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Unformatted text preview: Version 116/ABDBA – midterm 04 – Turner – (58220) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Simple harmonic motion can be described us ing the equation x = x m sin( ωt + φ ) . If x = initial position, v = initial velocity, then 1. tan φ = − ω x v 2. tan φ = − v ω x 3. tan φ = + ω x v correct 4. tan φ = + v ω x Explanation: x = x m sin( ω t + φ ) v = dx dt = x m ω cos( ω t + φ ) When t = 0, x = x m sin φ v = x m ω cos φ x m sin φ x m ω cos φ = x v tan φ = ω x v . 002 10.0 points Two harmonic waves traveling in opposite di rections interfere to produce a standing wave described by y = 2 sin( k x ) cos( ω t ) , where x is in meters, t is in seconds and k = 8 . 4823 m − 1 . What is the distance between the two adja cent antinodes? 1. 0.625 2. 0.47619 3. 0.4 4. 0.30303 5. 0.434783 6. 0.37037 7. 0.416667 8. 0.294118 9. 0.232558 10. 0.909091 Correct answer: 0 . 37037 m. Explanation: Let : k = 8 . 4823 m − 1 . For a standing wave y = 2 A sin( k x ) cos( ω t ) and its wavelength is λ = 2 π k = 2 π 8 . 4823 m − 1 = 0 . 740741 m . The distance between the two adjacent antin odes is onehalf of the wavelength, so x = λ 2 = . 740741 m 2 = . 37037 m . 003 10.0 points The sound of a man shouting at the top of his lungs from a rather large distance away from your ear has loudness of only 20 decibels. What would be the decibel level of four men shouting at the top of their (equally powerful) lungs from the same distance away from your ear? Assume that there is no interference from superposed waves and round off your answer to the nearest integer. 1. 80 dB 2. 10 dB 3. 60 dB 4. 6 dB 5. 26 dB correct 6. 40 dB Version 116/ABDBA – midterm 04 – Turner – (58220) 2 7. 14 dB 8. 5 dB 9. 20 dB 10. 160 dB Explanation: Let : β 1 = 20 dB . The decibel level β is a logarithmic measure of sound intensity I , specifically β 1 = 10 log 10 parenleftbigg I I parenrightbigg . Since we have assumed that there is no in terference from superposed waves, four men shouting together produce sound intensity four times greater than that of just one man ( I 4 = 4 I 1 ), so β 4 = 10 log 10 parenleftbigg 4 I 1 I parenrightbigg = 10 log 10 parenleftbigg I 1 I parenrightbigg + 10 log 10 4 = 20 dB + 10 log 10 4 = 26 . 0206 dB . 004 10.0 points The length of a hollow pipe is 46 . 8 cm . There is a standing wave in the pipe with wavelength 20 . 8 cm. Which figure schematically represents the standing wave? 1. L 2. L 3. L 4. L 5. L 6. L correct 7. L 8. L 9. L 10. L Explanation: Let : L = 46 . 8 cm and λ = 20 . 8 cm . Let N be the number of nodes. When both ends of a pipe are open, the wavelength is λ = 2 L N , where N = 1 , 2 , 3 , 4 , ··· ....
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This note was uploaded on 05/11/2010 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.
 Spring '08
 Turner
 Physics, Simple Harmonic Motion

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