Mathematical model of echolocation of fish-catching bats

The ability of bats to prey on the insects and catch fish on the wing by means of echolocation is remarkable, since the acoustic power transmission through air–water interface is very small. A mathematical model describing the way in which a bat can detect fish under the water surface is suggested in this article. The problem of scattering of the spherical acoustical wave from the water with the spherical air inclusion under the surface is considered and solved numerically. The frequency dependence on the backscattered pressure shows significant attenuation of the signal at some frequencies. This offers an explanation of the surprising efficiency of the acoustic acuity enjoyed by these animals.

► The model of echolocation of fish-catching bats is suggested.
► The scattering of acoustical wave on the air inclusion in water is considered.
► The frequency dependence of backscattered pressure is obtained numerically.
► The remarkable efficiency of echolocation acuity of bats is explained.