Book edition 14th edition

Author(s) Hugh D. Young, Roger A. Freedman

Pages 1596 pages

ISBN 9780321973610

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Short Answer

Question: (a) By what factor must the sound intensity be increased to raise the sound intensity level by 13.0 dB? (b) Explain why you don’t need to know the original sound intensity.

(a) the factor for the sound intensity to be increased to raise the sound intensity level by 13.0 dB is 20.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The increase in sound level intensity is 13 dB.

Step 2: Concept

Sound intensity can be measured as the number of wave particles falling on the surface that can be measured in 1 second.

Step 3: (a) Calculation of the factor

The sound intensity level was \({\beta _1}\) , and it got increased, and the value can be written as,\({\beta _2}\).

The formula for the initial level is,

\({\beta _1} = 10\log \left( {\frac{{{I_1}}}{{{I_0}}}} \right)\)

Here \({I_0}\) is the original intensity, \({I_1}\)is the measured intensity.

The expression for final intensity level is,

\({\beta _2} = 10\log \left( {\frac{{{I_2}}}{{{I_0}}}} \right)\)

Here \({I_2}\)is the measured intensity.

The increment or change is 13 dB; we can write it as,

\(\Delta \beta = {\beta _2} - {\beta _1}\)

Substitute the values in the above expression, and we get,

\(\begin{array}{c}13 = 10\log \left( {\frac{{{I_2}}}{{{I_0}}}} \right) - 10\log \left( {\frac{{{I_1}}}{{{I_0}}}} \right)\\13 = 10\log \left( {\frac{{\frac{{{I_2}}}{{{I_0}}}}}{{\frac{{{I_1}}}{{{I_0}}}}}} \right)\end{array}\)

Solving further as,

\(\begin{array}{c}13 = 10\log \left( {\frac{{{I_2}}}{{{I_1}}}} \right)\\1.3 = \log \left( {\frac{{{I_2}}}{{{I_1}}}} \right)\\\frac{{{I_2}}}{{{I_1}}} = 20\end{array}\)

Thus, the factor for the sound intensity to be increased to raise the sound intensity level by 13.0 dB is 20.

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University Physics with Modern Physics

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Short Answer

Question: (a) By what factor must the sound intensity be increased to raise the sound intensity level by 13.0 dB? (b) Explain why you don’t need to know the original sound intensity.

Step by Step Solution

Step 1: Given data

Step 2: Concept

Step 3: (a) Calculation of the factor

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University Physics with Modern Physics

Answers without the blur.

Short Answer

Question: (a) By what factor must the sound intensity be increased to raise the sound intensity level by 13.0 dB? (b) Explain why you don’t need to know the original sound intensity.

Step by Step Solution

Step 1: Given data

Step 2: Concept

Step 3: (a) Calculation of the factor

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