how far must you be from a 110 w speaker to have an intensity of 0.0439 w/m^2? (treat the speaker as a point…

Explanation:

Step1: Write the formula for intensity of a point source

The formula for the intensity (I) of a point source is (I=\frac{P}{4\pi r^{2}}), where (P) is the power of the source and (r) is the distance from the source.

Step2: Rearrange the formula to solve for (r)

From (I = \frac{P}{4\pi r^{2}}), we can get (r^{2}=\frac{P}{4\pi I}), then (r=\sqrt{\frac{P}{4\pi I}})

Step3: Substitute the given values

Given (P = 110\space W) and (I=0.0439\space W/m^{2}) [ \begin{align*} r&=\sqrt{\frac{110}{4\pi\times0.0439}}\ &=\sqrt{\frac{110}{0.551}}\ &=\sqrt{199.64}\ &\approx 14.13 \end{align*} ]

Answer:

(14.13)