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HW 33 - Morby Grant – Homework 33 – Due noon – Inst...

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Unformatted text preview: Morby, Grant – Homework 33 – Due: Apr 26 2006, noon – Inst: Drummond 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A transverse wave in a wire has form y ( x,t ) = (1 . 6 cm) × sin h (5 . 08 m- 1 ) × x- (7110 s- 1 ) × t i The wire has linear density μ = 7 . 59 g / m. What is its tension? Correct answer: 14868 N. Explanation: A sinusoidal transverse wave of the general form y ( x,t ) = A × sin( kx- ωt ) travels in the positive x direction at speed v = ω k . For the wave in question, this speed is v = 7110 s- 1 5 . 08 m- 1 = 1399 . 61 m / s . For a transverse wave in a wire, this speed fol- lows from the wire’s tension and linear density according to v = s F μ , hence F = μ × v 2 = 14868 N . 002 (part 1 of 1) 10 points A harmonic wave y = A sin[ k x- ω t- φ ] , where A = 1 meter, k has units of m- 1 , ω has units of s- 1 , and φ has units of radians, is plotted in the diagram below. +1- 1 A (meters) x (meters) 10 m 20 m 30 m At the time t = 0 Which wave function corresponds best to the diagram? 1. y = A sin • µ 2 π 15 m ¶ x- ω t- µ 4 π 3 ¶‚ 2. y = A sin • µ 2 π 3 m ¶ x- ω t- µ 2 π 3 ¶‚ 3. y = A sin • µ 2 π 9 m ¶ x- ω t- µ 5 π 3 ¶‚ 4. y = A sin • µ 2 π 9 m ¶ x- ω t- µ 2 π 3 ¶‚ 5. y = A sin • µ 2 π 3 m ¶ x- ω t- µ 1 π 3 ¶‚ 6. y = A sin • µ 2 π 9 m ¶ x- ω t- µ 4 π 3 ¶‚ 7. y = A sin • µ 2 π 3 m ¶ x- ω t- µ 4 π 3 ¶‚ 8. y = A sin • µ 2 π 15 m ¶ x- ω t- µ 1 π 3 ¶‚ correct 9. y = A sin • µ 2 π 15 m ¶ x- ω t- µ 2 π 3 ¶‚ 10. y = A sin • µ 2 π 15 m ¶ x- ω t- µ 5 π 3 ¶‚ Explanation: From the diagram of the wave function the wave-length λ = 15 m (6 horizontal scale di- visions of 2 . 5 m each, see diagram below). Notice: Since one wave-length is 2 π ra- dians, each horizontal division is 2 π 6 = π 3 radians. Morby, Grant – Homework 33 – Due: Apr 26 2006, noon – Inst: Drummond 2 The given wave function (sine function with t = 0) y = A sin • k x- φ ‚ = A sin • µ 2 π λ ¶ x- φ ‚ = A sin • µ 2 π 15 m ¶ x- φ ‚ (dark curve in diagram below) is shifted 1 divisions to the right (negative phase shift) of a no-phase-shift sine function y = sin • µ 2 π 15 m ¶ x ‚ (gray curve in diagram below), therefore φ = 1 π 3 = 1 π 3 radians ....
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HW 33 - Morby Grant – Homework 33 – Due noon – Inst...

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