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Sensors & detection
Sonar transmission loss
Loss of sound over range, from spherical spreading plus absorption in the water.
- Ref
- SEN-07
- Rev
- v1
- Field
- Sensors & detection
- Result
- TL [dB]
r is the one-way range in metres and α the absorption coefficient of the water in dB per kilometre, which rises steeply with frequency. TL has two parts: 20 log₁₀ r for spherical spreading of the sound over a growing area, and αr/1000 for absorption along the path. The result is in decibels relative to 1 m.
Loss of sound over range, from spherical spreading plus absorption in the water. Absorption rises with frequency.
Calculator
- Spreading loss 20 log₁₀ r66.02 dB
- Absorption loss αr0.2 dB
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 2 km spreading costs 66 dB and absorption only 0.2 dB (at 0.1 dB/km, typical of a few kilohertz). Spreading dominates at short range and low frequency.
- At high frequencies absorption takes over: at 100 kHz α is tens of dB per kilometre, which limits high-frequency sonar to short range but gives it fine resolution.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (dB) | Local step | Change in result |
|---|---|---|---|---|---|---|
| r Range | 10 to 1,000,000 m | 20 | 220 | 200 | +10% | +0.848 dB |
| α Absorption coefficient | 0.001 to 100 dB/km | 66.02 | 266 | 200 | +10% | +0.02 dB |
Sweep of Range
| Range (m) | Transmission loss (dB) |
|---|---|
| 10 | 20 |
| 42.17 | 32.5 |
| 177.8 | 45.02 |
| 749.9 | 57.57 |
| 3,162 | 70.32 |
| 13,340 | 83.83 |
| 56,230 | 100.6 |
| 237,100 | 131.2 |
| 1,000,000 | 220 |
Sweep one variable
Variables and how each one contributes
Transmission loss
What the equation gives you. Everything else feeds it.
Range
The one-way range from the source, in m. Logarithmic through spreading: doubling the range adds 6 dB. At the default a 10 % rise in r adds about 0.8 dB, plus a little for absorption.
Absorption coefficient
The absorption coefficient of seawater, in dB/km. Directly proportional in the absorption term only: raising α tenfold turns 0.2 dB into 2 dB at 2 km, but at 100 kHz α is tens of dB per km and then dominates.
Worked example with the values above
- Spreading: 20 log₁₀(2,000) = 66.02 dB.
- Absorption: α r = 0.1 × 2 km = 0.2 dB.
- TL = 66.02 + 0.2 = 66.22 dB.
Assumptions and limits
- Spherical spreading in deep, uniform water with a constant α.
- A straight path with no refraction, surface or bottom reflection.
Common mistakes
- Using α in dB/m when the value is in dB/km.
- Using spherical spreading in shallow water, where sound is trapped and spreads cylindrically (10 log₁₀ r).
Statistics and uncertainty
Spreading is the dominant term at low frequency, and in dB the error from range is small (10 % in r gives 0.8 dB). Absorption coefficients depend on temperature, salinity and depth and can be uncertain by 20 % or more, which matters only when αr is large. The biggest error is the propagation model itself, since real paths are bent by layers.
Where it is used
- Predicting how far a sonar signal carries.
- The transmission-loss term of the sonar equation.
Maths you need
- Decibels: 20 log₁₀ for amplitude-type ratios
- Absorption: a loss in dB per kilometre