Question

Suppose that sound is emitted uniformly in all directions by a public address system. The intensity at a location 30.2 m away from the sound source is 3.11 x 10^-4 W/m?. What is the intensity at a spot that is 94.1 m away?

Answer 1

Using the inverse square law, the intensity at a distance of 94.1 m from the point sound source is approximately 3.29 x 10⁻⁵ W/m².

Step-by-step explanation:

The intensity of sound at a distance from a point source in a uniform medium can be calculated using the inverse square law, which states that intensity is inversely proportional to the square of the distance from the source.

Therefore, if the intensity at 30.2 m is 3.11 x 10⁻⁴ W/m², then at 94.1 m, the intensity I₂ can be found using the formula:

I₁ / I₂ = (d₂ / d₁)²

Where:

I₁ = 3.11 x 10⁻⁴ W/m² (intensity at 30.2 m)

I₂ = Intensity at 94.1 m (which we need to find)

Rearranging this equation to solve for I₂ gives us:

I₂ = I1 * (d1 / d₂)²

Plugging in the values:

I₂ = (3.11 x 10⁻⁴ W/m²) * (30.2 / 94.1)²

I₂ = (3.11 x 10⁻⁴ W/m²) * (0.321 / 1)²

I₂ = (3.11 x 10⁻⁴ W/m²) * 0.103²

I₂ ≈ 3.29 x 10⁻⁵ W/m²

So the intensity at a distance of 94.1 m from the sound source is approximately 3.29 x 10⁻⁵ W/m².