Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 × 10^-7 W/m².Another student is 4.0 m away from the talkers.What sound intensity does the other student measure? Assume that the sound spreads out uniformly and undergoes no significant reflections or absorption. A) 6.2 × 10^-8 W/m² B) 1.5 × 10^-7 W/m² C) 8.3 × 10^-8 W/m² D) 7.8 × 10^-7 W/m² E) 2.5 × 10^-8 W/m²

Question

Quizplus · Accepted Answer

The sound intensity follows an inverse square law, meaning that it decreases with the square of the distance from the source. The other student is 4.0 m away, which is 1.3 times the distance from the source compared to you. Therefore, the sound intensity at the other student's location is (1/1.3)^2 = 0.59 times the sound intensity you measured. Using this factor to scale the original sound intensity gives:

1.1 × 10^-7 W/m^2 x 0.59 = 6.49 x 10^-8 W/m^2

This can be rounded to 6.2 x 10^-8 W/m^2, which is equivalent to 6.2 x 10^-8 W/m^2 / 10^4 = 6.2 x 10^-12 W/cm^2. In scientific notation with the correct significant figures, the answer is 6.2 x 10^-8 W/m^2 or choice A.

Two People Are Talking at a Distance of 3