A clarinet is a quarter wave resonator and overblows at a 12th, and a saxophone is a half wave resonator and overblows at an octave. The explanation for this is that the clarinet is a cylindrical tube closed at one end, and a saxophone is a conical tube closed at one end. I confess that I cannot intuitively grasp why this creates the difference.
But taking it as so, what about a standard expanding tqwt. I have been shown that this is a parabolic expansion. The fundamental resonance of the tube, in terms of the length of the tube, is between a quarter and a half wavelength. What happens to the harmonics?
But taking it as so, what about a standard expanding tqwt. I have been shown that this is a parabolic expansion. The fundamental resonance of the tube, in terms of the length of the tube, is between a quarter and a half wavelength. What happens to the harmonics?
It's a conical expansion by definition, hence only parabolic when built with flat [dividers] parallel sides.
Work through all these links and you'll know [or at least be exposed to] all you'll need to know re the basics of TL/horn wave propagation [and the rest of the site will keep you busy for probably years to come if interested]: Resonances of open air columns
GM
Work through all these links and you'll know [or at least be exposed to] all you'll need to know re the basics of TL/horn wave propagation [and the rest of the site will keep you busy for probably years to come if interested]: Resonances of open air columns
GM
Thanks for that GM. At first glance I could not see anything specifically about parabolic expansion tubes. But it did jog my memory of this:
http://www.quarter-wave.com/TLs/Alignment_Tables.pdf
This shows that in order to achieve the same resonant frequency with an expanding tube, the tube has to be longer. (and a contracting tube shorter) Looking at response curve of the harmonics does seem to show an interesting aspect. The harmonics are not multiples of the fundamental resonance, but seem related to the length of the tube. Compare the (estimated) harmonics of the straight tube, the expanding tube, and the contracting tube. All have a 30Hz resonance.
Straight, length 2.76 metres: 30,90,150,210, etc, just as expected
Expanding, length 3.92 metres: 30,74,120,160,200
Contracting, length 1.71 metres: 30,130,230,330,430
When I see that the quarter wave resonant frequencies of straight tubes of those lengths are 21Hz, 30Hz, and 48Hz, it looks that the tube length dictates the higher harmonics. So I end up with another question, why does the geometry of the tube change the fundamental, but not the harmonics? Or is my interpretation simply wrong.
http://www.quarter-wave.com/TLs/Alignment_Tables.pdf
This shows that in order to achieve the same resonant frequency with an expanding tube, the tube has to be longer. (and a contracting tube shorter) Looking at response curve of the harmonics does seem to show an interesting aspect. The harmonics are not multiples of the fundamental resonance, but seem related to the length of the tube. Compare the (estimated) harmonics of the straight tube, the expanding tube, and the contracting tube. All have a 30Hz resonance.
Straight, length 2.76 metres: 30,90,150,210, etc, just as expected
Expanding, length 3.92 metres: 30,74,120,160,200
Contracting, length 1.71 metres: 30,130,230,330,430
When I see that the quarter wave resonant frequencies of straight tubes of those lengths are 21Hz, 30Hz, and 48Hz, it looks that the tube length dictates the higher harmonics. So I end up with another question, why does the geometry of the tube change the fundamental, but not the harmonics? Or is my interpretation simply wrong.
You're welcome!
Did you check out the 'wave', 'resonance' concepts sections in my link?
Re parabolic expansion, I dismissed it as we normally have no use for them except as a consequence of box construction type and even then doesn't alter the response enough compared to conical to be an issue in the bass.
GM
Did you check out the 'wave', 'resonance' concepts sections in my link?
Re parabolic expansion, I dismissed it as we normally have no use for them except as a consequence of box construction type and even then doesn't alter the response enough compared to conical to be an issue in the bass.
GM
A standard TQWT (aka Voigt pipe) is a conical expansion. A Metronome is a parabolic expansion, but in most practical realizations close enuff to be modeled as an ML-Voigt.
dave
Didn't say it was, just is near enough conical that designing with conical, but built parabolic and the performance difference is typically too negligible to be a concern except when 'wringing' the last dB out of a prosound app alignment.
GM
The Metronome expands in both planes, so is conical; a typical TQWT such as the BIB or simple [tapped] TLs, horns with its parallel sides and straight divider board is parabolic. To make it conical, the divider must be curved on both sides so two plus filler is required, wasting space, adding unneeded complexity.
Use Hornresp's default to design a conical [con] folded TL or TH, save and convert to parabolic [par] to see the theoretical response difference. Many early TH designs posted used conical and while measured response showed a bit more accuracy when redone as parabolic, real world results were close enough either way.
GM
Actually that is a parabola thru the origin. y=ax^2 + bx + c is a parabola where a determines how narrow it is and Bx, and c are an offset from the origin.
dave
I'll take your word for it. 
Here's my normal frame of reference [scroll down]: Folded horn speaker design - explanation and calculator
GM
Here's my normal frame of reference [scroll down]: Folded horn speaker design - explanation and calculatorGM
Again, I only know real world results, you'll have to ask folks who can do the higher math required, which Dave and others here may know and of course MJK over on his yahoo group.
Note too that speaker/horn cabs are typically truncated to a greater or lesser extent at one or both ends, especially in the mid-bass on down, where only a small part of its HF BW is horn loaded to match up with the mid driver/horn, so the various flares can be very similar in reality in its TL modes BW.
GM
Note too that speaker/horn cabs are typically truncated to a greater or lesser extent at one or both ends, especially in the mid-bass on down, where only a small part of its HF BW is horn loaded to match up with the mid driver/horn, so the various flares can be very similar in reality in its TL modes BW.
GM
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