Giancoli 7th Edition textbook cover
Giancoli's Physics: Principles with Applications, 7th Edition

12-1: Characteristics of Sound
12-2: Intensity of Sound; Decibels
12-3: Loudness
12-4: Sources of Sound: Strings and Air Columns
12-5: Quality of Sound, Superposition
12-6: Interference; Beats
12-7: Doppler Effect
12-8: Shock Waves; Sonic Booms

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 13
Q

One CD player is said to have a signal-to-noise ratio of 82 dB, whereas for a second CD player it is 98 dB. What is the ratio of intensities of the signal and the background noise for each device?

A
Is1In1=1.6×108,Is2In2=6.3×109\dfrac{I_{s1}}{I_{n1}} = 1.6 \times 10^8, \dfrac{I_{s2}}{I_{n2}} = 6.3 \times 10^9
Giancoli 7th Edition, Chapter 12, Problem 13 solution video poster
Padlock

In order to watch this solution you need to have a subscription.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. This decibel formula can be used for other things than just sound. It can be used for, you know, signal to noise ratio for example, anything that has large ratios. OK. So, we'll say that for CD player 1 the signal to noise ratio, ratio in decibels equals 10 times logarithm of the intensity of the signal divided by the intensity of the noise. And then divide both sides by 10. And you get log of this ratio is β1 over 10. And make both sides powers of 10. And on the left side 10 to the power of a logarithm is just the argument of the logarithm. So, that's I signal 1 over intensity of the noise 1. And on the right hand side we have 10 to the power of β1 over 10. So, the signal to noise ratio in the first CD player is 10 to the power of 82 decibels over 10 which is 1.6 times 10 to the 8. So, the signal is this many times greater than the noise. And in the second CD player the signal to noise ratio is 10 to the power of 98 decibels over 10 which is 6.3 times 10 to the 9.

Find us on:

Facebook iconTrustpilot icon
Giancoli Answers, including solutions and videos, is copyright © 2009-2024 Shaun Dychko, Vancouver, BC, Canada. Giancoli Answers is not affiliated with the textbook publisher. Book covers, titles, and author names appear for reference purposes only and are the property of their respective owners. Giancoli Answers is your best source for the 7th and 6th edition Giancoli physics solutions.