lecture21 - Lecture 21- Marine Hydrodynamics Lecture 21 6.4...

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Unformatted text preview: Lecture 21- Marine Hydrodynamics Lecture 21 6.4 Superposition of Linear Plane Progressive Waves 1. Oblique Plane Waves v k k z z k x V p k v = ( z ) x x k , k (Looking up the y-axis from below the surface) Consider wave propagation at an angle to the x-axis x k = A cos( kx cos + kz sin t ) = A cos ( k x x + k z z t ) gA cosh k ( y + h ) = sin ( kx cos + kz sin t ) cosh kh = gk tanh kh ; k x = k cos , k z = k sin , k = k + k x z 1 2.20 - Marine Hydrodynamics, Spring 2005 2.20 2. Standing Waves + Same A, k, , no phase shift = A cos ( kx t ) + A cos ( kx t ) = 2 A cos kx cos t 2 gA cosh k ( y + h ) = cos kx sin t cosh kh 90 o at all times L , 3 , T T t = 5 3 T T T y x 2A t = , , L 2 2 t = 0, T, 2T, node amplitude antinode 4 4 4 n n = sin kx = 0 at x = 0 , = x x k 2 Therefore, x = 0. To obtain a standing wave, it is necessary to have perfect x reection at the wall at x = 0. A R Define the reection coecient as R ( 1). A I y A I = A R x A R R = = 1 A I 2 3. Oblique Standing Waves I = A cos ( kx cos + kz sin t ) R = A cos ( kx cos ( ) + kz sin ( ) t ) z I R R I x R = I Note: same A, R = 1....
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.20 taught by Professor Dickk.p.yue during the Spring '05 term at MIT.

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lecture21 - Lecture 21- Marine Hydrodynamics Lecture 21 6.4...

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