A source of sound (1200 Hz) emits uniformly in all directions. An observer 2.99 m from the source measures a sound level of 41.1 dB. Calculate the average power output of the source.

To calculate the average power output of the source, we need to use the relationship between sound level and power.

The sound level, measured in decibels (dB), is given by the formula:

L = 10 log10(I/I0)

Where L is the sound level in decibels, I is the intensity of the sound wave, and I0 is the reference intensity (which is usually set to 10^-12 W/m^2).

In this case, the sound level L is given as 41.1 dB. We can convert this value to intensity I by rearranging the formula:

I = I0 * 10^(L/10)

Substituting the given values, we have:

I = (10^-12 W/m^2) * 10^(41.1/10)
= (10^-12 W/m^2) * 10^4.11

Next, we need to calculate the power output using the formula:

Power = Intensity * Area

The given problem does not provide information about the area over which the sound is spreading. Typically, the area is assumed to be a sphere centered at the source, with the observer at a radius of 2.99 m. Therefore, the area of the sphere can be calculated using the formula:

Area = 4πr^2

Substituting the given radius, we have:

Area = 4 * π * (2.99 m)^2

Now, we can calculate the power output by multiplying the intensity by the area:

Power = Intensity * Area

Finally, we can substitute the values to calculate the average power output of the source.