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)

kjukks1234531 2022-09-25 Answered
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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Answers (1)

Davian Nguyen
Answered 2022-09-26 Author has 9 answers
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 = P 4 π r 2
r = P 4 π I
The provided decible level must first be converted to intensity before we proceed with the computation.
I 10 d B = 1.0 × 10 11 W m 2
Substitute all known values to the equation for r.
r = 0.050 W 4 π 1 × 10 11 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.
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