You are standing at a distance d from a point source that emits sound isotropically (equally in all directions). You walk 50.0 m toward the source and observe that the intensity of the waves has doubled. Calculate the distance d.
The distance d = m.
Using the fact that
or
Choose +d,
If we choose –d, we will get a distance of 29.2 m, which is less than our walking distance of 50 m toward the source, which is obviously wrong. The correct answer is d = 171 m.
The relationship between the intensity of sound, at a distance r away from the source, and the power delivered by the source is
Let us apply this relationship in our situation.
The intensity a distance d from the source is
Since the power of the source Ps is constant, the intensity a distance (d-50) from the source is
