How Internally Coupled Ears Generate Temporal and Amplitude Cues for Sound Localization

In internally coupled ears, displacement of one eardrum creates pressure waves that propagate through air-filled passages in the skull and cause displacement of the opposing eardrum, and conversely. By modeling the membrane, passages, and propagating pressure waves, we show that internally coupled ears generate unique amplitude and temporal cues for sound localization. The magnitudes of both these cues are directionally dependent. The tympanic fundamental frequency segregates a low-frequency regime with constant time-difference magnification from a high-frequency domain with considerable amplitude magnification.

Figure 1

Because of the coupling of the eardrums through the internal cavity, an animal equipped with ICE perceives internal rather than interaural time and level differences. The cavity is modeled as a cylinder of volume $V_{\mathrm{cav}}$ and length $L$ (radius ${\mathrm{a}}_{\mathrm{cav}}=\sqrt{V_{\mathrm{cav}}/\pi L}$). The bold arrows indicate our direction conventions along the $x$ axis, and the smaller circles at either end indicate the eardrums with radius $a_{\mathrm{tymp}}\le a_{\mathrm{cav}}$.

Figure 2

Left: exact membrane boundary conditions. The velocity of air ($v_x$) equals that of the membrane (${\dot{u}}_{0/L}$). Right: piston approximation. The membrane is approximated by a circular piston moving with the membrane’s average velocity and with boundary conditions (12) applied to (2) and (3). The piston approximation refers to (2) and the boundary condition for the pressure $p$ in the three-dimensional cavity, not to the motion (5) of the eardrum itself.

Figure 3

Experimental and calculated $v_{\mathrm{dB}}$ for ipsi- ($\theta =90°$) and contralateral ($\theta =-90°$) stimuli for Gecko (top) and Varanus (bottom). The flaccid membrane of Varanus (with low $\alpha$) gives peaks at $f_0$ as well as at higher membrane resonances. As elsewhere, all membrane eigenfrequencies are indicated by vertical dashed lines; cf. Fig. 5. The first resonant peak (or trough) allows a straightforward determination of tympanic eigenfrequency $f_0$ in the alive animal. All experimental data presented were gathered by using laser Doppler vibrometry.

Figure 4

Frequency and direction dependence of the iTDs for Gecko (top) and Varanus (bottom). (a) For Gecko, the iTDs exhibit a plateau of $\mathrm{iTD}\approx 3\mathrm{ITD}$ up to about $f=f_0$ and sharply fall thereafter. As indicated, the plateau exists irrespectively of the direction $\theta$; cf. left column. The iTDs can thus be effective low-frequency cues. (b) For Varanus, the iTDs slowly increase up to $f_0$ and then decrease; the discontinuity is an artifact of $2\pi$. The young animal can therefore only exploit a restricted low-frequency range of iTDs up to, say, 200 Hz, nevertheless illustrating that the time expansion factor iTD/ITD can differ from 3 appreciably.

Figure 5

Calculated frequency and direction dependence of the iLDs for Gecko (top) and Varanus (bottom). (a) For Gecko, the iLDs peak close to $f=f_0$ and decrease slowly thereafter. They can therefore serve both as effective high-frequency hearing cues and as an efficient means of determining $f_0$ in alive animals. Clearly, the higher tympanic eigenmodes play no role. (b) For juvenile Varanus with small $\alpha$ and $f_0\approx 400\mathrm{Hz}$, we see corresponding peaks also at higher membrane eigenmodes.

Figure 6

Transition between the iTD and iLD frequency regime for directions $\theta \ne 0°$. At lower frequencies iTDs work better as directional cues, e.g., with $\mathrm{iTD}/\mathrm{ITD}\approx 3$ (blue plateau) for adult geckos, while at higher frequencies the iLD becomes pronounced, even though for most lizards the external $\mathrm{ILD}\approx 0$. The transition between the two kinds of cues is governed by the eardrum’s fundamental frequency $f_0$.