Answer
Sound energy is produced by the loudspeaker at a rate of $0.099~W$
Work Step by Step
) We can find the intensity of the sound:
$\beta = 10~log\frac{I}{I_0}$
$71 = 10~log\frac{I}{I_0}$
$7.1 = log\frac{I}{I_0}$
$10^{7.1} = \frac{I}{I_0}$
$I = (10^{7.1})~I_0$
$I = (10^{7.1})~(1.0\times 10^{-12}~W/m^2)$
$I = 1.26\times 10^{-5}~W/m^2$
We can find the power of the source:
$P = I~A$
$P = I~4\pi~r^2$
$P = (1.26\times 10^{-5}~W/m^2)~(4\pi)~(25~m)^2$
$P = 0.099~W$
Sound energy is produced by the loudspeaker at a rate of $~0.099~W$
