A baseball coach shouts loudly at an umpire standing 2.9 m away. If the sound po

Question

A baseball coach shouts loudly at an umpire standing 2.9 m away. If the sound power produced by the coach is 16.82 10-3 W, what is the decibel level of the sound when it reaches the umpire? (Hint: Use the table below.)
dB

Intensity (W/m2) Decibel level (dB) Examples 1.0 10-12 0 threshold of hearing 1.0 10-11 10 rustling of leaves 1.0 10-10 20 quiet whisper 1.0 10-9 30 whisper 1.0 10-8 40 mosquito buzzing 1.0 10-7 50 normal conversation 1.0 10-6 60 air conditioning at 6 m 1.0 10-5 70 vacuum cleaner 1.0 10-4 80 busy traffic, alarm clock 1.0 10-3 90 lawn mower 1.0 10-2 100 subway, power motor 1.0 101 110 auto horn at 1 m 1.0 100 120 threshold of pain 1.0 101 130 thunderclap, machine gun 1.0 103 150 nearby jet airplane

Explanation / Answer

Given power P = 16.82 * 10^-3 W

distance r = 2.9 m

The intansity at this distance is given by

I = P / A

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

I = (16.82 * 10^-3) / (4pi * (2.9)^2))

I = 1.6 * 10^-4 W/m^2

The reference intensity I0 = 1 * 10^-12 W/m^2

The decibel level is measured by

beta = 10 * log(I/I0)

beta = 10 * log(1.6 * 10^-4 / 10^-12)

beta = 82.04 dB

From table this is similar to an example of busy traffic, alarm clock that is approximately 80 dB

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