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hw13 - al-ameri(aoa434 Hwk13 Stokes(19102 This print-out...

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al-ameri (aoa434) – Hwk13 – Stokes – (19102) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. This is ONLINE HOMEWORK No 13. It is due before 6.00 am on Tuesday 5 May, Abu Dhabi Time (9.00 pm on Monday in Texas) 001 10.0 points A harmonic wave is traveling along a rope. The oscillator that generates the wave com- pletes 44 . 0 vibrations in 23 . 2 s. A given crest of the wave travels 411 cm along the rope in a time period of 10 . 3 s. What is the wavelength? Correct answer: 0 . 210397 m. Explanation: Let : n = 44 . 0 vibrations , t = 23 . 2 s , Δ x = 411 cm = 4 . 11 m , and Δ t = 10 . 3 s . λ = v f = Δ x Δ t n t = t Δ x n Δ t = (23 . 2 s)(4 . 11 m) 44 (10 . 3 s) = 0 . 210397 m . 002 (part 1 of 3) 10.0 points A transverse wave of frequency 25 Hz propa- gates down a string. Two points 15 cm apart are out of phase by 7 π 3 . What is the wave length of the wave? Correct answer: 12 . 8571 cm. Explanation: Let : Δ x = 15 cm and δ = 7 π 3 . Let the positive x direction be the direction of propagation of the wave. The phase difference is δ = 2 π Δ x λ λ = 2 π Δ x δ = 2 π 15 cm 7 π/ 3 = 12 . 8571 cm . 003 (part 2 of 3) 10.0 points At a given point, what is the phase difference (as a multiple of π ) between two ‘displace- ments for times 5 ms apart? Correct answer: 0 . 25 π . Explanation: Let : t = 5 ms = 0 . 005 s and f = 25 Hz . The period is T = 1 f , so the phase difference is δ = 2 π t T = 2 π t f = 2 π (0 . 005 s) (25 Hz) = 0 . 25 π . 004 (part 3 of 3) 10.0 points What is the wave velocity? Correct answer: 3 . 21429 m / s. Explanation: v = f λ = (25 Hz) (12 . 8571 cm) parenleftbigg 1 m 100 cm parenrightbigg = 3 . 21429 m / s . keywords: 005 10.0 points The figure shows two wave pulses that are approaching each other. P Q
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al-ameri (aoa434) – Hwk13 – Stokes – (19102) 2 Which of the following best shows the shape of the resultant pulse when the centers of the pulses, points P and Q , coincide? 1. 2. 3. correct 4. 5. Explanation: Notice that the two pulses have the same width and amplitude. Choosing the the point P (the same as point Q when the two pulses coincide) as the origin, the two pulses can be described as: P : y 1 = A , d x d Q : y 2 = braceleftBigg A , d x < 0 A , 0 < x < d Using the principle of superposition, the re- sultant pulse is y = y 1 + y 2 = braceleftbigg 2 A , d x < 0 0 , 0 < x < d P Q P + Q 006 10.0 points A 2 . 5 kg block supported by a string rests on a frictionless incline. The length of the string
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