A certain factory whistle can be heard up to a distance of 2.5 km.Assuming that the acoustic output of the whistle is uniform in all directions,how much acoustic power is emitted by the whistle? The threshold of human hearing is 1.0 × 10^-12 W/m². A)0.079 mW B)0.026 mW C)0.26 mW D)0.79 mW E)2.6 mW

Question

Quizplus · Accepted Answer

We can use the inverse square law of sound intensity to find the acoustic power emitted by the whistle. The inverse square law states that the sound intensity decreases in proportion to the square of the distance from the source.

Let P be the acoustic power emitted by the whistle. Then, at a distance of 2.5 km (or 2,500 m), the sound intensity would be:

I = P / (4πr^2)

where r is the distance from the whistle and π is a mathematical constant (pi).

Substituting r = 2,500 m and I = threshold of human hearing = 1.0 × 10^-12 W/m^2, we can solve for P:

1.0 × 10^-12 = P / (4π(2,500)^2)

P = 0.079 mW

Therefore, the acoustic power emitted by the whistle is 0.079 mW, which corresponds to choice A.

A Certain Factory Whistle Can Be Heard Up to a Distance