A band at a concert is producing music at a power of 4.2 W. A student hears a so

Question

A band at a concert is producing music at a power of 4.2 W. A student hears a sound intensity of 90 dB. How far away is the student from the sound stage? Hint: First calculate sound intensity.

I've been given the answer (18m) I just can't for the life of me figure out how to get there. Not sure how to convert dB to to watts... Thanks in advance for the help!

JUST TO REPEAT: THE ANSWER IS 18 METERS. The professor gave us the answer! This is the third time I've posted this question now, but people keep giving me the wrong answer. All I need to know is the process for getting the answer (18m)

Explanation / Answer

Let I is the intensity of the sound at the location of student.

we know, sound intensity level, beta = 10dB*log(I/Io) (here Io (reference intebsity) = 10^-12 W/m^2)

90dB = 10dB*log(I/10^-12)

90/10 = log(I/10^-12)

9 = log(I/10^-12)

10^9 = I/10^-12

I = 10^9*10^-12

= 10^-3 W/m^2

we know, Intensity = the rate of energy transported per init area

= Power/Area

I = P/(4*pi*d^2)

d^2 = P/(4*pi*I)

d = sqrt(P/(4*pi*I))

= sqrt( 4.2/(4*pi*10^-3))

= 18.23 m <<<<----------------Answer

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