## Conceptual Physics (12th Edition)

Published by Addison-Wesley

# Chapter 21 - Think and Solve: 27

#### Answer

10 times. 1,000 times. 1,000,000 times.

#### Work Step by Step

The decibel scale is logarithmic, based upon powers of 10. Whenever the intensity of sound is increased by a factor of 10, the intensity level increases by 10 dB. a. A sound of 10 dB has an intensity 10 times greater than 0 dB, the threshold of hearing. A sound of 10 dB corresponds to an intensity of $10^{-11} \frac{W}{m^{2}}$, which is $10^{1} = 10$ times greater than the intensity of a 0 dB sound, $10^{-12} \frac{W}{m^{2}}$. b. A sound of 30 dB has an intensity 1000 times greater than 0 dB, the threshold of hearing. A sound of 30 dB corresponds to an intensity of $10^{-9} \frac{W}{m^{2}}$, which is $10^{3} = 1000$ times greater than the intensity of a 0 dB sound, $10^{-12} \frac{W}{m^{2}}$. c. A sound of 60 dB has an intensity 1,000,000 times greater than 0 dB, the threshold of hearing. A sound of 60 dB corresponds to an intensity of $10^{-6} \frac{W}{m^{2}}$, which is $10^{6} = 1,000,000$ times greater than the intensity of a 0 dB sound, $10^{-12} \frac{W}{m^{2}}$. This is discussed on page 394, and shown in Table 21.1.

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