Question

The intensity of sound is measured on the decibel scale, dB. The equation dB=10log(I) represents the decibel level, where I is the ratio of the sound to the human hearing threshold.

A noise registers a decibel level of 15. To the nearest whole number, how many times greater is the noise than the human hearing threshold?

Answer 1

The noise is approximately 31.62 times greater than the human hearing threshold.

Step-by-step explanation:

The decibel scale is used to measure the intensity of sound. The equation to calculate the decibel level is dB = 10 log(I), where I is the ratio of the sound to the human hearing threshold.

Given that the decibel level of the noise is 15, we need to find the ratio of the noise to the human hearing threshold. To do this, we need to rearrange the equation to solve for I and substitute the given value of dB:

15 = 10 log(I)
1.5 = log(I)
10^1.5 = I

Therefore, the noise is approximately 31.62 times greater than the human hearing threshold.