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 · Accepted Answer

Given:decibel level = 10dBP=0.050WSolution: 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        mThe 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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