Question

Spherical sound waves are emitted uniformly in all directions from a point source. The variation in sound level SL as a function of distance 'r' from the source can be written as

• A. SL = -b log r${}^a$
• B. SL = a - b (log r)${}^2$
• C. SL = a - b log r
• D. SL = a - b/r${}^2$

Answer 1

The correct option is C SL = a - b log r

we know $SL=10log\frac{I}{I_o}$

$I=\frac{P}{4\pi r^2}$ where P is the power of the source

$SL=10log\frac{P}{4\pi r^2{I}_o}=10log\frac{P}{4\pi I_o}-10log{r}^2=10log\frac{P}{4\pi I_o}-20logr=a-blogr$