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hw 12 - shah(rps587 HW 12 Kleinman(58225 This print-out...

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shah (rps587) – HW 12 – Kleinman – (58225) 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 HW covers Chs. 16 17. 001 10.0 points Andrea asked her brother to take a 4 ft float- ing raft out of the water near the wave-swept shore. Using this raft as a measuring tool, she estimated that the wavelengths of these particular ocean waves were about 10 ft. How fast are these surface ocean waves if the frequency remains 1 3 Hz? Correct answer: 3 . 33333 ft / s. Explanation: Let : λ = 10 ft and f = 1 3 Hz . v = f λ = parenleftbigg 1 3 Hz parenrightbigg (10 ft) = 3 . 33333 ft / s . keywords: 002 (part 1 of 2) 10.0 points A harmonic wave in a wire has amplitude 1 . 43 mm, wavelength 2 . 81 m, and frequency 907 Hz. What is the propagation speed of the wave? Correct answer: 2548 . 67 m / s. Explanation: Let : A = 1 . 43 mm , λ = 2 . 81 m , and f = 907 Hz . For a traveling wave, v = λ f = (2 . 81 m) (907 Hz) = 2548 . 67 m / s . 003 (part 2 of 2) 10.0 points The wire has linear mass density of 13 . 4 g / m. Determine the wire’s tension. Correct answer: 87042 . 6 N. Explanation: Let : μ = 13 . 4 g / m . v = radicalBigg T μ T = μ v 2 = (0 . 0134 kg / m) (2548 . 67 m / s) 2 = 87042 . 6 N . keywords: 004 10.0 points A wave on a string is described by the wave function y = (0 . 1 m) sin[(0 . 5 rad / m) x - (20 rad / s) t ] Determine the frequency of oscillation of a particular point at x = 2 . 0 m. Correct answer: 3 . 1831 Hz. Explanation: Let : ω = 20 rad / s . In fact, when a wave with frequency f trav- els along a string, any point of the string has the same oscillation frequency f . In this case, f = ω 2 π = 20 rad / s 2 π = 3 . 1831 Hz keywords: 005 6.0 points The figure shows two wave pulses that are approaching each other. P Q Which of the following best shows the shape of the resultant pulse when the centers of the pulses, points P and Q , coincide?
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shah (rps587) – HW 12 – Kleinman – (58225) 2 1. 2. correct 3. 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 8.0 points A pulse moves on a string at 1 m/s, traveling to the right. At point A , the string is tightly clamped and cannot move. 1 m/s 1 m A Which of the following shows how the string would look soon after 2 seconds? 1. A 2. A 3. A correct 4. A 5. A 6. A
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shah (rps587) – HW 12 – Kleinman – (58225) 3 7. A 8. A Explanation: The pulse travels to the right and is re- flected back from the fixed point. The wave cannot propagate to the right beyond the point A . Reflected pulses from fixed end points are inverted. 007 10.0 points In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide greater intensity. For example, the note at 136 Hz has two strings at this pitch.
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