Question

A sound system is being set up in a gazebo in a park. It needs to produce music so that everyone can hear it. How much power would the speakers need to produce in order for the intensity at 5 meters away to be 1 x 10^-8 W/m^2? (assume the shape of the propagation of the sound wave is a hemisphere)
1.87 x 10^-7 W
1.57 x 10^-6 W
1.14 x 10^-6 W
2.46 x 10^-7 W

Answer 1

Answer:

Power, P=1.57×$10^{-6}$ Watt

Explanation:

Given

Intensity, I=1×$10^{-8}$ W/m²

Distance, r=5 meter

Considering the hemispherical space with radius 5 meter centered on the speaker. Speaker emits sound wave continuously with Power P. Intensity I is constant throughout the space and defined as power per unit area.

I=$\frac{P}{A}$

so, P=I×A

where A is the area of shape of propagation.

since ,shape of propagation is hemispherical

so, A=2×p×r²=2×3.14×5×5=157 m²

P=1×$10^{-8}$×157

P=1.57×$10^{-6}$ Watt