# A certain microphone placed in the ocean is sensitive to sounds emitted by dolphins. Io produce a Usable signal, sound waves striking the microphone must have a decibel level of 10 dB. If dolphins emit sound waves with a power of 0.050 W, how far can a dolphin be from the microphone and still be heard? (Assume the sound waves propagate spherically, and disregard absorption of the sound waves)

A certain microphone placed in the ocean is sensitive to sounds emitted by dolphins. Io produce a Usable signal, sound waves striking the microphone must have a decibel level of 10 dB. If dolphins emit sound waves with a power of 0.050 W, how far can a dolphin be from the microphone and still be heard? (Assume the sound waves propagate spherically, and disregard absorption of the sound waves)
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Davian Nguyen
Given:
decibel level = 10dB
P=0.050W
Solution: The distance from the sourcer can be expressed in terms of intensity I and power P by rearranging the formula for the intensity of a spherical wave:
$I=\frac{P}{4\pi {r}^{2}}$
$r=\sqrt{\frac{P}{4\pi I}}$
The provided decible level must first be converted to intensity before we proceed with the computation.
${I}_{10dB}=1.0×{10}^{-11}\frac{W}{{m}^{2}}$
Substitute all known values to the equation for r.
$r=\sqrt{\frac{0.050W}{4\pi 1×{10}^{-11}\frac{W}{{m}^{2}}}}$
$r=2.0×{10}^{4}m$
The dolphin can be $2.0×{10}^{4}m$ away from the microphone and still be heard.
Result:
The dolphin can be $2.0×{10}^{4}m$ away from the microphone and still be heard.