A sound registers 77.9 decibels on a detector. What is the intensity in W/m2? Assume the threshold of human hearing is 1.0×10-12 W/m2. Give your answer in picowatts/m2.

1 pW = 1×10-12 W/m2

77.9 = 10 log I/10^-12 = log I/10^-11

7.79 = log (I*10^12)

10^7.79 = I * 10^12

6.17 * 10^7 = I * 10^12

I = 6.67 * 10^-5 W/m^2

To determine the intensity of the sound in W/m2, you can use the formula:

I = 10^((dB - dB0)/10),

where I is the intensity in W/m2, dB is the decibel level, and dB0 is the reference threshold of human hearing in decibels.

In this case, the decibel level is given as 77.9 dB, and the threshold of human hearing is 1.0×10^-12 W/m2, which is equivalent to 10^(-12/10) = 10^-1.2 dB.

Substituting these values into the formula:

I = 10^((77.9 - (-1.2))/10)
= 10^(79.1/10)
= 10^7.91

So the intensity of the sound in W/m2 is approximately 79432823.56 W/m2.

Now, to convert this intensity to picowatts/m2, we multiply by the conversion factor:

1 W/m2 = 1×10^12 pW/m2.

Therefore:

Intensity in picowatts/m2 = 79432823.56 W/m2
= 79432823.56 × 10^12 pW/m2
= 7.943282356 × 10^19 pW/m2.

Thus, the intensity of the sound in picowatts/m2 is approximately 7.943282356 × 10^19 pW/m2.