Inverse square law and infinite intensity

In summary, the conversation discusses the concept of sound and the decrease in intensity as distance from the source increases. However, the speaker realizes that this does not hold true for point sources, as they would create infinitely loud sounds. This leads to a discussion about the limitations of classical physics and the role of quantum effects, specifically vacuum polarization, in explaining the behavior of point sources at very small distances.
  • #1
fluidistic
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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 [itex]I_0[/itex]. But as r tends to 0, I(r) seems to tend to [itex]\infty[/itex].
 
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  • #2
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.
 
  • #3
rcgldr said:
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.

Thanks for the reply.
What about if we replace the word sound by EM radiation?
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.
 
  • #4
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.
 
  • #5
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.

Long answer: Read up on http://en.wikipedia.org/wiki/Vacuum_polarization" [Broken]
 
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  • #6
Thanks for the information.
So basically we can't deal with this question with classical physics? :/
I'm going to bed now, will think about this question...
 

1. What is the inverse square law?

The inverse square law is a principle that states that the intensity of a physical quantity (such as light, sound, or gravitational force) is inversely proportional to the square of the distance from the source. This means that as the distance from the source increases, the intensity decreases exponentially.

2. How is the inverse square law applied in science?

The inverse square law is used to describe a variety of phenomena in science, including the intensity of light from a point source, the strength of an electric field, and the gravitational pull between two objects. It is also used in fields such as photography, acoustics, and astronomy to understand how the intensity of a physical quantity changes with distance from its source.

3. What is the significance of the inverse square law?

The inverse square law is significant because it helps us understand how the intensity of a physical quantity changes with distance from its source. It allows us to make predictions and calculations, and it also helps us design experiments and technologies that rely on the principles of the inverse square law.

4. Can the inverse square law be applied to infinite distances?

No, the inverse square law is only valid for finite distances. As the distance approaches infinity, the intensity will approach zero, but it will never actually reach zero. This is because the inverse square law assumes that the source is a point source, and in reality, all sources have a finite size.

5. What is infinite intensity and is it possible?

Infinite intensity is a theoretical concept that describes the intensity of a physical quantity at a point that is infinitely close to its source. In other words, it is the limit of the intensity as the distance approaches zero. It is not possible to achieve infinite intensity in the real world, as it would require an infinitely large source, which is not physically possible.

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