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 of the speakers = 1.57 $\times 10^{-6} W$

Explanation:

There are speakers setup in a park and we have to find the power it would require to have intensity of sound to be $10^{-8} W/m^2$ at a distance of 5 meter.

In one dimension the intensity is constant as the wave travels. In two or three dimensions, however, the intensity decreases as you get further from the source.

Intensity is inversely proportional to the square of the distance from the point of sound production.

Here area = 2$\times \pi \times r^{2}$

area = 157 $m^{2}$

$Intensity = \frac{Power}{Area}$

$Power = intensity \times area$

Power = $10^{-8} \times 157Power = 1.57 [tex]\times 10^{-6} W$