AG = 20 dB

The transmission loss TL includes both sound spreading loss and attenuation. Sound spreading loss assuming spherical spreading for a range R of 10,000 m is:Spreading loss (dB) = 20 log R = 20 log (10,000) = 80 dB

The attenuation due to sound absorption calculated using the absorption coefficient α (alpha) of about 0.5 dB/km at a frequency of 8,000 Hz is:Attenuation (dB) = αR = (0.5 dB/km x 10 km) = 5 dB

The total transmission loss is then:TL = 80 + 5 = 85 dB

Measured target strengths TS for a submarine, as measured broadside to the submarine, vary widely, but a typical number is:TS = 25 dB

The noise level for a search sonar mounted on a destroyer is typically dominated by noise generated by water flowing past the ship and noise generated by the ship itself, which together are called self-noise. For a destroyer traveling at 15 knots, a typical self-noise level in a 1 Hertz wide frequency band at 8,000 Hz might be:NL = 63 dB re 1 μPa/√Hz

A typical sonar receives signals over frequency bands greater than 1 Hertz wide. The frequency band over which the receiver operates is called the bandwidth BW, given in Hertz. The total noise is:NLtotal (dB re 1 µPa) = NL + 10 log BW

Shorter sonar pulses have broader bandwidths, which means that the receiver bandwidth must be greater. The relationship between the sonar pulse length and receiver bandwidth is roughly:BW (Hz) = 1 / T, where T is the sonar pulse length in seconds.