Explanation Given data: Two people talk simultaneously and each creates a sound intensity level of 65 dB at a certain point. It is required to find the total sound intensity level of the two people at that particular point. Formula used: Refer to the equation (16.10) in the textbook, and write the expression for sound intensity level relative to the threshold of hearing as follows. β = ( 10 dB ) log ( I I 0 ) (1) Here, I is the sound intensity, and I 0 is the intensity of the reference level, which is 1.0 × 10 − 12 W m 2 . The sound intensity level is not added to get the total intensity level of the two people. Instead, the sound intensity level of each person is converted to sound intensity and then the sound intensity of each person is added. Then the total sound intensity of the people is again converted in terms of decibels (sound intensity level). Modify the expression in equation (1) for the sound intensity level created by the person 1 as follows. β 1 = ( 10 dB ) log ( I 1 I 0 ) (2) Here, I 1 is the sound intensity created by the person 1. Rewrite the expression in equation (2) to find the sound intensity created by the person 1 as follows. β 1 10 dB = log ( I 1 I 0 ) I 1 I 0 = 10 β 1 10 dB I 1 = I 0 10 β 1 10 dB Substitute 1.0 × 10 − 12 W m 2 for I 0 , and 65 dB for β 1 , I 1 = ( 1.0 × 10 − 12 W m 2 ) 10 65 dB 10 dB = ( 1.0 × 10 − 12 W m 2 ) ( 3.1622 × 10 6 ) = 3.1622 × 10 − 6 W m 2 Modify the expression in equation (1) for the sound intensity level created by the person 2 as follows. β 2 = ( 10 dB ) log ( I 2 I 0 ) (3) Here, I 2 is the sound intensity created by the person 2. Rewrite the expression in equation (3) to find the sound intensity created by the person 2 as follows. β 2 10 dB = log ( I 2 I 0 ) I 2 I 0 = 10 β 2 10 dB I 2 = I 0 10 β 2 10 dB Substitute 1

Cutnell & Johnson Physics - Eleventh Edition

11th Edition

ISBN: 9781119391869

Author: Shane Stadler David Young

Publisher: WILEY

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Question

Chapter 16.8, Problem 16CYU

To determine

To find: Whether the total intensity level of the two people is 130 dB or not.

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Chapter 16.7, Problem 15CYU

Chapter 16.8, Problem 17CYU

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Chapter 16 Solutions

Cutnell & Johnson Physics - Eleventh Edition

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