mt1soln_05

mt1soln_05 - Physics 9B-C Midterm 1 Solutions Cole 20...

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Physics 9B-C Midterm 1 Solutions Cole 20 points per problem UC Davis [1] a) upright, b) deep water, c) 0, d) antinodes, e) faster, f) dimmer, g) the same, h) dimmer, i) kinetic energy, j) antinodes. [2] Method 1: Start by applying the derivatives and using the chain rule. Let 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, ω 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 0 y t v y x = 2 2 2 2 2 2 0 dy du v du = dividing out the d 2 y / du 2 õ 2 - v 2 k 2 = 0 but v = ∑/k õ 2 - 2 = 0 Method 2: The first order wave equation for waves moving to the right is y t v y x += 0 , 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 0 õ dy du vk dy du 0 . v = , so - = 0.
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mt1soln_05 - Physics 9B-C Midterm 1 Solutions Cole 20...

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