tl2range

Compute range from underwater transmission loss

collapse all in page

Syntax

rng = tl2range(tl,freq,depth)

Description

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.

example

Examples

collapse all

Open Live Script

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

collapse all

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

Channel depth, specified as a positive scalar. The transition range from spherical to cylindrical spreading loss is one-half the channel depth. Units are in meters. The average depth of the ocean is 2000 m.

Example: 2000

Data Types: double

Output Arguments

collapse all

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

Data Types: double

Algorithms

  • The range2tl and tl2range functions model three sources of transmission loss in an underwater sound channel.

    • Absorption due to relaxation effects for boric acid and magnesium sulfate. Absorption is an important mechanism for frequency-based attenuation – the higher the frequency, the greater the absorption. Relaxation effects depend on seawater salinity (S). alkalinity (pH), and temperature (T). The model assumes constant seawater salinity of 35 ppt (parts per thousand), pH of 8, and water temperature of 10°C throughout the sound channel.

    • Wave damping and intensity loss caused by shear and bulk viscosity of pure water.

    • Geometric spreading loss. For ranges less than or equal to the transition range, the transmission loss is due to spherical spreading. For ranges greater than the transition range, the transmission loss is due to cylindrical spreading. Spherical spreading loss occurs when there are no boundaries (such as the water surface or sea floor) to reflect the acoustic energy. All of the acoustic energy spreads out isotropically in all directions from the source. The loss in intensity is proportional to the surface area of a sphere – the intensity decreases as the inverse square of the range for spherical spreading, TL = 20log(R), where R is the range. Alternatively, cylindrical spreading occurs when there are boundaries in the water column such as the water surface or bottom surface. The loss in intensity is proportional to the surface area of the cylinder – the intensity decreases as the inverse of the range TL = 10log(R), The transition range depends on the location of the source and the water depth. If the source is located halfway between the surface and bottom, it is reasonable to set the transition range to one-half the water columns depth. At this range, the surface of the sphere will just touch the bottom floor and the top surface. A good value for the transition range is 1000 m, since the average ocean depth is about 2000 m.

  • The transmission loss model used is valid for frequencies up to and including 2.0 MHz.

References

[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

expand all

Version History

Introduced in R2017b

See Also

| | |

Topics

External Websites