Solutionshw4 - Solutions to Homework 4 Due October 21 st Chapter 16 Problem 40 Comparing 0.35sin 10 3 4 y t x π π π = with 29 29 sin sin y A kx

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Unformatted text preview: Solutions to Homework 4: Due October 21 st Chapter 16 Problem 40: Comparing 0.35sin 10 3 4 y t x π π π =- + with ( 29 ( 29 sin sin y A kx t A t kx ϖ φ ϖ φ π =- + =-- + we have 3 k m π = , 10 s ϖ π = , 0.35 m A = . Then 10 s 2 3.33 m s 2 3 m v f f k π λ ϖ λ π π π = = = = = . (a) The rate of energy transport is ( 29 ( 29 ( 29 2 2 2 2 3 1 1 75 10 kg m 10 s 0.35 m 3.33 m s 15.1 W 2 2 A v μϖ π- = = × = P . (b) The energy per cycle is ( 29 ( 29 ( 29 2 2 2 2 3 1 1 2 m 75 10 kg m 10 s 0.35 m 3.02 J 2 2 3 E T A λ π μϖ λ π π- = = = × = P . Problem 44: The linear wave equation is 2 2 2 2 2 1 y y x v t ∂ ∂ = ∂ ∂ If ( 29 b x vt y e- = then ( 29 b x vt y bve t- ∂ = - ∂ and ( 29 b x vt y be x- ∂ = ∂ ( 29 2 2 2 2 b x vt y b v e t- ∂ = ∂ and ( 29 2 2 2 b x vt y b e x- ∂ = ∂ Therefore, 2 2 2 2 2 y y v t x ∂ ∂ = ∂ ∂ , demonstrating that ( 29 b x vt e- is a solution Problem 48: Compare the given wave function ( 29 4.00sin4....
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This note was uploaded on 08/31/2010 for the course PHYSICS 7E taught by Professor Staff during the Fall '08 term at UC Irvine.

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Solutionshw4 - Solutions to Homework 4 Due October 21 st Chapter 16 Problem 40 Comparing 0.35sin 10 3 4 y t x π π π = with 29 29 sin sin y A kx

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