Answer
Each therapy session should last 21 minutes.
Work Step by Step
We can find the intensity of the sound waves.
$I = I_0~10^{(\beta/10)}$
$I = (10^{-12}~W/m^2)~10^{(93/10)}$
$I = 2.0\times 10^{-3}~W/m^2$
We can find the area of the hemisphere.
$A = \frac{1}{2}(4\pi~R^2)$
$A = 2\pi~R^2$
$A = (2\pi)(0.080~m)^2$
$A = 0.040~m^2$
We can find the power received by the hemisphere.
$P = I~A$
$P = (2.0\times 10^{-3}~W/m^2)(0.040~m^2)$
$P = 8.0\times 10^{-5}~W$
We can find the number of seconds required to reach a total energy of 0.10 J.
$t = \frac{E}{P}$
$t = \frac{0.10~J}{8.0\times 10^{-5}~W}$
$t = 1250~s$
We can convert the time to minutes.
$t = (1250~s)(\frac{1~min}{60~s}) = 21~minutes$
Each therapy session should last 21 minutes.
