PRACTICE IT - C is not correct, please help. Use the worked example above to hel

Question

PRACTICE IT - C is not correct, please help.

Use the worked example above to help you solve this problem. A small source emits sound waves with a power output of 82.0 W. (a) Find the intensity 2.82 m from the source.
0.821 W/m2
(correct)
(b) At what distance would the intensity be one-fourth as much as it is at r = 2.82 m?
5.64 m
(correct)
(c) Find the distance at which the sound level is 35.2 dB.
4500 m (incorrect)
Your response differs from the correct answer by more than 10%. Double check your calculations.

Explanation / Answer

here,

power output , P = 82 W

a)

r = 2.82 m

the intensity , I = P /( 4 *pi * r^2)

I = 82 /( 4 * pi * 2.82^2)

I = 0.821 W/m^2

b)

let the distance be r'

I' = I/4

4 * P /( 4 * pi * r1^2) = P /( 4 * pi * r^2)

4 * r^2 = r'^2

r' = 5.64 m

the new distance is 5.64 m

c)

dB = 10 * log(I1/I0)

35.2 = 10 * log((82/(4 * pi * r^2))/10^-12)

solving for r

r = 4.39 * 10^5 m

the distance from the source is 4.39 * 10^5 m

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