Final answer:
The power output of a point source with a given intensity at a certain distance is calculated using the intensity and area of the sphere through which the sound is spreading. However, in this instance, the calculated power output does not match any of the provided options, indicating an error in the question.
Step-by-step explanation:
The sound intensity 5.0 m from a point source is 0.50 W/m². The power output of the source is calculated using the relationship between intensity, power, and distance for a point source emitting sound uniformly in all directions. Intensity (I) is power (P) divided by the surface area of a sphere (4πr²).
To find the power output we can use the formula:
I = P / (4πr²).
By rearranging the formula to solve for P, we get P = I × (4πr²).
Substituting the given values:
P = 0.50 W/m² × (4π × (5.0 m)²) = 0.50 W/m² × 4π × 25 m² = 0.50 W/m² × 314 m² = 157 W. However, this is not one of the given options, so there must be an error in the values or calculations presented in the question.