finalsoln_05

# finalsoln_05 - Physics 9B-C Final Exam Solutions Cole UC...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 9B-C Final Exam Solutions Cole, UC Davis 20 points per problem/200 points total [1] (a) isochoric (b) shallow water (c) dimmer (d) same (e) decreases (f) ( A 1 + A 2 ) 2 (g) virtual (h) decrease (i) Î S ≥ 0. (j) opposite. [2] [2] 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, ∂ ∂ ∂ ∂ ω y t dy du u t dy du = = − so that ∂ ∂ ∂ ∂ ∂ ∂ ω 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 − = ω 2 2 2 2 2 2 d y du v d y du − = dividing out the d 2 y / du 2 õ ∑ 2- v 2 k 2 = 0 but v = ∑/k õ ∑ 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 ∂ ∂ ∂ ∂ ω y t dy du u t dy du = = − Plugging into ∂ ∂ ∂ ∂ y t v y x + = õ − + = ω dy du vk dy du . v = ∑/k , so ∑ - ∑ = 0. [3] Match the boundary conditions. The free ends must have antinodes, and there must be a node at each support....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

finalsoln_05 - Physics 9B-C Final Exam Solutions Cole UC...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online