A John measures a sound intensity to be at 86dB in his location. If the source o

Question

A John measures a sound intensity to be at 86dB in his location. If the source of the sound is r = 15 m away from John and the threshold of human hearing is at the intensity I_th = 9.80 times 10^-13 W/m^2, compute (a) the intensity of the sound at John's location in Watts per square meter. (b) If the average area of the human eardrum is 8 times 10 mm, calculate the power received by one of John's ear: assume that the eardrum in his ear oriented to receive the sound emitted by the source. (c) Compute the power emitted by the source of the sound assuming that the source is omnidirectional.

Explanation / Answer

Io = 9.8*10^-13w/m^2

r=15m

dB=86dB

so, dB=10log(I/Io)

or, 86=10log(I/ 9.8*10^-13)

or, (a) I = 3.9*10^-4 W/m^2

3.9*10^-4 w/m^2 is incident on an area of 80mm^2 or 8*10^-5 m^2

so,(b) power received by John's ear is 3.9*10^-4 *  8*10^-5 = 3.12*10^-8 W

from the inverse proportionality, I=P/4*pi*r^2

or,(c) P = 3.9*10^-4 * 4*pi*15^2 = 1.102 W

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