Question

A rocket in a fireworks display explodes high in the air. The sound spreads out uniformly in all directions. The intensity of the sound is 4.16 x 10^-6 W/m? at a distance of 133 m from the explosion. Find the distance (in m) from the source at which the intensity is 2.25 x10^-6 W/m?

Answer 1

Using the inverse square law, the distance from the source at which the sound intensity is 2.25 x 10⁻⁶ W/m² can be found to be approximately 31.43 m.

Step-by-step explanation:

To find the distance from the source at which the sound intensity is 2.25 x 10⁻⁶ W/m², we can use the inverse square law. The intensity of sound is inversely proportional to the square of the distance from the source.

So if the intensity is 4.16 x 10⁻⁶ W/m² at a distance of 133 m, we can set up the following equation:

4.16 x 10⁻⁶ / (133²) = 2.25 x 10⁻⁶ / (x²)

Cross-multiplying and solving for x, we get:

x² = (133² * 2.25 x 10⁻⁶) / 4.16 x 10⁻⁶

x²= 987.81

Taking the square root of both sides, we find:

x = 31.43 m

Therefore, the distance from the source at which the intensity is 2.25 x 10⁻⁶ W/m² is approximately 31.43 m.