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homework13s_1061_09_2 - Manage this Assignment Print...

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Homework # 12 Due: 10:00pm on Thursday, December 10, 2009 Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy Ear Damage from a Small Firecracker Description: Find the sound intensity level one meter away from a firecracker. Then determine at what distance the sound of the firecracker would rupture be intense enough to rupture an eardrum. Learning Goal: To understand how to convert between different sound intensity scales and how the decibel intensity of a sound changes with distance. The decibel scale is logarithmic in intensity: . In this formula, is a reference intensity, which, for sound waves, is taken to be . This constant must be used to convert a particular physical intensity into a sound intensity level measured in decibels. Once we know the sound intensity level (in decibels) at a certain reference distance from a sound source, the decrease of intensity with distance can be accounted for by subtracting the decibel value appropriate to the ratio of the new distance to the reference distance. In this problem you will use the decibel scale to analyze a small firecracker that emits 1200 of peak power. To avoid confusion, intensities denoted by are in units of watts per meter squared; intensities denoted by are in units of decibels. Part A What is the peak intensity in decibels at a distance of 1 m from the firecracker? Hint A.1 Find at 1 m Find the peak intensity in watts per meter squared of the sound from the firecracker at a distance of 1 . Hint A.1.1 Start with geometry All of the power from the firecracker has to pass through a sphere 1 in radius. What is the area of this sphere? Express your answer numerically, in square meters, to two decimal places. ANSWER: = Express your answer numerically to one decimal place. ANSWER: = Hint A.2 Converting intensity to dB Use the formula in the introduction to convert into decibels. Note that the reference intensity is . Express in decibels to the nearest integer. 1 of 8 12/12/09 3:47 AM
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ANSWER: = dB Part B It takes a sound intensity of about 160 dB to rupture the human eardrum. How close must the firecracker described in the introduction be to the ear to rupture the eardrum? Hint B.1 How to approach the problem This problem can be worked from first principles. To do so, figure out the intensity in watts per meters squared corresponding to 160 , then divide this quantity into the 1200-W peak power of the firecracker. The result will be the surface of a sphere, centered on the firecracker, whose radius is the distance at which the sound intensity is 160 .
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