Question

How does the intensity of a sound wave change if the distance from the source is increased by a factor of 4?

A. The intensity decreases by a factor of 16.
B. The intensity decreases by a factor of 4.
C. The intensity increases by a factor of 4.
D. The intensity increases to by a factor of 16.

Answer 1

the intensity of waves is inversely proportional to the distance squared so: \[I = k/r^2 \\ I_{final} = k/(4*r)^2 = k/(16*r^2) \\so \ => \\ I_{final}/I=1/16 <=> I_{final}=I/16\]
in other words the intensity decreases by a factor of 16, k is a coefficient correlated to the particular type of wave and the medium, but keeping the medium identical and the nature of the wave identical we can assume that k is the same for both the Intensities. and thus we can eliminate it in the ratio.

Answer 2

thanks :)