2-5 Intensity and sound level

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.

Answer

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 P_{s} is
constant, the intensity a distance (d-50) from the source is

Example 1