set9-soln - Physics 1240 Homework 9 solutions Brief...

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Physics 1240 Homework 9 solutions Brief solutions to homework set #9. Your numbers will be different, but the idea is the same. I’m just using sample numbers here. 1. We’re in class with a decibel meter up front, and everyone is screaming at the top of their lungs, hooting and shouting and pounding on their desks, shooting off firecrackers, its Phys 1240 gone wild...and the meter is reading a reasonably steady sound intensity level of 120 dB. At a pre-arranged signal from Professor Betterton, seventy-five (75) percent of the class suddenly gets totally quiet, while the remaining students continue making the same noise. What sound intensity level would the meter now show? (Find the answer in dB, but do not enter units.) Long-answer questions (for question 6): Did you find the answer just a little surprising, or counter-intuitive? Most people who haven’t taken a course like this would guess the answer would be about 30 dB. Try to explain how someone might come up with that *wrong* answer, and then explain, qualitatively or informally, why *your* (correct) answer does really make more sense. (Imagine you were trying to explain this to someone who didn’t know much math and had never taken this course. You’re not trying to convince them of your specific numerical result, just why the dB level did not drop nearly so much as one might first imagine.) Initially 100% of the class is yelling, and afterwards only 25% of the class is yelling—a factor of 100/25 = 4 decrease in the number of people making noise. Assuming everyone in the class yells with the same sound intensity, decreasing the number of people yelling by a factor of 4 decreases the sound intensity by a factor of 4. Therefore the SIL decreases by 6 dB, to 114 dB. The SIL is a logarithmic scale, not a linear one. When we use a linear measure like sound intensity, changing by a factor of 4 changes the number a lot. But on a logarithmic scale, a factor of 4 change is not so much. The decibel scale has to be able to describe 12 orders of magnitude (factor of 10 12
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