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Unformatted text preview: Overton, Mays Homework 36 Due: May 4 2005, 4:00 am Inst: Turner 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 wire of mass 1 g and length 50 cm is stretched with a tension of 490 N. It is then placed near the open end of the tube shown in figure and stroked with a violin bow so that it oscillates at its fundamental frequency. The water level in the tube is then lowered until a resonance is obtained, which occurs at 16 cm below the top of the tube. Find the speed of sound in air. Correct answer: 316 . 784 m / s. Explanation: m = 1 g = 0 . 001 kg L string = 50 cm = 0 . 5 m L air column = 16 cm = 0 . 16 m F = 490 N L string L aircolumn The speed of the tranverse waves on the string is v = s F = r F L string m Since L string = 1 2 , v = f 1 1 f 1 = v 1 = v 2 L string = 1 2 L string r F L string m = 1 2 s F mL string For the tube open at one end, L air column = n n 4 , n = 1 , 3 , 5 ,... For n = 1, 1 = 4 L air column and v s = f 1 1 = 4 f 1 L air column v s = 2 L air column s F mL string = 2(0 . 16 m) s 490 N (0 . 001 kg)(0 . 5 m) = 316 . 784 m / s The method is not very accurate because it neglects end effects. 002 (part 1 of 1) 10 points A stretched string is fixed at both ends, 406 . 5 cm apart. If the density of the string is 0 . 017 g / cm and its tension is 600 N, what is the wavelength of the first harmonic? Correct answer: 813 cm. Explanation: For a string with both ends fixed, its wave- length of the nth harmonic is n = 2 d n , which doesnt depend on its other properties. So the wavelength of its first harmonic is 2 d. Overton, Mays Homework 36 Due: May 4 2005, 4:00 am Inst: Turner 2 003 (part 1 of 3) 10 points In the arrangement shown in the figure be- low, an object of mass 6 . 5 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is 3 . 3 m. When the vibrator is set to frequency of 150 Hz, a standing wave with six loops is formed....
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