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THE PROPAGATION PATH OF A WAVE IN A VARIABLE SPEED OF SOUND MEDIUM OBTAINED BY EMPLOYING FERMAT'S PRINCIPLE,
CALIFORNIA UNIV LOS ANGELES DEPT OF ENGINEERING
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Fermats Principle states that a wave will follow a path such that the time taken to move between two points is a minimum. According to this principle, the ray path of a sound wave in a variable speed of sound medium is derived using variational techniques. This leads to an integral which gives the horizontal position of the wave front explicitly as a function of the speed of sound variation with vertical distance. Several examples are worked out, including an explanation of the occurrence of sound channels and shadow zones. Further, it is shown that a hyperbolic cosine function closely approximates the actual velocity of sound as a function of depth. Using the hyperbolic cosine approximation, the integral is evaluated giving an explicit formula for a ray path. Author
APPROVED FOR PUBLIC RELEASE