The Physics of Sonar and Echolocation: How Submarines, Bats, and Dolphins See With Sound

Seeing Without Light

Imagine navigating the world without eyes. No light, no colour, no visual shapes. Just darkness. And yet, you know exactly where every wall is, where every obstacle stands, where every moth is flying. You build a complete three-dimensional model of your surroundings, updated dozens of times per second, with a precision of millimetres.

Bats do this every night. So do dolphins, in the murky water where visibility drops to nothing. They send out sound waves, listen for echoes, and construct a sonic image of the world around them. It’s not a vague sense of direction — it’s genuine perception, as rich and detailed as our vision, built entirely from reflected sound.

Humans reinvented this trick during World War I, when German submarines were sinking Allied ships by the thousands and the ocean was as dark as any cave. The result — sonar — changed naval warfare. And the physics behind it, from acoustic reflection to Doppler shifts, connects a bat hunting a moth to a submarine hunting another submarine across the ocean floor.

The Physics: Sound Bounces

Sonar and echolocation rest on the same principle as radar: send out a wave, wait for the echo, measure the delay.

For sound, the distance calculation is:

d = v × t / 2

where v is the speed of sound and t is the round-trip time. In air, v ≈ 343 m/s. In seawater, v ≈ 1,500 m/s. The factor of 2 accounts for the round trip.

A bat emits a pulse and hears the echo from a moth 3 metres away after about 17.5 milliseconds (3 m × 2 / 343 m/s). A submarine pings and receives an echo from a target 1.5 km away after 2 seconds (1,500 m × 2 / 1,500 m/s).

Direction is determined differently in biology and technology. Bats use their two ears — the slight differences in arrival time and intensity between the left and right ear tell the bat which direction the echo came from. A time difference of just 10 microseconds (corresponding to about 3.4 mm of path length difference) is enough to resolve direction to within a few degrees. Sonar systems use arrays of hydrophones (underwater microphones) to achieve similar directional resolution through beamforming — processing the signals from multiple receivers to determine the direction of the echo.

Underwater Acoustics: Why the Ocean Is Sonic, Not Visual

Light doesn’t travel well in water. Even in the clearest ocean, visibility rarely exceeds 50–80 metres. At depth, it’s completely dark beyond about 1,000 metres. Electromagnetic waves at most frequencies are absorbed within metres.

Sound, on the other hand, thrives in water. Low-frequency sounds (10–100 Hz) can travel thousands of kilometres through the ocean with remarkably little attenuation. Whales communicate across entire ocean basins using calls below 20 Hz.

The speed of sound in seawater (about 1,500 m/s) depends on temperature, pressure, and salinity. In the deep ocean, these variables create a sound speed profile with a minimum at about 1,000 metres depth — the SOFAR (Sound Fixing and Ranging) channel. Sound waves near this depth are refracted back toward the minimum, trapped in a natural waveguide. Sounds in the SOFAR channel can propagate for astonishing distances — during World War II, the US Navy discovered that small explosive charges detonated in the SOFAR channel could be detected thousands of kilometres away, enabling a rescue system for downed pilots.

This acoustic transparency makes the ocean fundamentally different from land environments. Underwater, sound is the primary sense for both biology (whales, dolphins, many fish) and technology (sonar, acoustic communication, oceanographic research). The ocean is not a silent world — it’s a sonic one.

Bat Echolocation: 50 Million Years of R&D

Bats are the masters of echolocation. About 1,100 species of microbats use ultrasonic echolocation to navigate and hunt in complete darkness, having evolved this ability roughly 50 million years ago.

The basic system works like active sonar. A bat emits a brief, intense ultrasonic pulse — typically 20–200 kHz, lasting 1–20 milliseconds — and listens for the echo. The time delay gives distance. The Doppler shift gives relative velocity. The binaural difference gives direction. The spectral content of the echo gives information about the target’s size, shape, and surface texture.

But the sophistication goes far beyond simple ranging.

Frequency-modulated (FM) sweeps. Many insect-hunting bats emit chirps that sweep from high frequency to low frequency over a few milliseconds (e.g., 100 kHz dropping to 30 kHz). This broadband signal provides excellent range resolution — the bat can distinguish two objects separated by as little as 0.3 mm, because different frequencies in the chirp echo at slightly different times.

Constant-frequency (CF) calls. Horseshoe bats emit long (50–100 ms), steady-frequency calls and analyse the Doppler shift of the echo with extraordinary precision. They can detect the wingbeat of a moth from the frequency modulation imposed on the reflected signal — essentially hearing the flutter of insect wings from several metres away.

Terminal buzz. During the final approach to prey, bats dramatically increase their pulse rate — from about 10 pulses per second during search to over 200 per second in the last few hundred milliseconds. This gives them almost continuous echo updates as they close in, like increasing the frame rate of a video to slow motion.

Beam steering. Some bats shape and steer their emitted sound beam using complex nose structures (noseleaves) that act as acoustic lenses. By adjusting the shape of these structures, they can narrow the beam for focused search or widen it for broad surveillance.

The entire system — emission, echo detection, neural processing, motor response — operates in real time, allowing bats to capture insects on the wing in complete darkness. A bat’s brain processes echo information as quickly and automatically as our brains process visual information. It’s not “hearing” in the way we experience it — it’s a full sensory world, built from sound.

Dolphin Sonar: The Biological Scanner

Dolphins produce focused beams of broadband clicks — brief pulses containing frequencies from about 20 kHz to over 130 kHz — from the melon, a fatty structure in their forehead that acts as an acoustic lens. The lower jaw contains fat-filled channels that conduct returning echoes to the inner ear.

Dolphin echolocation is astonishing in its capabilities. Experiments have shown that dolphins can distinguish between objects differing in wall thickness by less than 1 millimetre, can detect a ping-pong-ball-sized object 100 metres away, and can “see” inside objects — the click frequencies penetrate flesh and reflect differently from bone, air-filled cavities, and soft tissue. In effect, a dolphin’s sonar gives it a crude ultrasound image, similar in principle to medical ultrasound.

This may explain why dolphins often seem curious about pregnant women in the water — the foetus, with its different acoustic properties (fluid-filled cavity, developing bones), is clearly “visible” to the dolphin’s sonar.

Military Sonar: The Silent Hunt

Modern naval sonar operates in two modes:

Active sonar transmits a sound pulse (the classic “ping”) and listens for echoes. It provides direct range and bearing to targets but reveals the transmitter’s location — in submarine warfare, this is often a fatal trade-off. Active sonar ranges can exceed 100 km at low frequencies, but absorption, scattering, and the complex acoustic environment of the ocean limit practical performance.

Passive sonar is silent — it only listens. Every submarine, ship, and marine creature produces sound: engine vibration, propeller cavitation (the creation and collapse of tiny bubbles in the low-pressure region behind spinning blades), hull resonance, even cooling pumps. Passive sonar systems use large arrays of hydrophones towed behind the detecting vessel (towed arrays, sometimes kilometres long) to detect and classify these sounds.

The art of submarine warfare is acoustic stealth: making your submarine as quiet as possible while detecting the faintest sounds from the enemy. Modern attack submarines coat their hulls in anechoic tiles (rubber layers that absorb incoming sonar pings), mount machinery on vibration-damping rafts, and use pump-jet propulsors instead of conventional propellers to minimise cavitation noise. The quietest modern submarines produce less noise than the ambient ocean background.

Medical Ultrasound: Sonar for the Body

Medical ultrasound applies sonar principles to the human body. A transducer pressed against the skin emits high-frequency sound pulses (typically 2–18 MHz) into tissue. The pulses reflect from boundaries between tissues with different acoustic properties (density and compressibility), and the echoes are processed into an image.

Different tissues reflect different amounts of sound. Bone reflects strongly (dense, stiff). Muscle, liver, and other soft tissues reflect moderate amounts. Fluid-filled structures (bladder, cysts) transmit sound through with minimal reflection and appear dark on the image. Air reflects almost everything (huge impedance mismatch), which is why ultrasound requires gel between the transducer and skin — to eliminate the air gap that would reflect the sound before it enters the body.

Doppler ultrasound measures blood flow velocity by detecting the frequency shift of echoes from moving red blood cells — exactly the same Doppler physics used by bats and submarines. Colour Doppler imaging maps blood flow direction and speed in real time, allowing cardiologists to visualise blood flowing through the heart and detect valve problems without any invasive procedure.

The great advantage of ultrasound over X-rays is safety: sound waves at diagnostic intensities cause no known biological damage. This is why ultrasound is the standard imaging method for monitoring pregnancy — you can image a developing foetus safely and repeatedly.

What Sonar Teaches Us

Sonar and echolocation illustrate a principle I keep returning to: when one method of sensing fails, physics provides alternatives. Light doesn’t work underwater or in the dark. But sound does — and the physics of acoustic reflection, Doppler shifts, and wave propagation enables an entire world of perception that’s invisible to the eye.

What I find most remarkable is the convergent evolution. Bats, dolphins, oilbirds, shrews, and some cave-dwelling humans have all independently evolved or learned echolocation. Nature discovered sonar at least five separate times. Engineers rediscovered it in 1914. The physics that makes it work — the reflection of waves from boundaries, the relationship between delay and distance — is the same in every case.

The mathematics doesn’t care whether the wave is a bat’s ultrasonic chirp, a submarine’s low-frequency ping, or a doctor’s ultrasound pulse. The physics of echoes is universal. Send a wave, listen for the return, and the delay tells you what’s out there.

Bats have been doing this for 50 million years. We’ve been doing it for about a hundred. But the physics has been there forever, waiting to be used by anyone — or anything — clever enough to listen to what bounces back.