How fast is sound underwater?

About 1,500 m/s, more than four times faster than in air. It rises with temperature, salinity and depth (pressure). By Medwin's formula, surface seawater of salinity 35 gives 1,471 m/s at 5 °C, 1,507 m/s at 15 °C and 1,534 m/s at 25 °C, about 16 m/s faster at 1,000 m depth. These variations bend sound paths, forming channels that carry sound far.

How much does underwater sound weaken?

Through spreading and absorption. Spherical spreading from a point source loses 20 dB per tenfold distance. Absorption grows with frequency: by Thorp's formula 0.07 dB/km at 1 kHz, 1.2 dB/km at 10 kHz and 17 dB/km at 50 kHz. At 10 km, transmission loss is 81 dB at 1 kHz and 92 dB at 10 kHz.

How is sonar frequency chosen?

Low frequencies with little absorption reach far; high frequencies with short wavelengths resolve detail. 1 kHz has a 1.5 m wavelength, 50 kHz 3 cm. At 50 kHz absorption alone costs 17 dB per km, limiting range to a few kilometres, but it maps seabed features and fish schools finely. Long-range sonar such as submarine detection uses frequencies of a few kHz or less.

Underwater Acoustic Analysis

Category: Coupled Analysis – Acoustics | Revised 2026-10-01

Theory: sound speed and attenuation in the sea

Overview

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I've heard sound travels much farther underwater than in air. Why?

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Water quickly absorbs light and radio waves but hardly absorbs sound, especially at low frequency, so sound is how information travels far underwater. Sound weakens by spreading out and by absorption, and absorption grows roughly with frequency squared, so lower tones reach farther. Sea sound speed also varies with temperature, salinity and depth, and sound bends toward slower regions. Around 1,000 m depth lies a minimum-speed layer where trapped sound can travel thousands of kilometres. Underwater acoustic analysis includes this speed profile and absorption to calculate where and how strongly sound arrives.

Sound-speed formula (Medwin)

$$ c = 1449.2 + 4.6T - 0.055T^2 + 0.00029T^3 + (1.34 - 0.01T)(S - 35) + 0.016\,z $$

T is temperature (°C), S practical salinity and z depth (m).

Absorption and transmission loss (Thorp)

$$ \alpha = \frac{0.11f^2}{1 + f^2} + \frac{44f^2}{4100 + f^2} + 2.75\times10^{-4}f^2 + 0.003\ \ [\mathrm{dB/km},\ f\ \mathrm{in\ kHz}],\qquad TL = 20\log_{10}\frac{r}{1\,\mathrm{m}} + \alpha\,r $$

The first is Thorp's absorption coefficient (an approximation up to tens of kHz). Transmission loss sums spherical spreading and absorption; in shallow water spreading becomes cylindrical (10 dB per tenfold distance) beyond some range.

Coffee Break Trivia

The Titanic and sonar

The 1912 sinking of the Titanic spurred research on detecting icebergs by sound, and during the First World War Langevin built ultrasonic transducers with quartz piezoelectric elements. In the Second World War it emerged that sound-speed profiles bend sound, letting submarines hide in acoustic shadow zones, which advanced ocean sound-speed research. In the deep minimum-speed layer (the SOFAR channel), small explosions were heard thousands of kilometres away.

Worked examples

Example 1: sound speed by temperature and depth (salinity 35)

Temperature	Surface	1,000 m depth
5 ℃	1,470.9 m/s	1,486.9 m/s
15 ℃	1,506.8 m/s	1,522.8 m/s
25 ℃	1,534.4 m/s	1,550.4 m/s

Fresh water (salinity 0) at 15 °C gives 1,465.2 m/s. In the real ocean temperature falls with depth, so sound speed reaches a minimum at some depth.

Example 2: transmission loss by frequency and range (spherical spreading + absorption)

Frequency	Wavelength	Absorption	1 km	10 km	50 km
1 kHz	1.5 m	0.069 dB/km	60 dB	81 dB	97 dB
10 kHz	0.15 m	1.19 dB/km	61 dB	92 dB	153 dB
50 kHz	0.03 m	17.5 dB/km	77 dB	(out of practical range)	(out of practical range)

Treating spreading as cylindrical beyond 1 km in shallow water, loss at 10 km is 71 dB at 1 kHz and 82 dB at 10 kHz.

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Up to 1 km frequency matters little, but farther out high frequencies lose badly.

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Spreading loss is frequency-independent and grows with the logarithm of range, while absorption grows in proportion to range with a coefficient that varies greatly with frequency. Nearby, spreading dominates and frequency matters little; farther out absorption takes over. Absorption at 10 kHz is 1.2 dB at 1 km but nearly 60 dB at 50 km. High frequencies resolve small objects with short wavelengths and allow compact equipment, but don't reach far, so sonar frequency is chosen from target range and the size to resolve. In the real ocean, speed profiles bend sound into shadow zones and the surface and seabed reflect it, so propagation is computed with ray methods or parabolic equations.

Analysis workflow

Build a sound-speed profile from temperature, salinity and depth data.
Choose ray, normal-mode or parabolic-equation methods from frequency and range.
Include surface and seabed reflection, absorption and seabed geology.
Near transducers, solve structure–acoustic coupling (elements, domes) with FEM.
Calibrate seabed properties against measured transmission loss.

Coffee Break Trivia

“Sound that stopped arriving in summer”

An underwater communication link in a bay worked reliably over several kilometres in winter but dropped out at the same range in summer. Summer warming of surface water created a layer cooling with depth, so sound speed also fell with depth. Sound bent downward toward slower water, and the near-surface receiver fell into an acoustic shadow. Ray calculations reproduced the shadow, and moving the receiver deeper stabilised the link.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Constant sound speed	Shadow zones missed	Use the depth profile
Frequency-independent absorption	High-frequency range overestimated	Absorption per frequency
Spherical spreading in shallow water	Far-field loss overestimated	Cylindrical or modal
Ignoring seasons	Summer dropouts	Compute per season
Perfectly reflecting seabed	Loss underestimated	Model seabed geology

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