Question

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

A) 0.00025 W
B) 0.1 W
C) 0.04 W
D) 0.0000625 W

Answer 1

The sound power the explosion emit is D) 0.0000625 W. (option D)

Step-by-step explanation:

To determine the sound power (P) emitted by the firework explosion, you can use the formula:

P = I * A

where I is the sound intensity and A is the area through which the sound is spreading. In this case, you're measuring the sound intensity at your location, which is 0.01 W/m².

Now, consider the area A over which the sound is spreading. Since you are 400m away from the explosion, you can think of the sound spreading in a spherical manner. The surface area of a sphere is given by 4πr², where r is the distance from the source. So, in this case, A = 4π(400)².

Now, substitute these values into the formula to calculate the sound power:

`\[ P = 0.01 \cdot 4\pi(400)^2 \]`

After performing the calculation, the sound power P comes out to be approximately 0.0000625 watts.

Therefore, the correct answer is D) 0.0000625 W.

This calculation illustrates how sound power diminishes with distance from the source, following the inverse square law. (option D)