

Title of Thesis
DIFFRACTION OF ACOUSTIC WAVES 
Author(s)
Akhtar Hussain 
Institute/University/Department Details
Department of Mathematics/ QuaidiAzam University, Islamabad 
Session
1994 
Subject
Mathematics 
Number of Pages
105 
Keywords (Extracted from title, table of contents and abstract of thesis)
acoustic waves, water acoustics, plane harmonic acoustic wave, elastic half plane, cylindrical wave, spherical wave, wienerhopf techniques, saddle point method 
Abstract In this thesis, we have attempted a few problems in the theory of acoustic wave propagation which are relevant in under water acoustics. Firstly, we investigate the scattering of a plane harmonic acoustic wave from an absorbing half plane attached to an elastic half plane. The planes are subjected to heavy fluid loading limit in which the effect of the fluid inertia on the plate is dominant. Functional WienerHopf equation is obtained and the diffraction problem is solved using the Fourier transform and the saddle point method. Analytic expressions for the non attenuating subsonic surface wave travelling on the elastic plate and the scattered field are obtained. We extend this problem to consider cylindrical wave and spherical wave excitations. Finally, the transient fields (impulse response) in the cases of plane wave, line source and point source are studied and the corresponding time dependent surface waves and diffracted waves are obtained.






S. No. 
Chapter 
Title of the Chapters 
Page 
Size (KB) 





1 
0 
Contents 
0 
40.86 KB 





2 
1 
Mathematical Preliminaries 
10 
82.96 KB 

1.1 
The Wiener Hopf Techniques 
10 

1.2 
General Scheme Of Wiener Hopf Techniques 
14 

1.3 
Saddle Point Method 
17 

1.4 
Saddle Point Near A Pole 
21 





3 
2 
The Scattering Of An Acoustic Wave From The AbsorbingElastic Coupling Of Two Half Planes 
24 
107.29 KB 

2.1 
Formulation Of The Problem 
25 

2.2 
Solution Of The Problem 
29 

2.3 
Subsonic Surface Wave 
39 

2.4 
The Scattered Field 
40 





4 
3 
The Scattering Of An Acoustic Wave From AbsorbingElastic Coupling Of Two Half Planes Due To Line/Point Source 
42 
158.66 KB 

3.1 
Formulation Of The Line Source Problem 
43 

3.2 
Solution Of The Problem 
45 

3.3 
Point Source Problem 
51 

3.4 
Solution Of The Point Source Problem 
52 





5 
4 
Transient Response Of Absorbing Half Plane Coupled With An Elastic Half Plane 
56 
120.64 KB 

4.1 
Plane Wave Incidence 
57 

4.2 
Line Source Incidence 
61 

4.3 
Point Source Incidence 
63 





6 
5 
Appendix A 
67 
551.09 KB 

5.1 
Appendix B 
73 

5.2 
References 
83 

5.3 
Figures 
84 





