The biophysical properties of the external ear of the Tammar wallaby, Macropus eugenii (Desmarest), have been investigated using probe microphones implanted in the ear canal. An acoustic axis of the pinna exists above 2kHz which is located close to the horizonal plane for natural ear positions, whereas azimuthal location of the acoustic axis is determined by pinna orientation on the head. The maximum on-axis acoustic pressure gain of the external ear reaches 25–30 dB for frequencies near 5 kHz. This results from pressure transformation by the horn-like pinna combined with resonance of the auditory meatus. The directionality of the pinna is similar to the sound diffraction properties of a circular aperture with an average radius based on the circumference of the pinna face. These properties determine the acceptance angle of the main lobe containing the acoustic axis and the spatial location of nulls. Large binaural intensity differences, exceeding 30dB, can be produced by the interaction of peaks and nulls between monaural directivity patterns, depending on the relative position of each pinna.
Despite the prominence and mobility of the pinnae in many mammals, the role of the pinna in directional hearing has often been ignored by the use of closed field sound delivery (Erulkar, 1972). A notable exception has been in the study of hearing in bats, where the pinnae often exceed the dimensions of the head and have been clearly implicated in directional hearing (Grinnell, 1963; Grinnell & Grinnell, 1965; Neuweiler, 1970; Busnel & Fish, 1980; Guppy, Coles & Pettigrew, 1984; Jen & Sun, 1984). Recent neurophysiological studies on the mechanisms of sound localization in non-echolocating mammals have used real sound sources in space and have begun to re-examine the role of the pinna (Middlebrooks & Pettigrew 1981; Phillips et al. 1982; Semple et al. 1983; Aitkin, Gates & Phillips, 1984; Calford & Pettigrew, 1984; Moore, Semple, Addison & Aitkin, 1984).
The present study examines some of the acoustical properties of the mammalian external ear which determine the directionality and pressure gain at the eardrum. This study is based on the external ear of the Tammar wallaby (Macropus eugenii) which has an erect and highly mobile pinna, typical of many mammals. Some preliminary data have been presented previously (Hill & Coles, 1981).
MATERIALS AND METHODS
The left and right ears of nine Tammar wallabies (Macropus eugenii) were used in this study. The animals were obtained from a resident colony maintained by the Research School of Biological Sciences at the Australian National University. The wallabies were adult or sub-adult females weighing 3·5–4·5 kg.
Biophysical measurements were made in an anechoic room (2·6 ×2·5 m×2·0 m) with a primary echo level at least 39 dB below the signal. The room contained a mobile speaker assembly comprising a vertically mounted aluminium track of 1 m radius, which could be rotated through about 330°. A trolley on the track was able to move along its length, carrying a loudspeaker. Both the movement of the track and trolley were remotely controlled for changing azimuth and elevation angles, with an accuracy for speaker position of ±0·5°.
Small, calibrated microphones ( = 6·35 mm; Brüel & Kjaer Type 4135) were implanted into the left and right ear canals through a hole in the wall of the bony meatus close to the tympanic membrane. In order to protect the delicate microphone diaphragm the protection grid was not removed. A very short piece of heat-shrink plastic was also fitted to the end of the microphone and extended about 1 mm from the top of the protection grid. Any effect of the protection grid and plastic tubing on sound pressure measurement was calibrated. With microphones in position, the head of a fresh cadaver was mounted on a small platform at the centre of rotation of the mobile speaker assembly in the anechoic room. The orientations of the head and pinnae (Figs 1, 2) were adjusted to natural positions taken from photographs and single-frame analysis of ear and head movements (Coles & Hill, 1981).
Stimuli and recordings
Continuous pure tones (0·2·40 kHz) were generated from a Hewlett-Packard function generator (Model 3300A) amplified (Pioneer BP-320) and connected to a loudspeaker (Motorola piezohom KSN 1025A for frequency range 1·5-40kHz or Realistic 40-1909B for frequency range 0·2–3 kHz) via a Hatfield attenuator (Type 2125). A calibrated microphone ( in B & K Type 4135) was used to determine the free field sound pressure at the position of the wallaby head, which was maintained between 68–70 dB SPL re 20μPa. Free field measurements were taken with the microphone facing the speaker, without the head present, but at a position on the midline, in line with the open faces of the pinnae. The output voltage from the microphones implanted into each ear canal was determined either on a measuring amplifier (B & K Type 2510) in conjunction with a third octave filter set (B & K Type 1618), or a portable sound level meter (B & K Type 2203) using an octave filter set (B &K Type 1613).
The longitudinal axis was defined as the point 0° azimuth and 0° elevation (see Figs 2, 5) which projects from the centre of the head (where the free field was calibrated) to the surface of the imaginary sphere, at radius 94 cm, which is described by the speaker movements in two dimensions. The vertical plane at azimuth 0° normally contained the animal ‘s midline. Data points representing sound pressure level were determined by speaker position and plotted on a zenithal projection of a hemisphere. This projection is based on a 0° azimuth and 0° elevation centre point and extending for 90° in all directions (see Neuweiler, 1970 and also Fig. 5) with the poles represented vertically, at the north and south. Using this projection, distortion of area, and thus of solid angle, is within 5% except for positions closer than 30° to the poles. The platform mounting the head and either pinna could be repositioned in the horizontal plane to optimize data collection on the hemispheric projection. Polar plots were also collected for the horizontal plane and some elevational planes at various azimuths.
For frequencies above 2 kHz there was a region in space where the sound pressure developed at the tympanic membrane and measured by the implanted microphone was a maximum (see Fig. 2A). Such an area was defined in the present experiment within ±0·5 dB and can be represented as a single point in space accompanied by a 1 dB confidence limit in the form of an iso-intensity contour when plotted in two dimensions (Fig. 5). This zone is defined as the acoustic axis and is consistent with the definition of Middlebrooks & Pettigrew (1981) and Phillips et al. (1982) in the cat.
Acoustic pressure gain
The pressure gain of the external ear was plotted as a function of frequency by referencing the maximum sound pressure in the ear canal (i.e. at the position of the acoustic axis) to the free field. For each test frequency the speaker was repositioned as necessary. The results are shown in Fig. 3 as a gain curve for four ears producing the maximum on-axis value at each test frequency. For the most part, the sound pressure level at the tympanic membrane has positive gain, i.e. the sound pressure is amplified relative to the free field for frequencies between 1 and 30 kHz. From Fig. 3, it can be seen that there is a rapid increase in pressure gain above about 1· 5 kHz, rising to a peak of 25–30 dB between 4 and 5 kHz. Above 6 kHz the pressure gain starts to decline progressively to values below 10 dB for frequencies between 16 and 20 kHz. Additional decreases in pressure gain occur above 20 kHz resulting in attenuation of sound pressure relative to the free field between 30 and 40 kHz. Local sound diffraction inside the pinna and meatus may have contributed to the attenuation of sound at these high frequencies. In addition, it is possible that the equivalent acoustic volume of the probe microphone, although small, may become significant at high frequencies and thus affect the properties of a cavity such as the meatus. Since gain values became erratic and inconsistent above about 40 kHz detailed measurements were discontinued. There were no differences in acoustic pressure gain between left and right ears.
The effect of pinna removal on acoustic pressure gain is shown in Fig. 4A. The pinna was surgically removed until flush with the contour of the skin of the head. In the wallaby it is possible to remove almost the entire pinna flange (see Fig. 1C) but it is partially recessed in the muscles of the head and pinna itself. The most complete pinna removal that can be achieved leaves a small opening with an average diameter of about 08cm (see Table 1; Fig. 1C), which is very close to the entrance of the cartilaginous meatus. Fig. 4A shows the effect of pinna removal on pressure gain, and the difference between the two curves indicates that the amplifying effect of the pinna (Fig. 4B) increases progressively from 5 to 20dB in the frequency range 1·530 kHz. In the pinnaless condition (Fig. 4A), measurements at the tympanic membrane show a residual pressure gain curve which retains a distinct peak of about 15 dB in the 4–8 kHz region.
Since the length of the meatus is about l-6cm (Table 1; Fig. 1), the residual peak in pressure gain can be attributed to closed tube resonance where the sound wavelength is four times the length of the meatus (see Discussion). By removing the pinna as part of the external ear, it is possible to identify the contribution of the resonating meatus to the entire pressure gain although the pinna and meatus are normally acoustically coupled. In addition, the gain of the pinna as an acoustic transformer can be estimated (Fig. 4B) and compared to the expected amplification values for a simple acoustic horn. In Fig. 4B the expected excess pressure at the throat of a finite-length conical horn has been plotted as a function of frequency, based on the relevant physical dimensions of the pinna (Table 1; Fig. 1).
The possibility that the peak in the normal pressure gain curve seen in Fig. 4A was due to horn (pinna) resonance rather than meatus resonance was tested. This was done by making an artificial pinna from cardboard with the same shape as the normal pinna but approximately double the linear dimensions. The enlarged pinna was then placed over the normal pinna and was seen generally to increase the pressure by about 4–5 dB (Fig. 4A) as a result of increasing the surface area of the mouth of the pinna (see Discussion). Importantly, the peak in the gain curve is maintained around 5 kHz, which does not support the idea of a horn resonance at this frequency, which would otherwise have shifted to a lower frequency as a result of the increased path length of the enlarged pinna. Thus the normal peak in the amplification of sound pressure by the external ear results mainly from meatus resonance.
A typical frequency series of directionality plots is shown in Figs 5 and 6. The position of the acoustic axis in space can be determined from the peak sound pressure measured at the tympanic membrane and is either associated with a series of iso intensity contours (Fig. 5) or as a maximum from a polar plot for speaker movements in the horizontal plane (Fig. 6). In the wallaby, the position of the acoustic axis depends on the orientation of the pinna on the head. Under natural conditions each pinna can be rotated without distortion, through angles of up to 100° in the horizontal plane (Coles & Hill, 1981). For example in Figs 5 and 6 acoustic axes are about 45° from the midline when the ears are set to the ‘resting position’ that was used for data collection in this study (see Fig. 2). A physical re-positioning of the pinna, independent of head position, was found to move the acoustic axis and the entire directionality plot accordingly, with the forward or rearward limits normally determined by the muscular control of the pinna. It is useful to note that the acoustic axis is located approximately perpendicular to the open face of the pinna in the horizontal plane (for frequency effects see below). In the vertical plane the face of the pinna (in the living animal) is normally held in an inclined position, about 40° to the horizontal plane (see Figs 1, 2).
From the two-dimensional plots shown in Fig. 5, the 1 dB contour level surrounding the acoustic axis is almost circular for low frequencies up to about 6 kHz. As stimulus frequency increases to 20 kHz, the central, high sensitivity region of the directionality plot becomes elliptical and tilted towards the midline (see Fig. 5, at 10kHz). For frequencies above 20kHz there was a tendency for the axial region to become somewhat flattened in the vertical plane (Fig. 5, 20kHz). Above 30kHz, directionality became very difficult to determine reliably. This is likely to be due to the irregularities in the shape of the pinna, and the presence of the head producing increasingly complex sound paths at very high frequencies.
It was clear that as frequency increased the ear became more directional, which is indicated both by the closeness of the iso-intensity contours near the acoustic axis (Fig. 5) and the sharpness of the main lobe (Figs 2, 6). Changes in directionality were quantified by measuring the greatest difference in sensitivity (dBmax) between any two positions on the directionality plot for each test frequency. The results are shown in Fig. 7 for four ears, and indicate that for frequencies below 1·5 kHz no significant directionality exists from pressure transformation by the external ear. Directionality rises steeply above 4 kHz, ranging from 30 to 60 dB for frequencies between 5 and 20 kHz. Such high directionality is largely determined by the presence of nulls in the directivity patterns (Figs 2, 5, 6, see below) and also a combination of high positive pressure gain seen in the mid-frequency range (Fig. 3).
Another method of assessing directionality is to examine the angle covered by a given decrease in sensitivity from the acoustic axis. In physical systems, a 3 dB point (relative to the maximum response) is often used to compare directional devices (Beranek, 1954). Fig. 8 shows the estimated angular width or acceptance angle in degrees as a function of frequency, using the −3 dB point either side of the acoustic axis. Both the azimuth (Fig. 8A) and the elevation (Fig. 8B) acceptance angles have been calculated separately due to the asymmetry of the acoustic axis at high frequencies (see Fig. 5). From Fig. 8 it can be seen that the angular width of the main lobe of the directivity patterns, containing the acoustic axis, is inversely related to frequency in a systematic fashion. Non-directional directivity patterns have acceptance angles exceeding 180 ° and acceptance angles ranging from 120 ° to 180 ° are seen for weakly directional patterns up to 2 kHz, where the position of the (acoustic axis is difficult to define. As directionality starts to increase rapidly above 3 · 5 kHz (Fig. 7), the acceptance angle along the horizontal plane starts to decrease from 120 ° to about 20 ° for frequencies near 20 kHz. A similar effect is also seen in the vertical plane (Fig. 8B).
A significant feature of the directivity patterns generated by the wallaby external ear was the presence of regions of low pressure, forming minima. The formation of these approximate nulls became obvious as stimulus frequencies exceeded 4 kHz. In the lower frequency range, up to about 7 · 5 kHz, nulls were generated behind the pinna face up to 150 ° or so to the rear of the acoustic axis (Figs 2, 5).
The contour plotting method was unsuitable for examining the features of both the acoustic axis and rearward nulls due to their large angular separation and the use of a hemispherical projection. Polar plots were therefore best suited to showing the development of nulls, particularly at lower frequencies, providing the centre of the null was contained in the horizontal plane (see Figs 2, 6). As the frequency increased above 7 · 5 kHz a second null was seen to develop at the side of the main lobe containing the acoustic axis, i.e. within 90 °. This null normally occurred only on the leading side of the plane of the pinna face, towards the front of the head as shown in Figs 2, 5 and 6, and was particularly prominent near 10 kHz. At higher frequencies, multiple nulls were seen and the directivity patterns become very complex, including double sensitivity peaks above 20 kHz (see Fig. 5).
With the pinnae in the resting position (Fig. 2) it was possible to quantify the relationship between major null regions for the ear as a function of frequency. This was done by making measurements in a plane which contained both the null and the acoustic axis (see Figs 2, 5, 6). The results are summarized in Fig. 9 for 35 nulls determined at various test frequencies in seven ears. The rearward nulls are grouped between 160 ° and 90 ° from the axis in the frequency range 4 – 8kHz, whilst the sideward or leading edge nulls occur between 65 ° and 30 ° off-axis in the frequency range 8 – 20 kHz. The leading edge nulls tend to move progressively towards the acoustic axis as frequency increases, thus improving directionality in frontal space. The results shown in Fig. 9 represent a somewhat simplified view of null behaviour, since obviously several nulls can exist in a single directivity pattern and in different planes, particularly at high frequencies (see Figs 5, 6). Nevertheless, it is useful to compare the present data with the expected position of nulls based on diffraction by a circular aperture, in a similar fashion to that shown for the acceptance angle of the main lobe (Fig. 8).
Pinna removal, as described previously (see Fig. 4), in addition to causing decreases in pressure gain, resulted in a marked loss of directionality. For a directivity pattern at 6 kHz, removal of the pinna results in a considerable expansion of the iso-intensity contours emphasizing the decrease in directionality (Fig. 10A). In addition, the polar plot in Fig. 10B shows the loss in directionality and elimination of the null region. The presence of the pinna is therefore essential for the normal directivity patterns measured in the ear canal; however, the head will have an increased effect on sound diffraction at very high frequencies.
Frequency shift of acoustic axis
There was a tendency for the position of the acoustic axis to vary with frequency both in azimuth and elevation. For azimuth angles above 1 · 6 kHz (where an acoustic axis is first definable) the acoustic axis moves away from the midline from about 40 ° to a maximum of about 60 ° for frequencies above 10kHz (Fig. 11A). However, the effect is not completely regular and variation occurs between individual ears tested. In elevation (Fig. 1 IB) the acoustic axis moves gradually towards the horizontal plane. At low frequencies (below 3 kHz) the acoustic axis is at about 20 ° below the horizontal plane and for frequencies above 7 kHz the acoustic axis is maintained close to the horizonal plane. The results for azimuth position of the acoustic axis are dependent on the physical orientation of the pinna on the head, which for Fig. HA relate to the resting position (see Fig. 2). In the vertical plane, the pinna face has a natural angle of inclination (see Fig. 1C) which results in the elevation position for the acoustic axis being close to the horizontal plane for most frequencies. Overall, there was only a very weak relationship between the spatial location of the acoustic axis and stimulus frequency for the wallaby external ear.
The present study has demonstrated that the external ear of the wallaby provides frequency-dependent amplification and directionality for sound pressure reaching the eardrum. Moreover, an acoustic axis for the ear can be identified as a property of the pinna alone, which is consistent with observations in bats (Grinnell & Grinnell, 1965; Neuweiler, 1970) and the cat (Middlebrooks & Pettigrew, 1981; Phillips et al. 1982; Calford & Pettigrew, 1984). The wallaby is therefore typical of many mammals which rely on the pinna and its relative position on the head for directionality and pressure gain. This is clearly distinct from primates, which have immobile pinnae combined with an increased influence of head shadow (Harrison & Downey, 1970; Shaw, 1974).
Acoustic pressure gain
On-axis measurements show that sound pressure reaching the eardrum is amplified across the frequency range 1 – 30 kHz to varying degrees. The physical basis for the pressure gain of the external ear (Fig. 3) can be explained by two major components.
First, the removal of the pinna causes an overall decrease in gain or amplification eventually resulting in attenuation of high frequency sound above 10 kHz. The pressure gain curve for the pinna (Fig. 4B) shows a gradual increase producing maximum values of 15 – 20 dB above 10 kHz. If the pinna is considered to act as an acoustic transformer or horn, it is possible to calculate an expected amplification of sound pressure at the throat based on equations 1, 6 and 7 (see Appendix). A calculation based on comparing the area of the face of the pinna to the aperture at the junction of the pinna and meatus (the point at which the pinna was removed) results in an expected amplification of 16 dB (Table 1; equation 2) which, for an efficient horn, is the maximum pressure gain. Such an expected value is close to the experimentally observed values (Fig. 4B). However, the efficiency of an acoustic horn will depend on the size of the mouth and the length of the horn, relative to the wavelengths involved (Beranek, 1954). For a finite-length horn, such as the wallaby pinna, it can be considered an efficient sound collector when the wavelength is less than about 2 π x1, where x1 is the distance from the apex to the throat (Morse, 1948), which will occur for frequencies above about 3 · 5 kHz. The pressure gain curve of the wallaby pinna is reasonably close to the predicted curve for a conical horn and it is a useful first approximation considering the asymmetrical shape of the pinna. The gain curve for an equivalent exponential horn would rise too steeply compared to the experimental data. It should be noted that the expected gain curves shown in Fig. 4B are exact solutions for a finite-length conical horn and involve resonance. In principle, resonance is only eliminated from the calculations when a horn is long and the open end (mouth) is wide relative to the wavelength. In the case of the wallaby pinna, horn resonance should disappear when the ratio of the circumference of the mouth compared to the wavelength (ka) exceeds about 3, i.e. the diameter of the mouth starts to exceed the wavelength. In Fig. 4B, ka values for the wallaby pinna have been indicated and horn resonance may be expected below about 10 kHz (ka = 3). No significant resonance peaks can be seen at frequencies which would be multiples of the wavelength corresponding to twice the length of the pinna. The lack of such resonance is probably due to the oblique conical shape of the wallaby pinna, which may reduce the reflection coefficient at the open end. Furthermore, experimental enlargement of the pinna did not alter the peak in the normal gain curve for the external ear. A lower peak may have been expected if the pinna was resonating due to a slight increase in the length of the horn.
A second contributing factor to the acoustic gain seen in the external ear of the wallaby is revealed by the removal of the pinna. From Fig. 4A the remaining meatus section of the external ear retains a distinct peak in gain of 15 dB near 5 – 6 kHz. Referring to the anatomy of the wallaby ear (Fig. 1C), the pinna is removed at a point which is very close to where the meatus becomes tube-like. The residual peak in the gain curve after pinna removal strongly suggests that the flare of the external ear is sufficiently rapid to cause reflection at the junction of the pinna and meatus in the intact system (see Fig. 1C). The meatus has a length of about 1-6cm from the base of the pinna to the tympanic membrane with relatively little change in crosssectional area (Table 1).
If sound is reflected back into the meatus from the open end it is possible to expect tube resonance at a frequency where the wavelength is four times the length of the meatus, since the tympanic membrane represents a relatively rigid termination or closed end (Møller, 1983). Therefore the fundamental frequency for meatus resonance should occur at 5 · 4kHz, i.e. λ = 1 · 6 × 4cm, followed by possible additional resonance at 4/3 times the length of the meatus at 16 · 2 kHz, i.e. λ = 1 · 6 × 1 · 3 cm (odd harmonic series). The measured peaks in pressure gain for the normal and abbreviated (pinnaless) external ear both occur near 5 · 6 kHz, strongly suggesting meatus resonance (Fig. 4A). A second peak near 16-18 kHz may also be attributed to tube resonance, but is considerably smaller than the fundamental, because of reduced reflections from the open end, and perhaps also damping by the soft tissue of the ear canal, irregularities in shape, or even the small hairs lining the cavity. These factors would also contribute to the increasing attenuation of sound pressure in the external ear seen at high frequencies.
The present results compare favourably with the measurements of sound transformation in the cat by Wiener, Pfeiffer & Backus (1966), who found a maximum gain of 14 dB between the entrance to the meatus and the eardrum. The peak in gain, which occurred at 4 – 6 kHz was also predicted by modelling the meatus as a small rigid tube. Wiener et al. (1966) were able to establish a maximum pressure gain from (on-axis) free field measurements of 21 dB in the same frequency region, indicating a 7 dB increase in pressure gain due to the pinna. A more recent study of the cat external ear (Phillips et al. 1982) has claimed up to 28 dB amplification due to the pinna determined from cochlear microphonic measurements. In view of the similarity between the cat and wallaby pinna, it would seem that this value has been overestimated. The wallaby pinna produces up to 18 dB amplification based on direct acoustical pressure measurements in the intact and pinnaless condition.
The discrepancy between the two studies probably results from the extent to which the pinna and part of the meatus were removed in order to assess the contribution to pressure gain or amplification. In the study of Phillips et al. (1982), less than 5 – 8 mm of the meatus was left intact after pinna removal, compared to the normal meatus length of about 2 · 0 cm (Wiener et al. 1966). Consequently, the amplifying effect of meatus resonance on the sound pressure developed near the tympanic membrane would not be retained in the cochlear microphonic sensitivity functions studied by Phillips et al. (1982). By removing the pinna and most of the meatus, their results (Phillips et al. 1982, Fig. 6) are much closer to the sound pressure transformation by the intact external ear (free-field to eardrum) previously described in the cat by Wiener et al. (1966). Thus the apparent large ‘amplification by the pinna’ of about 25 – 30 dB around 3 · 5 kHz reported by Phillips et al. (1982) is more likely to result from meatus resonance of about 14 dB (Wiener et al. 1966) rather than pinna (horn) resonance as suggested by Calford and Pettigrew (1984). Similarly the present study of the wallaby external ear has also identified the contribution of meatus resonance to the pressure gain, and in addition the pressure gain resulting from the horn-like properties of the pinna.
Since there is amplification of sound pressure by the external ear in the wallaby, it may be expected to influence the hearing threshold curve. No data on absolute thresholds or frequency sensitivity exist for the wallaby. In other marsupials such as Trichosurus vulpecula (Gates & Aitkin, 1982) and Didelphis virginianus (Ravizza, Heffner & Masterton, 1969), neural and behavioural thresholds are most sensitive between 2 and 32 kHz. If similar auditory sensitivity exists for the wallaby, then the amplified sound pressure in the external ear is likely to have a significant effect on the frequency response. In the cat, there is evidence that pinnaless auditory thresholds can be up to 20 dB poorer than normal, particularly for frequencies above about 1 kHz (Flynn & Elliott, 1965). Such a result supports the present findings that the pinna acts as an acoustic transformer and would play a significant role in improving absolute sensitivity to sound.
There is now clear evidence that the pinna when placed on the top of the head can control the directional response of the external ear for many mammals. The directional responses of the two pinnae are in an essentially mirror-image relationship, and the direction of the acoustic axis of each response pattern simply shifts, to a first approximation, as the pinna is moved. In addition, normal directivity is abolished subsequent to pinna removal. These findings in the wallaby are supported by similar observations in the cat (Middlebrooks & Pettigrew, 1981; Phillips et al. 1982; Calford & Pettigrew, 1984).
The physical basis for the directionality of the pinna can be explained by the diffraction properties of its horn-like opening (Fig. 1), which was useful in scribing its action as an acoustic transformer (see above). From the present study, directionality increases with frequency, as is to be expected from standard wave theory. However, the wallaby pinna is not an ideal receiver due to its lack of complete symmetry and attachment to the head at one end. Nevertheless the pinna can be considered, to a first approximation, in terms of the diffraction properties of a circular aperture (Beranek, 1954). The pinna opening has a circumference of 16cm (Fig. 1; Table 1) and when treated as a circular aperture leads to an expected change in the acceptance angle of the main lobe as a function of frequency as shown in Fig. 8. Comparison between the directionality of the pinna and that expected for an equivalent circular aperture in an infinite baffle (−3dB down) has a very close correspondence for most of the frequency range tested. At very low frequencies, below 3 kHz, the pinna directionality behaves like a larger aperture, corresponding more closely with the long axis of the pinna face (taken as a diameter). Likewise at high frequencies, above 20 kHz, the pinna has directionality closer to that predicted from the short axis or width of the pinna.
At high frequencies, the wallaby pinna may be better represented by an elliptical opening since it has an elongated shape (Fig. 1; Table 1). This would help to explain the flattened appearence of the major lobe for directivity patterns at high frequencies (Fig. 5), since the diffraction patterns will become increasingly less directional in the plane orthogonal to the major axis of the opening (Beranek, 1954). Nevertheless, assuming diffraction by a circular aperture is a useful first approximation for understanding the directional properties of the wallaby pinna. Similar results have been obtained for the cat ‘s pinna by measuring the solid angle taken from the directional sensitivity of the cochlear microphonic (Phillips et al. 1982; Calford & Pettigrew, 1984).
The occurrence of nulls in the directivity patterns of the wallaby external ear compares favourably with the expected minima between the main lobe and the first diffraction ring (secondary lobe) of a circular opening of equivalent radius. Such nulls result from destructive interference by the sound waves entering the pinna face. In the case of a baffled opening with the same effective radius as the pinna face, the formation of diffraction nulls would be limited to frequencies above about 8 · 2 kHz. This is the limit for nulls occurring along the plane of the opening (90 ° off-axis) when 2a = 1 · 22 λ (see Results). The nulls in the wallaby ear directivity patterns which are less than 90 ° from the acoustic axis do not completely encircle the main lobe as would be expected in the ideal case (see Fig. 9). This may be due to the asymmetry of the pinna, particularly in the vertical plane, since the opening is formed from an oblique truncation of the pinna ‘s cone-like structure. The situation is also complicated by the presence of single rearward nulls below about 8 kHz which cannot occur for an opening in an infinite baffle. These nulls, which occur behind the plane of opening of the pinna, are probably comparable to the diffraction patterns which would result from an aperture at the end of a long pipe (Beranek, 1954) or possibly an oblique termination, considering the morphology of the pinna (see Fig. 1)
The directivity patterns for the wallaby ear are nearly non-directional below about 2 kHz, and similarly for the cat (Wiener et al. 1966; Middlebrooks & Pettigrew, 1981; Phillips et al. 1982; Calford & Pettigrew, 1984). A criterion for the onset of directionality is arbitrary, but the present data show a very sharp increase in directionality near 4 · 5 kHz (Fig. 7). This is close to the sound wavelengths which would produce significant directionality for a circular aperture using a 3 or 6dB criterion (see Fig. 7). Thus for the wallaby pinna and a circular aperture the relationship between the radius (or diameter) of the opening and the sound wave length is important for determining directionality. This is often conveniently expressed as the ratio of the circumference to the wavelength or ka value (Morse, 1948; Beranek, 1954). As shown in Fig. 7, an ideal receiver would be considered non-directional for ka < 0 · 5 and highly directional for ka > 3 (Beranek, 1954). On this basis, the wallaby external ear can be considered to be highly directional above 6 · kHz. The onset of directionality will occur at about ka> 1 · 25, i.e. the radius of the opening starts to exceed λ /5, which is about 2 · 7 kHz for the wallaby ear (Fletcher & Thwaites, 1979). Generally speaking, the average radius of a pinna opening can be used to determine the onset of directionality(ka = l · 25), and not the long axis or height of the pinna, as suggested by Phillips et al. (1982). For an elliptical type of opening, sound wavelengths equal to the long axis of the pinna face would be at the threshold of producing a high directionality response (ka = n or 3 · 14).
The wallaby external ear amplifies the sound pressure reaching the eardrum at frequencies where significant directionality starts to occur. A high degree of amplification is produced by the pinna acting as an acoustic transformer and by meatus resonance. A pressure gain is maintained for frequencies above the resonance peak of the meatus by the increasing efficiency of the horn-like pinna. Above 4 · 5 kHz, highly directional responses for the external ear are produced by a combination of sound pressure being amplified on-axis and severe attenuation from null points both behind and in front of the plane of opening of the pinna. From these findings, the design of the external ear, in particular the pinna, can be seen to have a strategic value in the detection and localization of sound. Each pinna can rotate independently through angles of up to 100 ° in the wallaby, and under normal circumstances the face is held at 40 ° to the horizontal plane (Coles & Hill, 1981). This results in the acoustic axis always being on the horizon for frequencies producing high gain and directionality (Fig. 11). In azimuth, there is some dependence on frequency for the acoustic axis position, probably due to the slight asymmetry of cross-section (see Fig. 1B), but for the most part the azimuthal orientation of the acoustic axis depends on the position of the pinna on the head. In the cat it has been suggested that the spatial location of the acoustic axis may be frequency dependent (Phillips et al. 1982; Calford & Pettigrew, 1984). Unfortunately, these results could be an artifact produced by distortion of the pinna following surgical procedures and unnatural positioning of the pinnae. The location of the acoustic axis of the pinna in the ghost bat (Guppy et al. 1984) and moustache bat (Fuzessery & Pollak, 1984) is frequency dependent in both azimuth and elevation. In addition, the bam owl ‘s facial ruff produces an acoustic axis which moves towards the midline sagittal plane with increasing frequency (Coles & Guppy, 1984).
In view of the directional properties of the external ear, in particular the acoustic axis, it would be a useful strategy for a wallaby to maximize its sensitivity to a sound by fixating a pinna on the source. The ability to locate a sound source containing frequencies above about 2 · 7 kHz would rely on the angular resolution or spatial gradient provided by the pinna ‘s directivity. Although angular resolution is low near the acoustic axis of the pinna (sensitivity is high) it is very high close to a null (sensitivity is low). Furthermore, the naturally inclined position of the pinna in the vertical plane ensures that the acoustic axis and diffraction nulls are located on the animal ‘s horizon. Monaurally, pinna movement could permit location of a sound source by providing a rising or falling angular gradient. Alternatively, a binaural comparison of sound pressure could retain absolute sensitivity (summation of outputs) and produce unambiguous directional cues (differential output) as has been suggested for mammals (for a review see Erulkar, 1972). From the present study, angular resolution can range up to 10dB/degree near nulls (see Figs 2, 5, 6) and, when contrasted neurally with a region of high sensitivity such as the acoustic axis, would yield binaural differences up to 60dB. Such interaural intensity differences would depend on the relative position of each pinna on the head and the bandwidth of the signal. In this sense, the prominent nulls located on the leading side of each pinna in the wallaby would be important in producing frontal spatial regions with high binaural contrast.
The present study, and those concerning mammals with mobile pinnae, raise the question of the neural coding of auditory space. There are several recent reports on the presence of a topographical representation of auditory space in the mammalian midbrain (Palmer & King, 1982; King & Palmer, 1983; Middlebrooks & Knudsen, 1984) or its absence (Wise, Irvine, Pettigrew & Calford, 1982; Wise & Irvine, 1983; Shimozawa, Sun & Jen, 1984). In future experiments, it will be important to establish for mammals with mobile ears, whether such maps are monaural or binaural and also the extent to which they are dependent on ear position. The mobility of the cat ‘s pinna has been overlooked by Harris, Blakemore & Donaghey (1981) when considering the neural coincidence between auditory and visual space. However, it is possible that an efferent copy of ear position as well as eye position may be incorporated into an auditory space map (Jay & Sparks, 1984).
The radiation impedance of the mouth R in equation 1 for a conical horn is a complicated expression involving Bessel functions. For convenience, values of R can be taken from the graphs found in Olson (1947).
We thank N.H. Fletcher for several helpful discussions on the theory of ears and also V. Rawlings for typing.