 # An outside loudspeaker (considered a small source) emits sOund waves with a power output of 100W. Find the intensity 10.0 m from the source Vorbeckenuc 2022-07-20 Answered
An outside loudspeaker (considered a small source) emits sOund waves with a power output of 100W. Find the intensity 10.0 m from the source
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In this problem, a sound wave has a power output of $\beta =100W$. For this part, we calculate the intensity at distance r=10.0m from the source.
The intensity is proportional to the power and inversely proportional to the square of the distance from the source. We have
$I=\frac{\beta }{4\pi {r}^{2}}$
$=\frac{100W}{4\pi \left(10.0m{\right)}^{2}}$
$=\frac{1}{4\pi }$
$=7.95775×{10}^{-2}W/{m}^{2}$
$I=7.96×{10}^{-2}W/{m}^{2}$
Result:
$I=7.96×{10}^{-2}W/{m}^{2}$

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$I=\frac{P}{4\pi {r}^{2}}$
$=\frac{100}{\left(4\right)\left(\pi \right)\left(10{\right)}^{2}}$
$=7.9577e-2W/{m}^{2}$
$\approx 0.0796W/{m}^{2}$
Result:
$0.0796W/{m}^{2}$

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