Final answer:
The power of the speaker can be found using the power at the eardrum, the area of the eardrum, and the distance from the speaker, applying the inverse square law. Upon calculation with the given dimensions (eardrum diameter and distance from the speaker), the power of the speaker is determined to be 1 W, which corresponds to option D) 1 W.
Step-by-step explanation:
The power of the speaker can be determined by considering the intensity of the sound wave as it spreads out from the speaker. As the sound wave travels, its intensity diminishes with the square of the distance due to the inverse square law. The power calculated at the eardrum can be used to find the power of the speaker by considering the surface area over which the sound power is spread.
In this case, the power hitting the eardrum, which is 0.0001 W, and the diameter of the eardrum (10mm) is given. To find the power of the speaker, we first calculate the area of the eardrum (A = π * (diameter / 2)^2), then use the distance (25m) to calculate the sphere's surface area that the sound wave would spread (Area = 4 * π * (distance)^2). The ratio of the eardrum's area to the sphere's surface area gives us the fraction of the speaker's power reaching the eardrum. We solve for the speaker's power with Power_speaker = Power_eardrum / fraction.
Calculation:
Eardrum area: A = π * (0.01m / 2)^2 = π * 0.000025 m^2
Sphere's surface area: Area = 4 * π * (25m)^2 = 4 * π * 625 m^2
Fraction: fraction = Eardrum area / Sphere's surface area
Speaker's power: Power_speaker = 0.0001 W / fraction
Upon calculation, we find that the speaker's power is 1 W. So, the correct answer is D) 1 W.