Final answer:
To find the total sound power P emitted by the source, we need to find the intensity at the speaker and the distance at which the intensity is 0.1 W/m². The calculation for the distance is provided using the inverse square law.
Step-by-step explanation:
To find the total sound power P emitted by the source, we need to first find the intensity at the speaker. Since the speaker emits sound uniformly in all directions, the intensity at the speaker is the same as the given intensity of 5.0 × 10−3 W/m² at a distance of 12 m from the source.
Next, we can use the inverse square law to find the distance at which the intensity is 0.1 W/m². The inverse square law states that the intensity of a spherical wave decreases with the square of the distance from the source. So, if the intensity is 0.1 W/m² at a distance of 12 m, the intensity would be 0.1*(12/√(d))² W/m² at a distance d from the source. Solving for d, we find d = 12*√(0.1/5.0 × 10−3) m.
Therefore, the total sound power P emitted by the source can be found using the equation P = IV, where I is the intensity at the speaker and V is the volume of the speaker. Since the intensity at the speaker is 5.0 × 10−3 W/m² and the volume of the speaker depends on its dimensions, we need further information to calculate the exact value of P.