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 =
Using the fact that
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.
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