Final answer:
The sound intensity at a distance of 1290 m from a source with an initial intensity of 0.160 W/m² at a distance of 53.0 m is approximately 2.69 × 10⁻´ W/m², calculated using the inverse square law for sound intensity.
Step-by-step explanation:
The question asks to determine the sound intensity at a distance of 1290 m from a source, given that the intensity is 0.160 W/m² at a distance of 53.0 m. Assuming the sound spreads out uniformly in all directions (spherically), and ignoring any absorption or reflection of the sound, the intensity at a given distance from the source can be found using the inverse square law for sound intensity:
I = I0 × (d0/d)²
where I is the intensity at distance d, I0 is the initial intensity at distance d0. Plugging in the values:
I = 0.160 W/m² × (53 m / 1290 m)² = 0.160 W/m² × (0.04109)² ≈ 2.69 × 10⁻´ W/m²
Therefore, the sound intensity at 1290 m is approximately 2.69 × 10⁻´ W/m².