Page 381 - The ROV Manual - A User Guide for Remotely Operated Vehicles 2nd edition

14.2 Sound propagation 373
FIGURE 14.2
Transmission loss due to geometrical spreading.
Let I and Io be the sound intensities in the distances r and ro. Then: Io=I5ðr=roÞ2
Expressed in decibels, the geometrical spread loss is:
TL1 5 10 log Io=I 5 20 log r=ro
Usually a reference point is taken 1 m in front of the source. Setting ro 5 1 m we get: TL1 5 20 log r
where r is measured in meters.
14.2.4.2 Absorption loss
When the sound propagates through the water, part of the energy is absorbed by the water and con- verted to heat. For each meter, a certain fraction of the energy is lost:
dI 5  AUIdr
where A is a loss factor. This formula is a differential equation with the solution:
IðrÞ 5 1⁄2IðroÞ=ðe  AroÞUeAr I(ro) is the intensity at the distance ro:
TL2 5 10 log IðroÞ=IðrÞ 5 αðr  roÞ
where α 5 10 A log (e).
Expressed in decibels, the absorption loss is proportional to the distance traveled. For each meter traveled, a certain number of decibels is lost.
If ro is the reference distance 1 m, and if the range r is much larger than 1 m, the absorption loss will approximately be:
TL2 5 αr
where α is named the absorption coefficient. Figure 14.3 shows absorption loss coefficient as a function of frequency. The value of α depends strongly on the frequency. It also depends on salin- ity, temperature, and pressure.
ro
r