At a distance of 15.0 m from a sound source,the intensity level is 60.0 dB.What is the intensity level (in decibels)at a point 2.00 m from the source if the source radiates equally in all directions?
A)55.7 dB
B)57.5 dB
C)75.5 dB
D)77.5 dB

Question

Quizplus · Accepted Answer

From the inverse square law of sound propagation, the intensity of sound decreases by a factor of $(15	ext{ m}/2.00 	ext{ m})^2 = 56.25$ times, since the distance from the source is reduced to $\frac{1}{7}$ of the initial value. Therefore, the intensity level at the new point is

$$60.0	ext{ dB} - 10\log_{10}(56.25) \approx 77.52	ext{ dB} \approx \boxed{77.5	ext{ dB}}$$

Note that choice (A) is close to the correct answer, but it is likely a result of rounding off the exact value of the logarithm, and thus not accurate enough. Choice (B) is too small compared to the initial level, and choice (C) is too large.

At a Distance of 15