Question

42. The number of decibels, d, produced by an audio

source can be modeled by the equation d = 10 log(K),


where I is the sound intensity of the audio source and


K is a constant. How many decibels are produced by an


audio source whose sound intensity is 1,000 times the


value of K?


F. 4


G. 30


H. 40


J. 100


K. 10,000

Answer 1

We are given that d = 10 log(K) where K is a constant and the sound intensity is 1000 times the value of K.

So, we can write I = 1000K

Substituting this value in the equation for d, we get:

d = 10 log(1000K)

d = 10 (log 1000 + log K)

d = 10 (3 + log K)

d = 30 + 10 log K

Since K is a constant, we can assume it to be 1.

Therefore, d = 30 + 10 log 1 = 30

So, an audio source whose sound intensity is 1000 times the value of K produces 30 decibels of sound.

Therefore, the answer is option G) 30.