Sound intensity and ocean microphone

[Corky]

The problem states:
A microphone in the ocean is sensitive to sounds emitted by popoises. To produce a usable signal , sound waves striking the microphone must have an intesity of 10.6 dB. If porpoises emit sound waves with a power of 0.0502 W, how far can a porpoise be from the microphone and still be heard? Disregard ansorbtion of sound waves by water.

I tried putting 10.6 decibels in the equation dB=10Log(I/Io)
and I solved for intensity to be 1.148E-10W/m^2

I then used that number in the I = P/4pi r^2 formula.
Solving for r I got 5.89E+3m.

But the right answer it the book is 1.87E+4
Can anyone tell me where I went wrong??

 

[ShawnD]

Originally posted by Corky
A microphone in the ocean is sensitive to sounds emitted by popoises. To produce a usable signal , sound waves striking the microphone must have an intesity of 10.6 dB. If porpoises emit sound waves with a power of 0.0502 W, how far can a porpoise be from the microphone and still be heard? Disregard ansorbtion of sound waves by water.

10log(I/(10^-12)) = 10.6
log(I/(10^-12)) = 1.06
I/(10^-12) = 10^1.06
I = 1.148e-11

I = P/(4pi r^2)
r^2 = P/(4pi I)
r^2 = 0.0502/(4pi 1.148e-11)
r^2 = 3.4797e8
r = 18654m
r = 1.87e4

I think the error was in what you thought the value for I was. Your I is 10x as big as mine.

 

[Corky]

Nice thanks