A person is initially 8 m from a point sound source which emits energy uniformly in all direction at a constant rate. If the intensity of the source is to be halved but the sound is to be as loud as before, what distance should the person be from the source?

Question

Ans: 4 square root 2 m

Answer 1

We know that the intensity of the omnidirectional source is proportional the energy rate and inversely proportional to the square of the distance (inverse square law).
So
1/8² = 0.5/d²

Solve for d.

Answer 2

Intensity is the same? But the question states that it is halved?
I don't quite get it........

Answer 3

The loudness is the amount of power passing through a square meter of area surrounding the source. As you get further from a constant power source, the loudness decreases because the area of a sphere surrounding the source increases.
( You know that. As you get further from a loudspeaker the loudness goes down)
d^2 = .5 * 8 * 8 = 4*4*2
d = 4 * sqrt 2
or about 5.66 meters

Answer 4

I don't understand