IJCRR - 7(14), July, 2015
Pages: 54-56
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SOLUTION OF 3-DIMENSIONAL WAVE EQUATION BY METHOD OF SEPARATION OF VARIABLES
Author: Rajan Singh, Mukesh Chandra, B.K. Singh
Category: Healthcare
Abstract:We study solutions of the 3-Dimensional wave equation with boundary Conditions on Cartesian co-ordinates, and we also study the analogous problem on a certain axis. This gives an alternative method of obtaining solutions of a corresponding problem in 3-Dimensional wave equation further, In this paper, we find the solution of 3-D wave equation .Three dimensional wave occur in earth quake, tsunami and many physical states. In this paper we discussed the 3-D wave equation in XYZ axis and using partial differential equation.
Keywords: 3-D wave equation, Partial differential Equation, Fourier series.
Full Text:
INTRODUCTION
Solutions of the wave equation with boundary conditions have many practical applications in engineering and physics. The paradigm of such textbook problems is that describing vibrations of a circular membrane (the shape of a drum) requiring solutions of the wave equation in a 3- dimensional. These solutions must vanish on the rectangular boundary of the membrane [8]. A theoretical application of much current interest, requiring such solutions, is the computation of sound energies for spherical boundary conditions. We show here that it is just as easy to set up such problems in a certain co-ordinate plane [3]
RESEARCH METHODOLOGY
The following Research Methodology is adopted for the proposed Research paper: • Identification of the problem
• Collection and study of related literature
• Mathematical formulation of the problem
• Analysis and numerical solution of the mathematical model
• Interpretation of results
• Conclusion
Mathematical formulation of the problem
The physical setting for our problem is as follows. We consider the three dimensional wave equations with the normal axis. Three dimensional wave equation is
CONCLUSION
In this paper, for a general solution of three dimensional of wave equations is fond and with the help of this solution, we have to find varies kind of solution wave equations for example radio waves, telephonic wave etc.
ACKNOWLEDGEMENT
Authors acknowledge the immense help received from the scholars whose articles are cited and included in the manuscript. The authors are also grateful to authors / editors / publishers of all those articles, journals and books from where the literature for this article has been reviewed and discussed. Authors are grateful to IJCRR editorial board members and reviewers for their useful comments that lead the improvement of the manuscript.
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