Question

4) The intensity I of a sound (in watts per square meter) varies inversely with the square of the distance d (in meters) from the sound's source. At a distance of 2 meters from the stage, the intensity of the sound at a Shostakovich opera is about 12 watts per square meter. What is the intensity of the sound, rounded to the nearest hundredth, you hear if you are sitting 15 meters from the stage?

Answer 1

At a distance d 1 = 2 m → d 1² = 4 m²
At a distance d 2 = 15 m → d 2² = 225 m²
We can use the proportion:
↑                                                    ↓
4 m² ----------------------- 12 W / m²
225 m² -------------------- x  W / m²
-----------------------------------------------
4 : 225 = x : 12
225 x = 4 · 12
225 x = 48
x = 48 : 225
x = 0.21333 ≈ 0.21 W / m²
Answer: The intensity of the sound is 0.21 W / m².