In a test,a subsonic jet flies overhead at an | vedclass

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(A) The loudness level $L$ in decibels is given by $L = 10 \log_{10} \left( \frac{I}{I_0} \right)$.Since the sound intensity $I$ follows the inverse s

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above $10 \, km$ from ground

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(A) The loudness level $L$ in decibels is given by $L = 10 \log_{10} \left( \frac{I}{I_0} ight)$.Since the sound intensity $I$ follows the inverse square law,$I \propto \frac{1}{r^2}$,where $r$ is the distance (altitude).Thus,$L = 10 \log_{10} \left( \frac{k}{r^2} ight) = C - 20 \log_{10}(r)$,where $C$ is a constant.For the first case: $160 = C - 20 \log_{10}(100)$.For the second case: $120 = C - 20 \log_{10}(x)$.Subtracting the two equations: $160 - 120 = 20 \log_{10}(x) - 20 \log_{10}(100)$.$40 = 20 \log_{10} \left( \frac{x}{100} ight)$.$2 = \log_{10} \left( \frac{x}{100} ight)$.$10^2 = \frac{x}{100} \implies x = 100 	imes 100 = 10,000 \, m = 10 \, km$.Therefore,the plane should fly at an altitude of at least $10 \, km$.

In a test,a subsonic jet flies overhead at an altitude of $100 \, m$. The sound intensity level on the ground as the jet passes overhead is $160 \, dB$. At what altitude should the plane fly so that the ground noise is not greater than $120 \, dB$?

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