Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to , where is the threshold of hearing for the average human ear. Find the loudness when I is 1,000 times .
A) 3
B) 30
C) 4
D) 300
E) 100

Question

Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to  , where  is the threshold of hearing for the average human ear. Find the loudness when I is 1,000 times  . ​
A) 3 
B) 30 
C) 4 
D) 300 
E) 100

Quizplus · Accepted Answer

From the given information, we know that loudness (in decibels) is given by:

L = 10 log (I/I_0)

where I is the intensity level of the sound and I_0 is the threshold of hearing for the average human ear.

If I is 1000 times I_0, then we have:

I = 1000 I_0

Substituting this into the equation for loudness, we get:

L = 10 log (1000 I_0 / I_0) = 10 log 1000 = 10 x 3 = 30

Therefore, the loudness of the sound is 30 decibels, which corresponds to choice B.

Use the Fact That the Loudness of Sound (In Decibels)