Answer
The speaker's power output is 5.0 W
Work Step by Step
We can find the intensity of the sound wave at a distance of 20 m as:
$I = I_0~10^{\beta/10}$
$I = (10^{-12}~W/m^2)~10^{90/10}$
$I = 10^{-3}~W/m^2$
We can find the power output of the speaker:
$P = I~A$
$P = I~(4\pi~R^2)$
$P = (10^{-3}~W/m^2)(4\pi)(20~m)^2$
$P = 5.0~W$
The speaker's power output is 5.0 W.
