Originally Posted by noah katz
I think you might be mixing up acoustic and Helmholz resonance.
I do not believe so.
I used Helmholtz as most people seem to equate them with a ported enclosure, and are able to understand that you have to account for pressure differences at the ends of the duct, which are caused by differences in mouth geometry/boundary position, and that this alters the effective length of the duct. This is what I was getting at, the pressure chamber can be left off here.
Another example could be a simple open end air column formula, but I seem to loose everyone when I bring up air columns, and it requires some tweaking as well.
It was a simplified analogy, that I thought would get the concept across to the greatest number of people.
The thing that is key is that the wave is not forced to reflect off the side at the bend back up the horn, unless the corner dimensions are greater than 1/4WL. It has somewhere to "flow." What you end up with is defined by opposing pressure zones created by the drag of the extreme corner point, and the lesser pressure area on the inside of the bend.
If the wave is small enough it sees the corner as a "wall," and is turned back around.
With a flared horn the measurements at each corner will be different, and will effect the frequencies differently than the last.
If you look at the path time around the bend, the inside track has less distance to cover, while the outside one is forced to cover more distance. This means that when both sides hit the end the inside track is further ahead in time/phase. Where the distance is ahead by 1/2 wave length the two sections are out of phase with one another, and cancel each other out. Well, the middle area blends it all together, so it isn't a total cancellation, just a nice big dip.
Standing waves from parallel walls are your standard SW fare.