PHY 9B - Physics 9B-C Midterm 1 Solutions Cole, UC Davis 20...

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Physics 9B-C Midterm 1 Solutions Cole, UC Davis 20 points per problem/120 points total. [1] a) both b) steel c) left d) | A 1 - A 2 | 2 e) both f) above g) dimmer h) converging i) virtual j) antinodes. [2] a) (8 pts) Plug the solution into the wave equation. First calculate the second derivatives: ! " y t A kx t = # # ( ) cos 2 2 2 y t A kx t = # # ( ) sin Also, 2 2 2 y x k A kx t = # # ( ) sin . Plug into the wave equation: -∑ 2 A sin( kx - ∑t) + u 2 k 2 A sin( kx - ∑t ) + å A sin( kx - ∑t ) = 0 Divide by the A sin and solve for ∑: ∑ = u k 2 2 + $ which is the dispersion relation. b) (4 pts) v p = k u k = + 2 2 c) (4 pts) v g = d dk d dk u k u k u k = + = ( ) + 2 2 1 2 2 2 2 2 õ v g = u k u k 2 2 2 + d) (4 pts) Write the phase velocity in terms of ¬ using k = (2π)/¬: v p = u 2 2 2 4 + % Thus, longer wavelengths will have a greater phase velocity. [3]
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This note was uploaded on 02/17/2009 for the course PHY na taught by Professor Richardscalettar during the Spring '09 term at UC Davis.

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PHY 9B - Physics 9B-C Midterm 1 Solutions Cole, UC Davis 20...

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