Diffraction of Impulse Sound Signals on Spheroidal Body, Put in Plane Waveguide

With the help o f the Fourier t ransform and characteristics of the stationary (continuos) sound signal are calculated the impulses, scattered by the ideal spheroid, placed in the waveguide. In the first part of the paper is presented the method of the imaginary sources and imaginary scatterers from the solution of the problem of the sound diffraction on the spheroidal body, put in the plane waveguide. In the second part of the paper are calculated the impulse signals with different filling, scattered by the the ideal soft spheroid, placed in the plane waveguide.


Introduction
At the basis of the method of the imaginary sources and imaginary scatterers is calculated the pulse sequence, got fro m the spheroidal scatterer, acco mmodated in the plane waveguide with the ideal boundary conditions. The impulse signals put the energy, therefore they are propagating with the group velocity (as and the energy), wh ich lie in the principles of the method of the imaginary sources and imaginary scatterers.

The Method of the Imaginary Sources and Imaginary Scatterers for the Spheroidal Body, Put in the Plane Waveguide
The scattering of sound by the bodies, placed in the waveguide, are investigated in the papers[1] - [9]. In thepaper [1] were calculated the spectral characteristics of the idial spheroid, placed in the sound channel, by the impulse irradiation; in the papers[8] and [9] with the help of the method of the imaginary sources and scatterers are found the vertical d istributions of the scattered sound field of the ideal soft spheroid, placed in the p lane waveguide, at the irradiation his by the harmonic signal. In the present paper are investigated and calculated the impulse signals with the different filling.
Let's put the ideal soft spheroid into the liquid layer with the thickness H and the constant sound velocity. At the upper boundary of the waveguide is fulfilled Dirichlet condition, at the lower boundary -Neimann condition. The axis of the rotation of the prolate spheroid will be orientated parallel to the boundaries of the waveguide and perpendicular to the plane of the figure 1.
The dimensions of the scatterer, distance from it to the boundaries and the thickness of the waveguide H are supposed to be such that we can do without taking into consideration the scattering of the second order of the waves reflected fro m the boundaries of waveguide are not taken into account in the further process of the diffraction.
The centre of the scatterer is fixed on axis X at the distance 200 m. fro m the bottom, at the horizontal distance L fro m it and on the axis X ( Figure 1) is placed the point-source 01 of the impulse sound signal. Using the method of the imag inary sources and scatterers[8. 9], are found the scattered impulse signal in the point 0. The sound impulse signals were the two appearance: with the harmonic and frequency-modulated filling. In the point 0 arrive the signals from everybody scatterers and everybody sources.    S πν is connected with ( ) i t Ψ by the return Fourier transform: The spectrum of the reflected signal where:

Calculation of the Pulse Sequence, Got from Spheroidal Scatterer
By the chosen orientation of the scatterer his angular characteristic ( , , ) D η ϕ ν is found oneself by "isotropic" in the correlation fro m the angle ϕ in the chosen range of the wave dimensions of the spheroid C ( h -the half -focal d istance of the spheroid, λ -the length of the sound wave in the liquid ) [1,8]. We map into the source 01 and the scatterer 01 relatively of the boundaries of the waveguide like this, in order that we had 9 the imaginary sources and 9 the imaginary scatterers. The formulas for the calculat ion of the angular characteristics of the spheroid ( , , ) D η ϕ ν are given in [11 -15, 1, 8]. For the chosen system of the sources and scatterers we will calculate the series of the reflected impulses in the point 0. The distance L between the source 01 and the scatterer 01 we accept equal 1000 m., H -400 m., the correlat ion of the half-axises of the spheroid is equally 10, but his half-focal distance is equally 0,2777 m. At Figure 4

Conclusions
In the paper is shown the effectiveness of the method of the imaginary sources and imaginary scatterers for the pulse sequence, got from spheroidal body and based at the use of the group velocity of the sound. The calculations of the scattered impulse signals with the different filling were done with the help of the Fourier transform and the characteristics of the scattering of the stationary (continuos) sound signal.
The applied interest is concluding in the detection of the underwater object in the sma ll sea.