea at the cut distal end of the fore femur. The effective gain was +15 to +20
dB between 15 and 20 kHz which was similar to the difference in auditory
sensitivity in the intact animal and after removal of the sound input via the
acoustic trachea and also correlated with the gain predicted from the dimensions of
the acoustic trachea. Diffraction by the side of the head or body also provides a
useful increase in sound pressure of ca. 6 dB on the side facing the sound source at
frequencies above one halfto one third (see Olson 1957).
4.4 Coupling the Primary Vibrating Structure to the Sensory
Cells
The major impedance mismatch in an auditory system is likely to be between the
light thin primary vibrating structure (e.g., an ear drum) and the sensory cells
because the specific acoustic resistances of the two structures differ so greatly
(Sect. 2.2, Table 1): ideally a 60-fold transformation of pressure is required for
optimal impedance matching. Pressure transformers are common in engineering
and typically use levers or hydraulic mechanisms. In the simple ear of noctuid
moths, two sensory cells are attached near the centre of a thin tympanic membrane:
the attachment site of these cells is only about III 0 the diameter of the tympanum
so their relative areas are about I to I 00 (measured from figures in Treat and
Roeder 1959). The coupling between the tympanum and the sensory cells in cicada
ears appears to involve a lever system (Daws 1996, Doolan and Young 1981 ).
Unfortunately, there are no data about the relative areas or lever ratios in these
systems.