# Intuitive explantion of acoustic edge scattering?

Commonly the phenomena of leading edge noise is explained by the fact that disturbances in the flow scatter as sound. In the figure from Chapter 13 in Aeroacoustics of Low Mach Number Flows, at typical problem description is shown. And following (p. 328)

"Both at and downstream of the trailing edge there can be no pressure jump across the surface (the Kutta condition), and so an acoustic wave field must be added that exactly cancels the incident pressure disturbance for x1>0, x2=0."

In a way it makes sense, however I fail to have an intuitive explanation of the edge scattering. Why exactly is the pressure fluctuation scattered? In particular, why is it typical that edge noise is 'loud' whereas the pressure fluctuations without the body in the flow are not? Moreover, what is meant an 'acoustic' wave field?

## 1. Basics

It's important to leave the view of classical mechanics and to adopt Huygens principle of elementary waves. It's most often demonstrated in 2D water waves, and it holds for any other wave too, like longitudinal waves. So it's a basic concept to know and to apply.

The essence is:

• there are elementary waves, i.e. waves starting at a point and traveling the medium
• for waterwaves you'll see radial or circular waves
• any wave front is a superposition of (an infinite number of) such elementary waves.

This explains very many wave phenomena at a glance:

• it all boils down to picking out elementary waves
• i.e. introducing disturbances, like the end of a wall, or its perforation
• so you replace intution by checking for elementary waves and their superposition (which becomes intuitive after a while, as well)

In (the middle of) this video Huygens' Principle and Diffraction of Waves there are several drawing you (need to) find presented on this subject.

As a rule of thumb for dimension $$d$$ of objects you:

• can view the situation classically (particles), WHEN $$d \gg \lambda$$
• have to adopt the Huygens principle, once $$d \approx \lambda$$ or $$d \le \lambda$$

If you are more interested in room acoustics, look for Schroeder frequency, which gives a more room-specific (= its geometry) frequency ranges for wave effects. In this respect water isn't too different from air.

## 2. Fig. 13.1

This diagram is worth a discussion. On one hand it shows a spatial wave already via $$e^{i k x}$$. It seems to represent propagation to the right on the left side.

For the right side, with the perforations, it's incomplete: it should present two waves traveling in opposite directions, with different amplitudes, i.e. $$a_1 e^{i k x}$$ and $$a_2 e^{-i k x}$$. Instead it seems to argue with a pressure drop $$\Delta p_s$$.

This may be intuitive to some readers, as there must be a pressure difference between a solid (reflecting) part of a wall and a hole in the wall (diffraction). You can argue that any inhomogenous zone, like a regular pressure drop pattern, acts as a scatter center $$\dots$$ creating $$\dots$$ elementary waves.

So at least via this route you are back to Hyugens principle. But you can also argue like in my second sketch below:

• blue: incoming wave
• as it travels over the perforated part ...
• you can't distinguish it from a ssituation, where a skewed blue wave is coming from below (because differences in arrival time)
• which creates elementary waves at each opening (pinkish; their part below the wall not shown !)
• which superpose to the resultant red wavefront
• which states a reflection FROM the perforated part
• which also propagates back to some extend into the left part of Fig. 13.1

## 3. Summary

Abstract into the right effects and concepts. Then you can't go wrong, as intution often fails and fools you.

You can find many examples on this in history. The discussion, whether a wave is a particle, or when particles do behave like waves, is very old, and culmulated into the development of quantum physics, where classical intuition is a guaranteed fail.

• It's worth mentioniong that we're talking about a semi-infinte flat plate, not a perforated one. Nevertheless, I presume your explanations still remains as valid. Additionaly, what exactly causes the scattering to be 'efficient' and audible wheares the disturbance itself is not necessarly? Mar 18, 2023 at 11:44
• Right, I overlooked the semi-infinite plate. // No idea, what the book talks about. Sorry. Mar 18, 2023 at 11:53