Module 2: Hearing Spectral Atlas

Georg von Békésy (Experiments in Hearing, 1960; Nobel 1961) demonstrated the traveling wave on the basilar membrane: a pressure pulse injected at the oval window launches a wave that propagates from the stiff, narrow base toward the compliant, wide apex, growing in amplitude to a peak at a frequency-dependent location, then rapidly decaying. High frequencies peak at the base; low frequencies at the apex.

The Greenwood Function

Greenwood (1961, 1990) fitted the frequency-to-position map across species by a single exponential form:

Hair-Cell Mechanoelectrical Transduction

On the basilar membrane sit the hair cells: \(\sim 3500\) inner hair cells (IHCs) that transmit to the brain, and \(\sim 12000\) outer hair cells (OHCs) that motorise the cochlea. Each stereocilium is tipped by a mechanoelectrical transduction (MET) channel—identified as TMC1 and TMC2 (Pan et al., 2013; Kawashima et al., 2011)—gated by tension in the tip-link protein complex (cadherin-23 + protocadherin-15). The gating force is\(\sim 100\) pN, applied over a \(\sim 3\) nm stereocilium deflection, yielding \(\sim 10\) μs latency.

OHC Prestin Amplifier

Outer hair cells express prestin, a piezoelectric membrane motor (Zheng et al., 2000) that expands and contracts in phase with sound at audio frequencies. The cochlear amplifier raises sensitivity by \(\sim 50\) dB and sharpens frequency tuning by a factor of\(\sim 3\). Loss of prestin produces severe but not total deafness.

Most teleosts hear poorly—fish tissue is acoustically transparent to water so there is no pressure contrast on the inner-ear otoliths. The Otophysi (catfish, carp, minnows, zebrafish) solve this with Weberian ossicles: four bones derived from vertebrae that mechanically link the gas-filled swim bladder to the inner ear (Weber, 1820). The bladder acts as a pressure-to-displacement transducer and the ossicles transmit that displacement—effectively an analogue of the mammalian middle ear.

Zebrafish with Weberian ossicles hear up to \(\sim 4\) kHz, compared to \(\sim 500\) Hz in non-otophysans. This is another case of convergent engineering: mammalian malleus-incus-stapes and fish Weberian apparatus both solve the fluid-gas impedance mismatch, achieving\(\sim 30\text{--}40\) dB gain.

The Lateral Line System

Dijkgraaf (1963) characterised the lateral line, a trunk-spanning line of mechanosensory organs called neuromasts. Each neuromast is a cluster of hair cells whose stereocilia are embedded in a gelatinous cupula; water motion deflects the cupula and hence the hair bundle. Canal neuromasts (under the skin in ossified canals) respond to pressure gradients, while superficial neuromasts respond to flow velocity.

The lateral line is how schooling fish maintain constant spacing with neighbours without visual contact, and how cave fish (Astyanax mexicanus) image obstacles in total darkness using their own self-generated flow (hydrodynamic imaging; Windsor et al., 2010). It is an evolutionary precursor to hair-cell hearing: the inner ear is essentially a lateral-line organ moved inside the skull.

Mammalian Middle-Ear Impedance Matching

Air has acoustic impedance \(Z_{\text{air}} \approx 413\) Pa·s/m while water is \(Z_{\text{water}} \approx 1.5 \times 10^{6}\)Pa·s/m. Direct air-to-water sound transmission loses\(\sim 30\) dB by reflection. The mammalian middle ear recovers almost all of this loss via (i) the 17:1 area ratio of tympanic membrane to stapes footplate and (ii) the ~1.3:1 lever ratio of the malleus-incus-stapes chain. The ossicles act as a mechanical transformer (Fletcher, 1992).

Donald Griffin (1944) coined “echolocation” after showing that Myotis bats emit ultrasonic pulses and listen for returning echoes. Two call strategies dominate.

FM Bats (e.g., Myotis, Eptesicus)

Emit brief (2–10 ms) downward-sweeping frequency-modulated calls covering\(\sim 25\text{--}100\) kHz. The echo’s time-of-arrival encodes range; the echo’s spectral shape encodes target texture and size. Simmons (1979) measured range resolution in Eptesicus fuscus at\(\sim 10\) ns—equivalent to a 1.7 mm range difference—astonishingly precise.

CF-FM Bats (e.g., Rhinolophus, Pteronotus)

Emit long constant-frequency (CF) calls, 30–100 ms, followed by a brief FM terminal sweep. The CF portion allows Doppler-shift compensation: as the bat flies toward a target, it lowers its emission frequency so that the returning echo always lands at the species-specific auditory fovea(\(\sim 83\) kHz in R. ferrumequinum). The cochlea has disproportionately many hair cells tuned to this narrow band (Schuller, 1977). Moving insect wings modulate the echo at wing-beat frequencies, producing spectral sidebands that the bat reads as prey identity (Neuweiler, 2003).

Range via Pulse-Echo Latency

Dolphin Bioacoustics

Odontocete dolphins echolocate at \(\sim 100\) kHz using clicks of\(\sim 40\) μs duration. The call is focused by the melon, a fatty lens-shaped organ in the forehead whose sound speed varies spatially to collimate the beam (Cranford et al., 1996). Return echoes enter through thin “acoustic windows” in the lower jaw, where fatty tissue channels sound directly to the middle ear (Norris, 1964). The dolphin thus has a separate transmit and receive pathway, solving the “my own click overwhelms my ears” problem elegantly.

Oilbird: A Bird That Echolocates

Steatornis caripensis nests in caves in Venezuela and Trinidad. It emits audible (~2 kHz) clicks and uses the echoes to navigate the cave in total darkness (Konishi & Knudsen, 1979). Because 2 kHz has a wavelength of\(\sim 17\) cm, the oilbird can only detect objects larger than\(\sim 20\) cm—enough to avoid cave walls but not to find prey (it forages by smell). A cheaper, coarser analogue of bat echolocation.

African and Asian elephants communicate at frequencies below human hearing (< 20 Hz). Payne, Langbauer & Thomas (1986) recorded elephant infrasonic rumbles at 14–35 Hz travelling over 10 km through the air on calm evenings. The calls are produced by the 7-cm vocal folds vibrating at sub-audible fundamental frequencies, with substantial harmonic energy reaching into the audible band.

Seismic Transmission

O’Connell-Rodwell (2007) showed that elephant footsteps and low-frequency vocalisations travel through the ground as Rayleigh surface waves. Elephants can detect these seismic signals at distances up to 30 km, sensed through:

• Pacinian corpuscles in the soles of the feet, exquisitely sensitive to low-frequency vibration (\(\sim 10\)–300 Hz).
• Bone conduction up the leg to the inner ear, bypassing the airborne path.
• Somatosensory integration with airborne cues, creating a unified percept of distant conspecifics.

Why Low Frequency?

Atmospheric absorption scales approximately as \(f^2\), so the 10 km propagation range that elephants exploit would be impossible at, say, 100 Hz (where attenuation is \(\sim 0.1\) dB/km) let alone 1 kHz (several dB/km). Low-frequency signals also diffract around obstacles (trees, termite mounds) whose size is small compared to the wavelength (\(\lambda \approx 17\) m at 20 Hz). These are the same reasons why fin whales and blue whales use infrasonic calls for ocean-basin-scale communication.

The barn owl Tyto alba can strike a mouse in pitch darkness using sound alone. Payne (1971) demonstrated that the owl achieves angular resolution of\(\sim 1^\circ\) in both azimuth and elevation—the sharpest auditory localisation in any vertebrate.

ITD Encodes Azimuth

Jeffress (1948) proposed a neural delay-line coincidence detector: axons from the two ears converge on a map of neurons, each tuned to a specific ITD. Carr & Konishi (1990) physiologically confirmed this map in the owl’s nucleus laminaris. Each neuron fires maximally when the two inputs arrive simultaneously, i.e. when the external delay matches the internal axonal delay—implementing ITD measurement with microsecond precision despite millisecond-scale spikes.

ILD Encodes Elevation

Unique to owls (and to a lesser extent to some bats, pinnipeds), the two ears are asymmetrically placed: the right ear opening is tilted upward and the left ear downward. A sound from above produces a louder signal in the right ear; from below, in the left ear. The difference between the ears in dB—the interaural level difference (ILD)—thus directly encodes elevation (Knudsen & Konishi, 1979; Moiseff & Konishi, 1981).

ITD (azimuth) and ILD (elevation) are processed in parallel through separate brainstem pathways and converge only in the external nucleus of the inferior colliculus, where they form a two-dimensional auditory space map. This map is registered with the visual map in the optic tectum: an owl can swivel its head to the sound source as accurately as to a visual one.

Insects evolved hearing at least 19 independent times, with tympanic organs appearing on almost every body part: forelegs (crickets, katydids), abdomen (cicadas, locusts), thorax (moths), wings (lacewings), antennae (mosquitoes). This is the strongest known example of parallel evolution of a sensory modality.

Katydid Tympanic Hearing

Katydids (Tettigoniidae) have tibial tympana: a pair of oval drums on the foreleg tibia, backed by an acoustic spiracle and a chitinous trachea that acts as an impedance-matching horn. Udaykumar et al. (2012) showed the tracheal horn behaves as a travelling-wave biological cochlea: frequencies disperse along its length, giving tonotopic encoding by a mere\(\sim 40\) auditory receptors—a stunning convergent miniaturisation of the mammalian cochlea.

Moth Ears: Two-Cell Bat Detectors

Noctuid moths have the simplest known ear: a membrane on each side of the metathorax innervated by only two auditory neurons, A1 and A2, both most sensitive at 20–80 kHz—exactly the bat echolocation band (Roeder & Treat, 1961; Roeder, 1962).

• A1 has a lower threshold; it detects a distant bat and triggers a directed turn away.
• A2 has a higher threshold; it fires only for a nearby (imminent) bat and triggers evasive last-ditch flight: the moth closes its wings and drops passively from the sky.

The entire bat-moth arms race is thus encoded on only four neurons per moth. Some tiger moths (Arctiidae) have further evolved ultrasonic “clicking” organs that jam bat sonar (Corcoran et al., 2009) or advertise toxicity.

Cricket Phonotaxis

Female crickets orient to the 4–5 kHz calling song of males, a behaviour called phonotaxis. Huber (1975) isolated the tympanic organ to a single receptor cell bundle on each foreleg and showed that identified interneurons—ON1, AN1, AN2— implement a hard-wired pattern recogniser for the conspecific song. The central pattern generator is so stereotyped that it has become a textbook model for neuroethology. A female walking on a spherical treadmill will steer toward the louder of two calls with millisecond-scale accuracy.

Water is an excellent sound conductor: sound travels \(\sim 1500\)m/s and loses only \(\sim 0.001\) dB/m at 1 kHz. Marine mammals have exploited this with a remarkable diversity of hearing ranges.

Manatee Low-Frequency Hearing

The West Indian manatee Trichechus manatus has a hearing optimum at 1–2 kHz and poor high-frequency sensitivity (Gerstein et al., 1999). Boat noise, by contrast, concentrates energy below 500 Hz, creating an auditory mask that explains the epidemic of boat-strike deaths. Adding a high-frequency component to boat acoustic signatures has been proposed as a conservation measure (an “acoustic beacon”).

Dolphin Jaw Conduction

Odontocete dolphins have no external ear canal; sound reaches the inner ear through a thin-walled region of the lower jaw filled with acoustic fat. Cranford et al. (2008) used finite-element models to show that this pan bone conducts sound with almost zero reflection loss due to its carefully tuned fat composition (n-3 wax esters). The acoustic window is directional, explaining why dolphins point their heads at targets of interest.

Baleen Whale Infrasound

Blue whales (Balaenoptera musculus) and fin whales produce 10–40 Hz calls at source levels up to 189 dB re 1 μPa—the loudest biological sounds on Earth. These calls travel in the SOFAR channel (deep sound channel) at ~1 km depth and can be detected hundreds of km away. Anthropogenic shipping noise in the same band is now comparable, raising concerns about communication masking across whole ocean basins (Clark et al., 2009).

The audiogram plots threshold as a function of frequency. For humans (Fletcher & Munson, 1933), the threshold is lowest near 3–4 kHz (the resonance of the external ear canal) at approximately 0 dB SPL, and rises steeply above 10 kHz and below 100 Hz. Equal-loudness contours (ISO 226) trace how sound pressure level must change with frequency to preserve perceived loudness—a psychophysical footprint of the cochlea’s filter bank.

The Critical Band & Equivalent Rectangular Bandwidth

Fletcher (1940) discovered that masking of a tone by noise depends only on the noise energy within a narrow band around the tone—the critical band. Moore & Glasberg (1983) parameterised the band’s width:

Sharpness of Tuning (Q10 dB)

The filter sharpness \(Q_{10} = f_{\text{CF}}/\Delta f_{10\text{dB}}\)varies dramatically across species: humans have\(Q_{10} \approx 4\text{--}6\), cats\(\sim 5\text{--}10\), horseshoe bats\(> 200\) at the 83 kHz auditory fovea (the highest biological Q). Bats achieve this partly through passive cochlear design (stiff specialised basilar-membrane region) and partly through OHC-driven active amplification.

Species Audiogram Comparison

Mammalian hair cells are post-mitotic; once killed by acoustic trauma, ototoxic aminoglycosides, or simple ageing (presbycusis), they are not replaced. Birds, fish and amphibians, by contrast, regenerate hair cells throughout life via proliferation of supporting cells. Corwin & Cotanche (1988) first demonstrated chick basilar-papilla regeneration after noise exposure. The molecular basis—Atoh1-driven transdifferentiation of supporting cells—has become a central target for gene-therapeutic hearing restoration (Izumikawa et al., 2005).

Why Did Mammals Lose Regeneration?

One hypothesis: the cochlea’s organ of Corti is so mechanically precise that any regeneration must produce cells in exactly the right position with the right stereocilium orientation. The developmental cost of this precision may preclude easy replacement. A competing hypothesis: the energetic cost of indefinite cellular turnover was traded against longevity. Comparative genomics of Atoh1 enhancers across vertebrates (Bermingham-McDonogh & Reh, 2011) may eventually decide the question.

Noise-Induced Hearing Loss (NIHL)

Chronic exposure to sound \(> 85\) dB(A) causes cumulative damage. The OSHA 5 dB exchange rule: each 5 dB increase halves allowable exposure time. Kujawa & Liberman (2009) discovered “hidden hearing loss”: noise-induced synaptopathy between IHCs and auditory nerve fibres occurs even without threshold elevation, explaining “difficulty hearing in noise” in people with normal audiograms.

Swim-Bladder Resonance in Teleosts

A gas-filled cavity submerged in water has a predictable Helmholtz resonance. For a fish swim bladder of volume \(V\) connected to water via an effective opening of area \(A\) and neck length \(L\), the resonant frequency is:

The bladder thus acts as an acoustic transformer, concentrating far-field pressure onto the inner-ear otoliths. Fay & Popper (1999) catalogued the spectacular variation in bladder-to-ear coupling across teleosts: some species have anterior bladder extensions touching the skull (squirrelfish); some have entirely decoupled bladders; and the Otophysi use the Weberian ossicles described earlier.

Mosquito Johnston’s Organ

Mosquitoes do not have ears in the traditional sense; they hear with their Johnston’s organ, a mechanosensory structure in the second antennal segment. The male’s plumose antenna resonates at \(\sim 400\) Hz—exactly the wing-beat frequency of the conspecific female (Göpfert & Robert, 2001). The male phase-locks his own wing beat to a harmonic of the female’s, producing a duet that is essential for mating (Cator et al., 2009).

Drosophila uses the same organ for a broader repertoire: courtship song detection, wind detection, and gravity sensing. The molecular mechanotransducer is NompC (Walker et al., 2000), a TRP-family channel that is also the direct force-gated detector in bristle mechanoreceptors.

Cicada Tymbal Sound Production

Male cicadas of the family Cicadidae are the loudest animals per gram on Earth, producing songs at 100–120 dB SPL at 1 m. The mechanism is the tymbal, a ribbed cuticular membrane that buckles under muscle contraction, emitting a sharp click; a chain of clicks repeated at ~100 Hz produces the species-specific song. The abdomen is hollow and acts as a Helmholtz resonator amplifying the click spectrum (Young & Bennet-Clark, 1995). Females have auditory organs on the abdomen tuned to the male’s fundamental.

Once the cochlea has distributed frequency across place, the auditory nerve fibres encode sound through a combination of rate and phase locking. Up to\(\sim 5\) kHz in mammals, fibres fire in synchrony with the stimulus waveform. Above 5 kHz, phase locking fades and only rate and place codes remain.

The Volley Principle

Wever & Bray (1930) proposed that frequency information can be preserved beyond the single-fibre refractory period by having populations of fibres each firing every \(n\)-th cycle. The population-level interval histogram then reproduces the stimulus period. This is how the auditory system encodes pitch in the region where cochlear place becomes too coarse.

Cochlear Nucleus Cell Types

The cochlear nucleus houses a zoo of specialised cells: bushy cellspreserve precise timing for binaural processing; stellate cells encode spectral envelope; octopus cells sum brief transients and signal coincidences. Each targets a different downstream brainstem nucleus, distributing the auditory signal into parallel streams for localisation, speech-like pattern recognition, and reflexive response.

Pitch Perception & Missing Fundamental

The perceived pitch of a complex tone follows the frequency of the (possibly absent) fundamental harmonic. This missing-fundamental phenomenon (Schouten, 1940) reveals that pitch is a population computation over harmonics, not a simple place-code readout. Bendor & Wang (2005) found pitch-selective neurons in marmoset auditory cortex that fire to the virtual pitch regardless of which physical frequencies produced it.

Corollary Discharge & Self-Generated Sound

Echolocating bats and vocalising monkeys suppress auditory-cortical responses to their own vocalisations via a corollary-discharge signal from motor cortex (Eliades & Wang, 2008). This prevents the animal from being deafened by its own call, the same problem dolphins solve anatomically with jaw-conduction separation. The corollary-discharge solution is computational; the dolphin solution is mechanical.