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Chapter 5: Q. 128 (page 300)

Loudness of Sound Problems 127–130 use the following discussion: The loudness $L (x)$ measured in decibels (dB), of a sound of intensity measured in watts per square meter, is defined as $L (x) = 10 \log \frac{x}{I_{0}}$ where watt per square meter is the least intense sound that a human ear can detect. Determine the loudness, in decibels, of each of the following sounds?
Amplified rock music: intensity of $10^{- 1}$ watt per square meter.

Short Answer

Expert verified

The loudness of amplifier rock music is $110$ decibels.

Step by step solution

01

Step 1. Given information

It is given that $L (x) = 10 \log (\frac{x}{I_{0}}),$ where $I_{0} = 10^{- 12}$ watt per square. We need to determine the loudness of amplified rock music intensity of $10^{- 1}$ watt per second.

02

=10×11.Step 2. Simplify

Substitute $10^{- 1}$ to $x$ and $10^{- 12}$ to $I_{0}$ in,

$L (x) = 10 \log (\frac{x}{I_{0}}) .$

$= 10 \log (\frac{10^{- 1}}{10^{- 12}}) .$

$= 10 \log (10^{- 1 + 12}) .$

$= 10 \log (10^{11}) .$

$= 10 \times 11 .$

$= 110 .$

$L (10^{- 1}) = 110$ decibels.

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Most popular questions from this chapter

Solve the equation $2^{- x} = 16$

and verify your results using a graphing utility

In Problems $33 - 40$ , the graph of an exponential function is given. Match each graph to one of the following functions.

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$f (x) = \frac{3 x}{x + 2}$

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