Question

If a source radiates sound uniformly in all directions and you triple your distance from the sound source, what happens to the sound intensity at your new position?
a. The sound intensity drops to 1 / 27 of its original value.b. The sound intensity increases to three times its original value.c. The sound intensity drops to 1 / 3 of its original value.d. The sound intensity drops to 1 / 9 of its original value.e. The sound intensity does not change.

Answer 1

Sound intensity (energy) falls inversely proportional to the square of the distance  from the sound:

$I \propto \frac{1}{r^2}$

Therefore if we have two values of intensities we have

$\frac{I_1}{I_2} = \frac{r_2^2}{r_1^2}$

As we have that

$r_1 = 3 r_2$

Then we have that

$\frac{I_1}{I_2} = \frac{r_2^2}{(3r_2)^2}$

$\frac{I_1}{I_2} = \frac{1}{9}$

Therefore the correct answer is D. The sound intensity drops to 1 / 9 of its original value.