Question

a decibel is a logarithmic unit that can be used to measure the intensity of a sound. the function \\(y = 10 \log x\\) gives the intensity of a sound in decibels, where \\(x\\) is the ratio of the intensity of the sound to a reference intensity. the reference intensity is generally set at the threshold of hearing.

use the graphing utility to graph the decibel function.

the sound intensity of rustling leaves is 100 times the reference intensity. use your graph to determine the sound intensity of rustling leaves in decibels.
20 decibels

a whisper has a sound intensity of 30 decibels. use your graph to help you complete the following statement.

the sound intensity of a whisper is times the reference intensity.

Explanation:

Identify the given function and values

We are given the logarithmic function:

$$y = 10 \log x$$

where:

• \(y\) represents the sound intensity in decibels.
• \(x\) represents the ratio of the sound intensity to the reference intensity (i.e., how many times the reference intensity it is).

We need to find the value of \(x\) when the sound intensity of a whisper is \(y = 30\) decibels.

Substitute the given decibel value

Using the Logarithmic Functions concept, we substitute \(y = 30\) into the equation:

$$30 = 10 \log x$$

Solve for the ratio x

Divide both sides of the equation by 10:

$$3 = \log x$$

Since \(\log\) denotes the common logarithm (base 10), we rewrite the logarithmic equation in its equivalent exponential form:

$$x = 10^3$$

$$x = 1000$$

Answer:

The sound intensity of a whisper is <blank>1000</blank> times the reference intensity.