Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.7 Applications of Exponential Functions and Logarithmic Functions - 12.7 Exercise Set - Page 834: 18

Answer

The loudness of this sound level is about 65 decibels.

Work Step by Step

The intensity of the sound in a normal conversation is about $\text{3}\text{.2}\times \text{1}{{\text{0}}^{-6}}\text{ W/}{{\text{m}}^{\text{2}}}$. Thus, $I=3.2\times {{10}^{-6}}$. Substitute $I=3.2\times {{10}^{-6}}$ and ${{I}_{0}}={{10}^{-12}}$ in the formula $L=10\cdot \log \frac{I}{{{I}_{\left( 0 \right)}}}$ and solve as follows: $\begin{align} & L=10\cdot \log \frac{I}{{{I}_{\left( 0 \right)}}} \\ & =10\cdot \log \frac{3.2\times {{10}^{-6}}}{{{10}^{-12}}} \\ & =10\cdot \log \left( 3.2\times {{10}^{-6}}\times {{10}^{12}} \right) \\ & =10\cdot \log \left( 3.2\times {{10}^{6}} \right) \end{align}$ $\begin{align} & L=10\cdot \log \left( 3.2\times {{10}^{6}} \right) \\ & \approx 10\cdot 6.505 \\ & \approx 65.05 \end{align}$
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