Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Group Activity - Sound Intensity - Page 899: 1

Answer

Please see the table.

Work Step by Step

Whispering: $10^{-15}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-15}}{10^{-16}}$ $D=10 log_{10} \frac{10^{1}}{10^{0}}$ $D=10 log_{10} \frac{10}{1}$ $D=10 log_{10} 10$ $D=10*1$ $D=10$ Rustling leaves: $10^{-14.2}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-14.2}}{10^{-16}}$ $D=10 log_{10} \frac{10^{1.8}}{10^{0}}$ $D=10 log_{10} \frac{10^{1.8}}{1}$ $D=10 log_{10} 10^{1.8}$ $D=10*1.8$ $D=18$ Normal conversation: $10^{-13}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-13}}{10^{-16}}$ $D=10 log_{10} \frac{10^{3}}{10^{0}}$ $D=10 log_{10} \frac{10^{3}}{1}$ $D=10 log_{10} 10^{3}$ $D=10*3$ $D=30$ Background noise in a quiet residence: $10^{-12.2}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-12.2}}{10^{-16}}$ $D=10 log_{10} \frac{10^{3.8}}{10^{0}}$ $D=10 log_{10} \frac{10^{3.8}}{1}$ $D=10 log_{10} 10^{3.8}$ $D=10*3.8$ $D=38$ Normal office noise or a quiet stream: $10^{-11}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-11}}{10^{-16}}$ $D=10 log_{10} \frac{10^{5}}{10^{0}}$ $D=10 log_{10} \frac{10^{5}}{1}$ $D=10 log_{10} 10^{5}$ $D=10*5$ $D=50$ Air conditioning: $10^{-10}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-10}}{10^{-16}}$ $D=10 log_{10} \frac{10^{6}}{10^{0}}$ $D=10 log_{10} \frac{10^{6}}{1}$ $D=10 log_{10} 10^{6}$ $D=10*6$ $D=60$ Freight train at 50 feet: $10^{-8.5}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-8.5}}{10^{-16}}$ $D=10 log_{10} \frac{10^{7.5}}{10^{0}}$ $D=10 log_{10} \frac{10^{7.5}}{1}$ $D=10 log_{10} 10^{7.5}$ $D=10*7.5$ $D=75$ Vacuum cleaner: $10^{-8}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-8}}{10^{-16}}$ $D=10 log_{10} \frac{10^{8}}{10^{0}}$ $D=10 log_{10} \frac{10^{8}}{1}$ $D=10 log_{10} 10^{8}$ $D=10*8$ $D=80$ Nearby thunder: $10^{-7}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-7}}{10^{-16}}$ $D=10 log_{10} \frac{10^{9}}{10^{0}}$ $D=10 log_{10} \frac{10^{9}}{1}$ $D=10 log_{10} 10^{9}$ $D=10*9$ $D=90$ Air hammer: $10^{-6.5}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-6.5}}{10^{-16}}$ $D=10 log_{10} \frac{10^{9.5}}{10^{0}}$ $D=10 log_{10} \frac{10^{9.5}}{1}$ $D=10 log_{10} 10^{9.5}$ $D=10*9.5$ $D=95$ Jet plane at takeoff: $10^{-6}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-6}}{10^{-16}}$ $D=10 log_{10} \frac{10^{10}}{10^{0}}$ $D=10 log_{10} \frac{10^{10}}{1}$ $D=10 log_{10} 10^{10}$ $D=10*10$ $D=100$ Threshold of pain: $10^{-4}$ watts/$cm^3$ $D=10 log_{10} \frac{I}{10^{-16}}$ $D=10 log_{10} \frac{10^{-4}}{10^{-16}}$ $D=10 log_{10} \frac{10^{12}}{10^{0}}$ $D=10 log_{10} \frac{10^{12}}{1}$ $D=10 log_{10} 10^{12}$ $D=10*12$ $D=120$
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