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Two boys are whispering in the library. The radiated sound power from one boy's mouth is 1.2 times 10^-9 W; and it spreads out uniformly in all directions. What is the minimum distance the boys must be away from the librarian so that she will not be able to hear them? The threshold of hearing for the librarian is 1.00 times 10^-12 w/m^2.

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MechEngineer

Answer:

19.54m

Explanation:

We can first calculate the minimum area for the sound to spread so that the librarian cannot hear them

[tex] A = \frac{1.2\times10^{-9}}{10^{-12}} = 1200 m^2[/tex]

For the sound to cover this area then the distance between the boy and the librarian must be

[tex]A = \pi r^2 = 1200[/tex]

[tex]r^2 = 1200 / \pi = 381.97 [/tex]

[tex]r = \sqrt{381.97} = 19.54 m[/tex]

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