5. You are investigating the report of a UFO landing in an isolated portion of N

Question

5. You are investigating the report of a UFO landing in an isolated portion of New Mexico, and encounter a strange object that is radiating sound waves uniformly in all directions. Assume that the sound comes from a point source and that you can ignore reflections. You are slowly walking toward the source. When you are 7.5 m from it, you measure its intensity to be 0.11 W/m2·An intensity of 1.0W/m2 is often used as the "threshold of pain". How much closer to the source can you move before the sound intensity reaches this threshold?

Explanation / Answer

Sound Intensity from a point source will obey Inverse Square Law if there are no reflections

Inverse square law states that the sound intensity varies inversly proportional to the square of distance from the source

I = k/r2 where k is a constant

now, as we are given intensity at a given distance, and need to calculate distance for threshold intensity

I1 /I2 = (r2 /r1)2

Substituting the values given

I1 = 0.11W/m2

I2 = 1W/m2

r1 = 7.5m

r2 = ?

0.11/1 = (r2/7.5)2

r2 = 7.5 *(0.11)1/2

r2 = 2.487 m - if we move closer than this, we are listening sound of intensity higher than threshold value

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