A certain factory whistle can be heard up to a distance of 9.8 km.Assuming that the acoustic output of the whistle is uniform in all directions,at what distance from the factory is the intensity level of the whistle sound equal to 25 dB? The threshold of human hearing is 1.0 × 10^-12 W/m². A)550 m B)660 m C)830 m D)940 m E)1,100 m

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Quizplus · Accepted Answer

The intensity level is given by:$$ \beta = 10 \log_{10} \frac{I}{I_0} $$where I is the intensity of the sound and I0 is the threshold of human hearing.We are given that I0 = 1.0 × 10-12 W/m2 and β = 25 dB.Substituting these values into the equation, we get:$$ 25 = 10 \log_{10} \frac{I}{1.0 	imes 10^{-12}} $$Solving for I, we get:$$ I = 1.0 	imes 10^{-10} 	ext{ W/m}^2 $$The intensity of the sound decreases with the square of the distance from the source.Therefore, the distance from the factory at which the intensity level is 25 dB is:$$ d = \sqrt{\frac{I_0}{I}} = \sqrt{\frac{1.0 	imes 10^{-12}}{1.0 	imes 10^{-10}}} = 550 	ext{ m} $$

A Certain Factory Whistle Can Be Heard Up to a Distance