![]() ![]() The density of the material of the shell is ρ 1, the Lame’s coefficients―λ and μ. In the quality of such scatterer, we are going to consider the terminal isotropic elastic cylindrical shell with the semi-spheres on its ends (see Figure 5). We are going to spread the method of the integral equations, used in for the ideal non-analytical scatterers, on the elastic shell of the non-analytical form. The surface S consists of S 2 and the surfaces S 1 и S 3 (see Figure 1).įor the calculation of the integrals (2), (3) and (5), (6) on surface we are choose the grid of the nodal points ( Figure 2, Figure 3).Īt Figure 4 is present for the chosen parameters by (the curve 1 corresponds to method of the T―matrixes, but the curve 2―to the method of the integral equations). The scattered pressure can find either with the help of the integral (2), (3) (for the Fredholm equation of the first kind), or with the help of the Equation (5), (6) (for the Fredholm equation of the second kind). The scattered pressure in the point we are express through the function Ф: With the help Ψ we are find and the scattered pressure in the any point of the medium :įor the Neimann’s condition, we are bring the function ―the solution of the Fredholm equation of the second kind : The integral to the left of (4) must understand in the sense of the main meaning. The function we are find from the solution of the non-homogeneous Fredholm equation of the second kind : The non-analytical smooth scatterer in the form of the cylinder with the semispheres. In this thesis I m going to study at which rotational angle α the signal disappears when sending a sound signal pulse with frequency f = 100k H z and a normalized frequency μ = 25, and compare it with human listening.Figure 1. where a is radius of the circular transducer. This angle limitation depends on the normalized frequency μ = ka = 2πa/λ value. This has its limitations, and for some rotational angle on the transducer the sound wave is not possible to detect. Otherwise the sound signal is diffracted and travels along the sur- face of the transducer (with different sound velocity from as in water) until it has a "direct" path to the receiver. For circu- lar and spherical arrays, (just like the human head), the sound wave travels direct to the receiver as long as the elements has a "direct" path to the re- ceiver. Sound velocity in water is divided into four different regions and is temperature dependent. In sonar the distance to the sound source is calculated by the travel time and the sound velocity of the incoming sound wave. ![]() There are three types of sonar equations described in this thesis, the active sonar equation for noise background, the active sonar equation for reverberation background and the passive sonar equation. Sound propagation is affected by absorption, re- fraction, reflection and scattering. Sound is pressure perturbations that travels as a wave spreads spherically or cylindrically in the water by describing the decrease of the signal. Sonar technology was actively used under World War I and World War II, and had an increase of interest among the scientists after this period. Sonar means Sound Navigation and Ranging, and has its roots from as early as the beginning of World War I. The sound is diffracted by the human head if the dimension of the head is smaller compared to 2λ/3. Diffraction of sound by human head is described by the diffraction formula. Sound loc- alization is described by three dimensions: azimuth angle, elevation angle and distance or velocity detection for static or moving source. The space can be de- scribed by three planes: vertical-, horizontal- and median plane. With help of these three effects humans can sense where in the space the signal is coming from. ![]() AbstractHumans can localize a sound source with the help of three effects, Head Related Transfer Function (HRTF), Interaural Time Difference (ITD) and Interaural Level Difference (ILD). ![]()
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