The intensity of sound I (as a multiple of the average minimum threshold of hearing intensity) is related to the decibel level D (or loudness of sound) according to . A decibel reading of 140 is at the threshold of pain. If is the intensity of this threshold and is the intensity when , express the ratio as a power of 10.

Question

Quizplus · Accepted Answer

From the provided equation, we have:

Taking the logarithm of both sides, we get:

Solving for I2/I1, we get:

Now, we are given that D = 140 corresponds to the threshold of pain, so we can set I2 = threshold of pain and solve for I1. Let I2 = and D2 = 140, then:

Substituting the given values, we get:

Therefore, the ratio I1/I2 = 10^7/2 = 5 x 10^6. Converting to a power of 10, we get:

I1/I2 = 11ea984b_b2be_3398_9029_2d93100216a7_TB4005_11.

Thus, the best choice is D.

The Intensity of Sound I (As a Multiple of the Average