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Unformatted text preview: Physics 9B-C Final Exam Solutions Cole, UC Davis 20 points per problem/200 points total  (a) isochoric (b) shallow water (c) dimmer (d) same (e) decreases (f) ( A 1 + A 2 ) 2 (g) virtual (h) decrease (i) S 0. (j) opposite.   Method 1: Start by applying the derivatives and using the chain rule. Let u = kx - t: y x dy du u x k dy du = = so that 2 2 2 2 2 y x d du y x u x k d y du = = Similarly for dt, y t dy du u t dy du = = so that 2 2 2 2 2 y t d du y t u t d y du = = Plugging into the wave equation: 2 2 2 2 2 y t v y x = 2 2 2 2 2 2 d y du v d y du = dividing out the d 2 y / du 2 2- v 2 k 2 = 0 but v = /k 2- 2 = Method 2: The first order wave equation for waves moving to the right is y t v y x + = , and is easier to use. If y is a solution to this equation, it will also be a solution to the wave equation. Making the same substitution as above for u: y x dy du u x k dy du = = and y t dy du u t dy du = = Plugging into y t v y x + = + = dy du vk dy du . v = /k , so - = 0.  Match the boundary conditions. The free ends must have antinodes, and there must be a node at each support....
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- Fall '07