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Unformatted text preview: To exhibit this phenomenon, consider igure 1 where a harmonic plane wave ~u = u I i c L e i c L ( ~n ~x-c L t ) ~n ~n = sin ~ e 1 + cos ~ e 2 impinges on the free surface x 2 = 0 at an angle of incidence . 1. Derive the expression of the reFected wave in the form of a linear combi-nation of a longitudinal wave ~u L = u L i c L e i c L ( ~n L ~x-c L t ) ~n L propagating in the direction of ~n L and a transverse wave ~u = u T i c T e i c T ( ~n T ~x-c T t ) ~ e 3 ~n T propagating in the direction of ~n T , where ~n L = sin L ~ e 1-cos L ~ e 2 and ~n T = sin T ~ e 1-cos T ~ e 2 that is, nd L , 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 for = 1 4 . 3. Explain why the change in type of the incident wave is a three-dimensional eect. 4. Report any other interesting observation. 2...
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This note was uploaded on 06/17/2010 for the course AA 242B taught by Professor Charbelfarhat during the Spring '10 term at Stanford.
- Spring '10