Module 3: Echolocation & Sonar

For most of the 20th century the laryngeal origin of dolphin clicks was assumed by analogy with human phonation. Careful anatomical and behavioral work from the 1990s onward (Cranford, Amundin, Norris) established that odontocete sound production occurs in the phonic lips (also called dorsal bursae or “monkey lips” — museau de singe, for the ape-face appearance of the structure in sperm whale dissections). These are paired elastic structures embedded in the upper nasal passages.

Driven air flow from the lungs causes the phonic lips to open and close at a rate set by their elastic properties. Each closure generates a pressure pulse: the “click” itself. For toothed whales other than sperm whales, clicks are broadband with peak frequency ~100–200 kHz and duration ~30–70 µs. Sperm whales produce long (~10 ms) multi-pulse clicks where the initial phonic-lip pulse reflects repeatedly off distal and frontal air sacs to form the famous “inter-pulse interval” signature used to estimate body length via the bent-horn model.

1.1 Source Level and Radiated Power

The source level (SL) is the on-axis sound pressure level at a nominal reference distance of 1 m. For a bottlenose dolphin, SL ≈ 220 dB re 1 μPa. For a sperm whale, SL reaches 230 dB re 1 μPa (broadside) or even 236 dB on-axis (Møhl et al. 2003). The radiated intensity is:

For SL = 230 dB, \(p = 10^{-6}\cdot 10^{11.5} = 3.16\times10^{5}\,\text{Pa}\)— over 3 atmospheres of peak acoustic pressure. Intensity:\(I = (3.16\times10^5)^2/(1025\cdot 1500) \approx 6.5\times10^4\,\text{W/m}^2\). Integrated over the ~5° beamwidth, the sperm whale radiates roughly 25 kW of peak acoustic power per click — more than a large pop-concert loudspeaker.

The melon — encountered already in Module 0 — occupies the forehead of toothed whales and functions as an acoustic lens. Its graded lipid composition produces a smoothly varying sound speed \(c(\mathbf{x})\) from ~1310 m/s at the center to ~1500 m/s at the edges, setting up a refractive-index profile that focuses sound from the phonic lips into a narrow forward beam.

2.1 Eikonal Ray Equation

In the high-frequency (ray optics) limit, sound propagation is governed by the eikonal equation:

The ray trajectory \(\mathbf{r}(s)\) satisfies:

With the center of the melon having the lowest sound speed, rays emitted from the phonic lips are bent toward the optical axis. The melon acts as a positive (converging) lens. If the composition is tuned carefully, the lens is nearly aplanatic: all rays from the phonic lips emerge parallel (a collimated beam) rather than diverging.

2.2 Sperm Whale Bent-Horn Model

The sperm whale's spermaceti organ complicates the picture. Sound is generated at the museau de singe at the front of the head and directed backward through the spermaceti organ (the low-density oil-filled component), bouncing off a frontal air sac and then forward through the junk (denser, segmented organ below spermaceti) out the front of the head. The multiple internal reflections both shape the temporal structure of the click (the characteristic multi-pulse form) and amplify the on-axis intensity. The inter-pulse interval (IPI) between the first and second pulses of a click is proportional to twice the spermaceti organ length:

Whaling records correlate spermaceti organ length with whole body length (~23%), so passively recording clicks allows acoustic “measurement” of sperm whales in the wild without capture.

Echolocation performance is captured by the passive sonar equation, borrowed directly from ASW (anti-submarine warfare) acoustics:

Terms: EL echo level at receiver (dB), SL source level (dB re 1 μPa @ 1 m), TL one-way transmission loss (dB), TStarget strength (dB). The factor of 2 on TL accounts for the round trip.

3.1 Transmission Loss

Transmission loss has two components: geometric spreading and absorption:

Seawater absorption is dominated by two relaxation processes (boric acid at ~1 kHz and magnesium sulfate at ~100 kHz) plus viscous bulk absorption at very high frequency. Typical values:

Thus high-frequency dolphin clicks are limited to ~100 m effective range (the absorption alone accounts for 4 dB at that distance), while low-frequency whale calls can propagate for thousands of kilometers. This constraint shapes the acoustic behavior of each species: dolphin sonar is short-range & high resolution; large-whale vocalizations are long-range & low resolution.

3.2 Target Strength

The target strength quantifies how much of the incident sound a target reflects back toward the source:

For fish with gas-filled swimbladders, TS at the swimbladder resonance frequency can exceed −25 dB; at other frequencies TS is dominated by flesh impedance contrast (low). Cephalopods (squid, octopus) lack gas inclusions and have tissue impedance nearly matched to seawater — they are acoustically “cryptic,” with TS often below −55 dB. Despite this, sperm whales subsist almost entirely on deep-sea squid, demonstrating extraordinary acoustic discrimination.

A foraging odontocete does not emit a continuous acoustic stream but rather discrete clicks separated by an inter-click interval (ICI). The ICI is constrained by the round-trip time to the most distant echo:

At \(d = 100\,\text{m}\), the round-trip time is \(2\cdot 100/1500 = 133\,\text{ms}\): the animal can emit ~7 clicks/s. As the whale approaches its prey, ICI shrinks proportionally. In the final stage of a capture, the toothed whale transitions from ordinary clicks to a very rapid sequence called the buzz phase, with ICIs of 2 ms or less (corresponding to distances of ~1.5 m). The buzz is an acoustic analog of the rapid fire-control burst a sonar would use on a closing target.

4.1 Discrimination Limits

Bottlenose dolphin psychophysical experiments (Au 1993, Branstetter et al. 2007) show remarkable discrimination:

• Distinguish solid vs hollow targets differing by 1-mm wall thickness at 5 m range
• Discriminate cylinders of the same size but differing materials (Al vs PVC vs steel) — apparently using material resonance signatures
• Classify targets through sediment, clay, or water-bottom clutter — target strength discrimination of ~1 dB
• Identify individual objects in dense fish schools

4.2 Signature Whistles

Beyond echolocation, dolphins produce tonal whistles in the 1–25 kHz band. The signature whistle, described by Caldwell & Caldwell (1965), is a frequency-modulated pattern unique to each individual — functionally an acoustic “name.” Mother dolphins appear to teach their calves signature whistles, and dolphins use each other's signature whistles to address specific individuals (King & Janik 2013). This is one of the clearest demonstrations of referential vocal learning outside humans.

The cetacean auditory system bears little resemblance to that of a terrestrial mammal. There is no pinna (external ear); the external auditory meatus is reduced to a tiny canal filled with wax. Sound reaches the inner ear via a novel pathway: entering through the lower jaw, propagating through a fat-filled channel along the mandible, and coupling into the middle ear bones. This “acoustic fat” has impedance closely matched to seawater, serving as an efficient sound conductor from the exterior into the acoustically isolated ear bones.

5.1 Tympano-Periotic Complex

The middle and inner ears of cetaceans sit in a bony capsule (the tympano-periotic complex) that is isolated from the rest of the skull by air-filled sinuses and a ligamentous suspension. This isolation is crucial for directional hearing: without it, sound arriving through the water-filled skull would reach both ears almost simultaneously, destroying the interaural time difference cues that mammals normally use for sound localization. By suspending each ear capsule in its own acoustic enclosure, cetaceans preserve binaural directional hearing at frequencies up to 150 kHz.

5.2 Ultrasonic Hearing Range

Audiograms for bottlenose dolphins show a hearing range from ~75 Hz to ~150 kHz, with peak sensitivity at 40–80 kHz. Humans hear up to ~20 kHz; dogs and cats reach ~50–60 kHz; only bats (to ~200 kHz) and toothed whales approach these upper limits. Low-frequency hearing is less developed; this limits cetacean sensitivity to many anthropogenic noise sources in the 100–1000 Hz shipping band.

5.3 Interaural Time and Intensity Differences

With the two ears separated by ~20 cm on a bottlenose dolphin, interaural time differences (ITD) for sounds arriving from the side are:

At 120 kHz (echo frequency), the period is 8 µs; ITD resolution finer than this has been demonstrated behaviorally, indicating that dolphins exploit phase differences at very fine temporal resolution, much as humans do at lower frequencies. Interaural intensity differences (IID) from head-shadow effects are also used; combined, these provide angular resolution of ~2°.

Bats (order Chiroptera) are the other major mammalian lineage that evolved biological sonar. Despite diverging from cetaceans roughly 85 Mya at the base of the Laurasiatheria, the two groups show extraordinary convergence in their echolocation systems:

• Both use high-frequency, short-duration broadband clicks or chirps
• Both exhibit “buzz phases” with shrinking inter-pulse intervals during prey capture
• Both have modified middle ear ossicles and isolated inner ear capsules
• Both possess specialized laryngeal (bats) or nasal (whales) structures for click production
• Both use target strength and spectral content to identify prey

Remarkably, molecular studies by Liu et al. (2010) demonstrated that the gene Prestin — encoding the motor protein driving outer hair cell motility that determines cochlear frequency selectivity — shows near-identical amino acid substitutions in bats and toothed whales. This is one of the clearest documented cases of molecular convergence in mammalian evolution: echolocation selected for the same biochemistry independently in two lineages separated by 85 Myr.