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quiz_soln

# quiz_soln - 13.811 Advanced Structural Dynamics and...

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13.811 Advanced Structural Dynamics and Acoustics Quiz - Acoustics April 21, 2004 Question 1. 1 ik z h p ( x, y ; 0) = e p ( k x , k y , h ) e ik x x e ik y y dk x dk y (4) 4 2 −� −� Solution Problem 1 Fourier transform of field at distance h p ( k x , k y ; h ) = p ( x, y, h ) e ik x x e ik y y dxdy (1) −� −� Backpropagate to radiator p ( k x , k y ; 0) = p ( k x , k y ; h ) e ik z h (2) where k z is the vertical wavenumber x k 2 k 2 + k 2 k 2 k 2 y , x y k 2 (3) k z = i k 2 + k 2 y k 2 , k 2 + k 2 > k 2 x x y Question 2. ik x 0 x θx e ik x 0 x e (5) p ( x, y, h ) = sin( ) = 2 c 2 i where k x 0 = k/ 2 = θ/ 2 c . Insert into eq. 1 and use EGW eqn. 1.5 4 2 p ( k x , k y ; h ) = [ ( k x k x 0 ) ( k x + k x 0 )] ( k y ) (6) 2 i Insert into Eq. (4) 1 [ e ik z 0 h e ik x 0 x e ik z 0 h e ik x 0 x ] p ( x, y ; 0) = 2 i θx = e ik z 0 h sin( ) (7) 2 c with k z 0 = k 2 k 2 = k 1 0 . 25 = k 3 / 2 x 0 1

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quiz_soln - 13.811 Advanced Structural Dynamics and...

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