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.Calculate a reasonable estimate for the sound intensity that the other student measures. 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 $I$ at a distance $r$ from a point source in a free field varies inversely with the square of the distance, according to the inverse square law: $I \propto \frac{1}{r^2}$. Given the initial intensity $I_1 = 1.1 \times 10^{-7} \, \text{W/m}^2$ at $r_1 = 3.0 \, \text{m}$, and the distance to the second student $r_2 = 4.0 \, \text{m}$, the intensity $I_2$ at $r_2$ can be found using the formula:$$\frac{I_1}{I_2} = \frac{r_2^2}{r_1^2}$$Solving for $I_2$:$$I_2 = I_1 \times \frac{r_1^2}{r_2^2} = 1.1 \times 10^{-7} \times \frac{3.0^2}{4.0^2} = 1.1 \times 10^{-7} \times \frac{9}{16} = 6.2 \times 10^{-8} \, \text{W/m}^2$$

Two People Are Talking at a Distance of 3