Final answer:
The power of the source is calculated using the equation for intensity of a spherical wave and the surface area of a sphere at a given distance. Knowing the intensity at 4.90 m allows us to work backward to find the power by multiplying the intensity by the area.
Step-by-step explanation:
To find the power of the source, we use the fact that the intensity of a spherical wave from a point source decreases with the square of the distance. Since the intensity at a distance of 4.90 m is 2.91×10⁻⁴ W/m², we can determine the power using the equation intensity (I) = power (P) / area (A), where the area (A) is the surface area of a sphere with radius equal to the distance from the source. Thus, the area A at a distance of 4.90 m is 4π(4.90 m)².
Calculating this gives: A = 4π(4.90²) = 4π(24.01) m². The power, P, can then be found by rearranging the equation to P = I × A, which yields P = (2.91×10⁻⁴ W/m²) × A. Substituting the known values gives us the power of the source.