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A firework explodes high in the sky. You know you are 400 m away from the explosion and you measure the sound intensity at your location to be 0.01 W/m\(^2\). How much sound power does the explosion emit?

Answer :

Final Answer:

The sound power emitted by the explosion can be calculated using the formula for sound intensity, which is 20,118.72 watts

Explanation:

Given:

Distance from explosion (r) = 400 meters

Sound intensity (I) = 0.01 W/m²

Calculating Area (A) of the Sphere:

The formula for the area of a sphere in 3D space is

A = 4 * π * r²

where r is the radius (distance from the source).

Given the distance from the explosion (r) is 400 meters:

A = 4 * π * (400)²

A = 4 * π * 160,000

A ≈ 2,011,872.44 m²

Determining Sound Power (P) using Sound Intensity Formula:

Sound intensity (I) = Sound power (P) / Area (A)

Rearrange the formula to solve for sound power (P):

P = I * A

Given the sound intensity (I) is 0.01 W/m² and the calculated area (A) is approximately 2,011,872.44 m²:

P = 0.01 W/m² * 2,011,872.44 m²

P ≈ 20,118.72 watts

In summary, the sound power emitted by the explosion is 20,118.72 watts, calculated using the known sound intensity at the given distance and applying the formula for sound intensity, taking into account the area over which the sound spreads.

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Rewritten by : Brahmana