Question

The decibel scale measures the intensity of sound $D$ using the equation $D = 10 \log I$ , where $I$ is the intensity ratio of a sound.

On the decibel scale, the purr of a cat measures $D = 10 \log 330 = 25.2 (3 s.f)$ decibels.

Sound intensity is measured on a traffic light system:

Green: no ear protection needed. $1 - 75 D B$

Orange: ear protection recommended. $80 - 120 D B$

Red: ear protection necessary. $120 + D B$ . Calculate the sound intensity of the following noise and determine whether or not ear protection equipment is recommended or necessary.

A flowing river has an intensity ratio of $3100000$ . [Use $\log 3.1 = 0.491361694$ ]

Accepted Answer

Given: The decibel scale measures the intensity of sound $D$ using the equation $D = 10 \log I$ , where $I$ is the intensity ratio of a sound.

On the decibel scale, the purr of a cat measures $D = 10 \log 330 = 25.2 (3 s.f)$ decibels.

Sound intensity is measured on a traffic light system:

Green: no ear protection needed. $1 - 75 D B$

Orange: ear protection recommended. $80 - 120 D B$

Red: ear protection necessary. $120 + D B$ .

According to the question, we have $I = 3100000$

Therefore, $D = \log (3100000)$

$\Rightarrow D = \log (3.1 \times 10^{6})$

$\Rightarrow D = \log 3.1 + \log 10^{6}$

$D = 10 \log 330 = 25.2 (3 s.f)$

$\Rightarrow D = 0.491361694 + 6$

$\Rightarrow D = 6.49136169$

$\Rightarrow D = 6.49$ [to three significant figures]

Hence, no ear protection equipment is required as the intensity of sound is $D = 6.49$ decibels.

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