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Compute range from underwater transmission loss



rng = tl2range(tl,freq,depth) returns the range, rng, to the source of a sound wave with frequency freq from the transmission loss, tl. The channel depth is depth and the sound frequency is freq. The transmission loss is due to geometrical spreading and frequency-dependent absorption. This function is the inverse of range2tl function.


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Find the distance traveled by a sound wave with a transmission loss of 50 dB. The sonar operates at 2 kHz in a channel 200 m deep.

tl = 50.0;
freq = 2000.0;
depth = 200.0;
rng = tl2range(tl,freq,depth)
rng = 972.1666

Input Arguments

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Transmission loss from source to receiver, specified as a positive scalar. Units are in dB.

Data Types: double

Frequency of sound, specified as a positive scalar less than or equal to 2 MHz. Units are in Hz.

Example: 1e3

Data Types: double

Depth of sound channel, specified as a positive scalar. Units are in meters.

Example: 200

Data Types: double

Output Arguments

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Distance from source to receiver, returned as a positive scalar. Units are in meters.

Data Types: double


  • The transmission loss model assumes that seawater salinity is 35 ppt, pH is 8, and temperature is 10°C.

  • The transmission loss model is valid for frequencies less than or equal to 2.0 MHz.


[1] Ainslie M. A. and J.G. McColm. "A simplified formula for viscous and chemical absorption in sea water." Journal of the Acoustical Society of America, Vol. 103, Number 3, 1998, pp. 1671--1672.

[2] Urick, Robert J, Principles of Underwater Sound, 3rd ed. Peninsula Publishing, Los Altos, CA, 1983.

Extended Capabilities

Version History

Introduced in R2017b