# hw33 - Overton Mays – Homework 33 – Due 4:00 am –...

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Unformatted text preview: Overton, Mays – Homework 33 – Due: Apr 27 2005, 4:00 am – Inst: Turner 1 This print-out should have 14 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 The lowest A on a piano has a frequency of 27 . 5 Hz. Assume: The tension in the A piano wire (of length 1 . 8 m) is 303 N, and one-half wave- length occupies the wire. What is the mass of m the wire? Correct answer: 0 . 0556474 kg. Explanation: Basic Concepts: v = s F μ for waves on wire . v = λ f L Solution: If one half-wavelength occupies the wire, then the wavelength λ = 2 L , where L is the length of the wire. Then the velocity of waves on the wire is v = λ f . But this velocity is also given by v = s F μ , where μ is the mass per unit length of the wire. The total mass of the wire is m = μ L . Thus we have m = L F v 2 = L F [2 L f ] 2 = (1 . 8 m) 303 N [2 (1 . 8 m) (27 . 5 Hz)] 2 = 0 . 0556474 kg . 002 (part 1 of 1) 10 points An astronaut on the moon wishes to measure the local value of g by timing pulses traveling down a wire that has a large mass suspended from it. The wire used has mass 3 . 22 g and is of length 2 . 47 m. When a(n) 4 . 43 kg mass is suspended from the wire, the astronaut finds that a pulse requires 35 . 8 ms to traverse the length of the wire. Assume: You may neglect the mass of the wire when calculating its tension. Calculate g from these data. Correct answer: 1 . 40082 m / s 2 . Explanation: The tension on the wire is T = M g , so the speed of the waves is v = s T μ = r M g L m . On the other hand, the speed of the waves can be computed as v = L t , so M g L m = L 2 t 2 g = m L M t 2 = 1 . 40082 m / s 2 . 003 (part 1 of 1) 10 points A simple pendulum consists of a ball of mass 5 . 77 kg hanging from a uniform string of mass . 0772 g and length L . The period of oscilla- tion for the pendulum is 2 . 53 s. The acceleration of gravity is 9 . 8 m / s 2 . Determine the speed of a transverse wave in the string when the pendulum is stationary and hangs vertically. Correct answer: 1078 . 81 m / s. Explanation: Given : m = 0 . 0772 g = 7 . 72 × 10- 5 kg , M = 5 . 77 kg , and T = 2 . 53 s . For a simple pendulum, its period is T = 2 π s L g L = T 2 g 4 π 2 . Overton, Mays – Homework 33 – Due: Apr 27 2005, 4:00 am – Inst: Turner 2 When the pendulum is vertical and station- ary, the tension in the string is T s = M g ....
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## This note was uploaded on 03/22/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

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hw33 - Overton Mays – Homework 33 – Due 4:00 am –...

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