Question

An isotropic point source S of sound emits constant power. Two points A and B separated by a distance r are situated near the source as shown in figure. The difference of the intensity level of sound at the points A and B is about

• A. 3 db
• B. 2db
• C. 6 db
• D. 12 db

Answer 1

Answer: (C)

6 db

Intensity at A , $I_A=\frac{P}{4\pi r^2};$

Intensity at B , $I_B=\frac{P}{4\pi (2r{)}^2}$

Sound level at A, $S_A=10log\frac{I_A}{I_0}$

Sound level at B, $S_B=10log\frac{I_B}{I_0}$

Difference of sound level at A and B is

$S_A-S_B=10log\frac{I_A}{I_0}-10log\frac{I_B}{I_0}=10log\left(\frac{I_A}{I_B}\right)$

$=10log4=20log2=6db$