Diffraction of sound in a moving fluid

Abstract

The purpose of this thesis is to discuss some problems of diffraction of sound waves by half plane, slit and strip, satisfying absorbing boundary conditions. The mathematical route to these problems consists of Wiener- Hopf technique, integral transforms, modified method of steepest descent etc. The diffraction of a cylind rical and spherical acoustic wave from a slit in a moving fluid using Myres' co ndit ions [133] is investigated in chapters three (3) and four (4), respectively. The solutions of these problems provided the corrective terms which were not present in the previous work on t his topic. The mathematical results obtained were well supported by the graphical discussion showing how the absorbing parameter and Mach number affect the amplitude of the velocity potential. Point source consideration is important because it is regarded as a fundamental radiating device and the solution of the point source problem is ca lled the fundamental solution of the given differential equation. The introduction of point source changes the incident field and the method of sol ution requires a carefu l analysis in calculating the diffracted field. The point sources are regarded as better su bstitutes for real sources than line sources or plane waves. The mathematical significance of the problem of point source is that it will introduce another variable. The difficulty, that arises in t he solution of the integral occurs in the inverse transform. These integrals are normally difficult to handle because of the presence of the branch points and are only amenable to solution using asymptotic approximations. Transient nature of the field is an important area in the theory of acoustic diffraction and provides a more complete picture of the wave phenomenon. In chapter five, the problem of diffraction due to an impulse line source by an absorbing half plane, satisfying Myers' impedance condition in the presence of a subsonic flow has been discussed. The problem of acoustic diffraction by an absorbing half plane in a moving fluid using Myers' condition was discussed by Ahmad [46]. He considered the diffraction of sound waves by a semi-infinite absorbing half plane, when the whole system was in a moving fluid. In [46], the time dependence was considered to be harmonic in nature and was suppressed throughout the ana lysis. While, in t his chapter, the time dependence has been taken into account throughout. The tempora l Fourier transform has been applied to obtain the transform function in the transformed plane using the Wiener-Hopf technique [13] and t he method of modified stationary phase [12]. The timedependence of field is introduced by a delta function with temporal and spatial Fourier transform. II) line with the solution for diffracted field, asymptotic solutions are sought for spatial integrals in far-field approximation. It has been shown that how the frequency of incident wave is effected by the amplitude of the diffracted field in different limiting positions. Also, the effects of different parameters on the field can be seen t hrough t he graphs. In chapter six, the diffraction of waves due to an impulsive line source by an absorbing half plane in a moving fluid using Myers' impedance condition in the presence of a subsonic fluid flow is studied and the effect of the Kutta-Joukowski condition has been examined by introducing the wake (trailing edge) attached to the half plane. The time dependence of the field requires a temporal Fourier transfor.m in addition to the spatial Fo urier tra nsform. Expressions for the tota l far field for the tra iling edge (wake present) situation are given. To the best of aut her's knowledge, no attempt has been made to ca lcu late t he diffracted field at an intermediate range, from an absorbing ha lf plane with a wake attached to it using Myres' condition. In chapter seven, the diffraction of waves, in the intermediate zone, due to a line source by an absorbing ha lf plane with a wake attached to it, in a moving fluid using Myres' condition is ana lyzed and the effects of t he Kutta-Joukowski condition has been examined by introducing the wake {trailing edge} attached to t he half plane. The solution for the leading edge situation ca n be obtained if t he wake, and consequently a Kutta-Joukowski edge condition, is ignored. In chapter eight, the diffraction of an acoustic wave from a finite absorbing barrier at an intermediate range by using Myers' impedance boundary cond itions have been investigated . In the ca lculations of the integrals [46) the terms of 1/{KRo}I\{1/ 2}are retained. If we consider intermediate range approximation in terms of source position we need to retain the next terms of 1/{KRo}I\{3/2 } in the expansion of the Hankel function. It is observed that the solution so obtained are much better than the solution obtained earlier.