15.0 meters from a sound source that radiates freely in all directions, the intensity is 0.000550 W/m2. What is the rate at which the source is emitting sound energy? answer in Watts.

To find the rate at which the source is emitting sound energy, we can use the formula for intensity:

Intensity (I) = Power (P) / Area (A)

Rearranging this formula, we can find the power of the source:

Power (P) = Intensity (I) * Area (A)

Given that the intensity is 0.000550 W/m² and assuming the sound source radiates equally in all directions, we can calculate the surface area of a sphere with a radius of 15.0 meters.

The surface area of a sphere (A) = 4πr², where r is the radius.

Plugging in the values, we can calculate the surface area:

A = 4π * (15.0 meters)²

A ≈ 2827.43 m²

Now, we can calculate the power emitted by the source:

Power (P) = 0.000550 W/m² * 2827.43 m²

P ≈ 1.555 W

Therefore, the rate at which the source is emitting sound energy is approximately 1.555 Watts.