# Inverse square law and infinite intensity

Gold Member

## Main Question or Discussion Point

This is weird, I have no clue on how to solve the following question that I "invented" while walking in the street due to car sounds.
I know that the intensity of sound -let's say the source of sound is a dot/point- decreases as 1/r² do. If I'm at a distance 1 m, I can hear 4 times "stronger" than if I'm at 2 m from the source. Now if I approach the point source I'll be getting an extremely loud sound and if I eventually reach the point-like source, I'd get an infinitely loud sound. I know this doesn't happen in reality so I went wrong somewhere.
Where did I go wrong?!! I really can't see!
Edit: I know I should reach a finite value, say $I_0$. But as r tends to 0, I(r) seems to tend to $\infty$.

Related Classical Physics News on Phys.org
rcgldr
Homework Helper
The issue is that a point source doesn't generate sound, only an object of finite size, and the size of the object and how much it's moving limits how close you can get to the object.

Gold Member
The issue is that a point source doesn't generate sound, only an object of finite size, and the size of the object and how much it's moving limits how close you can get to the object.
If we look at http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html, we make the sphere radius tend to 0, we get huge values for I. Even if r is a very little larger than 0, we still get a HUGE value for I. I'd have thought we'd reach a limiting value, say I_0.

rcgldr
Homework Helper
The closest real world example of this would be an electron and positron approaching each other and annihilating (converted into energy). I don't know how close they get to each other before the transition from matter to energy takes place.

This is actually a profound question. To avoid the complexities of sound being a pressure wave, let's instead look at the electrostatic fields of a point charge (Coulumb's law). The force of one electron on another electron depends on the inverse of the square of the distance between them. So if we were strong enough to push two electrons right on top of each other, there would be an infinite force. But infinities cannot exist in real life, so where did we go wrong?

It turns out that the inverse square law itself is not exactly right. When you get close enough to something, weird quantum effects take over which cause the force to actually not reach infinity, but taper off. In this case, the electrostatic force at very short range gets screened by the vacuum polarization, which is caused by constant electron-positron pair production/annihilation in vacuum allowed by the uncertainty principle. In summary:

Short answer: Weird quantum effects take over for very small distances so that inverse square laws no longer apply exactly.