Question

Suppose that a public address system emits sound uniformly in all directions, and that there are no reflections. The intensity at a location 27 m away from the sound source is 3.0 x 10⁴ W/m². What is the intensity at a spot that is 74 m away?

a) 7.1 x 10³ W/m²
b) 1.1 x 10⁴ W/m²
c) 5.6 x 10³ W/m²
d) 2.5 x 10⁴ W/m²

Answer 1

Using the inverse square law for sound intensity, we can find the power being emitted from the source with the given intensity at 27 meters and then calculate the intensity at 74 meters from the source to find the correct answer.

Step-by-step explanation:

To find the intensity at a different distance from a sound source, we use the inverse square law which states that the intensity of a sound is inversely proportional to the square of the distance from the source. The formula used to calculate this relationship in the case of a point source spreading sound uniformly in all directions is:

I = P / (4πr²)

where I is the intensity, P is the power of the sound source, and r is the distance from the source.

Given that the intensity at 27 m is 3.0 x 10⁴ W/m², we can find the power P of the sound source by rearranging the formula:

P = I × (4π × (27 m)²)

With the power P found, we can now calculate the intensity at 74 m using the same formula:

I = P / (4π × (74 m)²)

By plugging in the values, we can calculate the new intensity and find the correct answer option.