- #1

ngn

- 20

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- TL;DR Summary
- Given spherical propagation of a sound wave. If pressure = force/area, and the increase in spherical surface area is proportional to r^2, why does pressure not decrease in an inverse square law, given that area is in the denominator of the pressure equation?

Hello,

I am confused as to how to think about sound pressure and the distance from a sound source. Let's assume that a sound wave is omnidirectional and propagating away from a source in a sphere. We have the following two equations:

Pressure = Force/Area

Intensity = Power/Area

Many texts I've read start with intensity and show that since the surface area of the sphere is increasing by 4

Pressure = Force/Area

Given that Area is in the denominator of the pressure equation, I would assume an inverse square law to the change in pressure given the change in distance. However, given that pressure follows an inverse distance law, this must mean that Force increases with distance? Does force change over distance? Or is there a better way of thinking about this?

In short, given only the equation for pressure, how is it that pressure follows an inverse distance law and not an inverse square law? I know that area has r^2 in its equation (unless I'm incorrect when it comes to the area in the pressure equation), and area is in the denominator of the pressure equation. So, what is happening to the force and how should I think about this?

Thank you!

I am confused as to how to think about sound pressure and the distance from a sound source. Let's assume that a sound wave is omnidirectional and propagating away from a source in a sphere. We have the following two equations:

Pressure = Force/Area

Intensity = Power/Area

Many texts I've read start with intensity and show that since the surface area of the sphere is increasing by 4

*π*r^2, and the same quantity of power is distributed across the surface area, that the intensity is decreasing in a 1/r^2 fashion. This is the inverse square law. From there, the texts then explain that power is proportional to the square of Pressure and conclude that pressure then must decrease in a 1/r fashion. This makes sense mathematically. However, I'm confused as to how to think about pressure alone if I knew nothing about intensity and only had the pressure equation. In other words, instead of deriving the change in pressure from what I know about it's relationship to intensity, how would I derive the change in pressure if I knew nothing about intensity, and was just working with a concept of pressure? Here is where I get confused because the equation for pressure is:Pressure = Force/Area

Given that Area is in the denominator of the pressure equation, I would assume an inverse square law to the change in pressure given the change in distance. However, given that pressure follows an inverse distance law, this must mean that Force increases with distance? Does force change over distance? Or is there a better way of thinking about this?

In short, given only the equation for pressure, how is it that pressure follows an inverse distance law and not an inverse square law? I know that area has r^2 in its equation (unless I'm incorrect when it comes to the area in the pressure equation), and area is in the denominator of the pressure equation. So, what is happening to the force and how should I think about this?

Thank you!