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Unformatted text preview: To exhibit this phenomenon, consider Â²igure 1 where a harmonic plane wave ~u = u I iÏ‰ c L e i Ï‰ c L ( ~n Â· ~xc L t ) ~n ~n = sin Î±~ e 1 + cos Î±~ e 2 impinges on the free surface x 2 = 0 at an angle of incidence Î± . 1. Derive the expression of the reFected wave in the form of a linear combination of a longitudinal wave ~u L = u L iÏ‰ c L e i Ï‰ c L ( ~n L Â· ~xc L t ) ~n L propagating in the direction of ~n L and a transverse wave ~u = u T iÏ‰ c T e i Ï‰ c T ( ~n T Â· ~xc T t ) ~ e 3 âˆ§ ~n T propagating in the direction of ~n T , where ~n L = sin Î± L ~ e 1cos Î± L ~ e 2 and ~n T = sin Î± T ~ e 1cos Î± T ~ e 2 â€” that is, Â³nd Î± L , Î± T , u L and u T as functions of the given data. 1 Figure 1: Interface and incident wave. 2. Plot u L u I and u T u I as functions of Î± for Î½ = 1 4 . 3. Explain why the change in type of the incident wave is a threedimensional eÂ±ect. 4. Report any other interesting observation. 2...
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 Spring '10
 CHARBELFARHAT
 Transverse wave, symmetric strain tensor

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