To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, you can
A) reduce the amplitude by a factor of 12 and increase your distance from the speaker by a factor of 3.
B) reduce the amplitude by a factor of 4 and increase your distance from the speaker by a factor of 3.
C) reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3.
D) reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 4.
E) reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 12.

Question

Quizplus · Accepted Answer

The intensity of sound decreases with the square of the distance from the source, and with the square of the decrease in amplitude.

Let x be the factor by which we need to reduce the amplitude and y be the factor by which we need to increase the distance from the speaker. Then we have:

y^2 x^2 = 36
Taking the square root of both sides:
yx = 6

We want to find the values of x and y that satisfy this equation.

Option A: reduce the amplitude by a factor of 12 and increase your distance from the speaker by a factor of 3.

This gives us x = 1/12 and y = 3. But yx = 3/12 = 1/4, not 6, so option A does not work.

Option B: reduce the amplitude by a factor of 4 and increase your distance from the speaker by a factor of 3.

This gives us x = 1/4 and y = 3. But yx = 3/4, not 6, so option B does not work.

Option C: reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3.

This gives us x = 1/2 and y = 3. Then yx = 3/2 which is approximately 2.8284, so option C works.

Option D: reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 4.

This gives us x = 1/3 and y = 4. But yx = 4/3, not 6, so option D does not work.

Option E: reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 12.

This gives us x = 1/3 and y = 12. But yx = 4, not 6, so option E does not work.

Therefore, the best choice is option C: reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3.

To Decrease the Intensity of the Sound You Are Hearing