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# 13_811ps1 - A i K θ A o z x A plane harmonic acoustic wave...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF OCEAN ENGINEERING 13.811 Advanced Structural Dynamics and Acoustics Second Half - Problem Set 1 Assigned: 5 Apr 2004 Due: 14 Apr 2004 Problem 1 Earl G. Williams Problem 2.3 Problem 2 Consider a 2-D water halfspace with sound speed c m/s and density ρ kg/m 3 and a lower halfspace that consists of a massless plate covering the entire z = 0 axis and resting on an elastic foundation. The elastic foundation has a static stiffness of K N/m 3 , such that ( ( x P ) = x w K ) Where: P(x): Pressure along plate surface w(x): Vertical Displacement along plate surface

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Unformatted text preview: A i K θ A o z x A plane harmonic acoustic wave of frequency ω at an angle θ is incident on the plate surface from the water halfspace as illustrated in the diagram above with pressure amplitude of A i . The reflected wave has amplitude of A o . 1 (a) Derive an expression for A o in terms of A i , θ , ω , c, K and ρ . (b) Investigate asymptotic behavior of the expression derived in (a) as the following approaches limits: i. Stiffness of the elastic foundation, K ii. Frequency of wave, ω Discuss the physical meaning of any asymptote that arises. 2...
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13_811ps1 - A i K θ A o z x A plane harmonic acoustic wave...

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