Question

The sound intensity a distance d1 = 15.0 m from a chain saw is 0.260 W/m2. What is the sound intensity a distance d2 = 27.0 m from the chain saw? (Enter your answer in W/m

Answer 1

Answer:

0.08024 W/m²

Explanation:

P = Power

$d_1$ = Distance = 15 m

$I_1$ = Intensity at 15 m = 0.26 W/m²

$d_2$ = Distance = 27 m

$I_1$ = Intensity at 27 m

Sound intensity is given by

$I=\frac{P}{4\pi d^2}$

$\\\Rightarrow I\propto \frac{1}{d^2}$

So, we have the relation

$\frac{I_1}{I_2}=\frac{d_2^2}{d_1^2}\\\Rightarrow I_2=\frac{d_1^2\times I_1}{d_2^2}\\\Rightarrow I_2=\frac{15^2\times 0.26}{27^2}\\\Rightarrow I_2=0.08024\ W/m^2$

The sound intensity at the given distance is 0.08024 W/m²