Measurements of the width of the dynamic backscatter cone show that its inverse square grows approximately linearly with time t as predicted by scattering theory: D t, with D the scattering coefficient of sound (Fig. 5). However, this growth is very slow. It allows us to estimate the energy transport velocity V_E = 3D/ ℓ* ≈ 35 m/s, which is much slower than the speed of sound in water (1500 m/s). Despite the fact that the energy seems to be transported mostly by pressure waves (longitudinal waves) which are the only ones that exist in water, V_E is closer to the speed of shear waves (transverse waves) in fish flesh ( 10 m/s). The explanation of this phenomenon lies necessarily in the complex structure of a fish as a sound diffuser. The calculation of this velocity is the objective of this task. To perform this calculation, we will use the theoretical approaches developed previously for resonant scatterers (atoms, Mie spheres) as well as numerical simulations taking into account all the complexity of the problem: swim bladder, flesh and skeleton of the fish. An understanding of the physical reasons behind the low value of V_E as well as its prediction as a function of fish size, weight and age will be the main outcome of this task.

Figure 5. The inverse square of the backscatter cone width for two fish schools of different densities. The lines show the theoretical predictions.