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Physics / Physics with MasteringPhysics 4 / Chapter 14 / Problem 39P

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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Chapter 14, Problem 39P

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QUESTION:

Problem 39P

Twenty violins playing simultaneously with the same intensity combine to give an intensity level of 82.5 dB. (a) What is the intensity level of each violin? (b) If the number of violins is increased to 40, will the combined intensity level be more than, less than, or equal to 165 dB? Explain.

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QUESTION:

Problem 39P

Twenty violins playing simultaneously with the same intensity combine to give an intensity level of 82.5 dB. (a) What is the intensity level of each violin? (b) If the number of violins is increased to 40, will the combined intensity level be more than, less than, or equal to 165 dB? Explain.

ANSWER:

a.)

Step 1 of 2

We have to find the intensity level of each violin, if twenty violins playing simultaneously with the same intensity combine to give an intensity level of 82.5 dB.

The intensity level of 20 violins is given by the expression.

Where,

${I}_{o}=$ Intensity of faintest sound that

can be heard in W/m2

$I=$ Intensity of one string in W/m2

${\beta{}}_{1}=$ Intensity level of each violin in dB

${\beta{}}_{20}=$ Intensity level of 20 violins = 82.5 dB

Thus,

$equals 82.5 \ d cap b minus 10 log left parenthesis 20 right parenthesis$

$equals 82.5 \ d cap b minus 13 d cap b$

$equals 69.5 \ d cap b$

Therefore, the intensity level of each violin is 69.5 dB.

b.)

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