Hi All,
I had read somewhere that there's a formula which relates pipe length to circumference and cross sectional area for determining the Q of a pipe. Can anyone provide the formula or point me to a link? I tried to Google this, but was unsuccessful.
I'm evaluating a design for a Hegeman style subwoofer, but need to adjust the pipe dimensions to better fit a larger driver. I'd like to find out if there are any constraints I'll need to contend with.
I had read somewhere that there's a formula which relates pipe length to circumference and cross sectional area for determining the Q of a pipe. Can anyone provide the formula or point me to a link? I tried to Google this, but was unsuccessful.
I'm evaluating a design for a Hegeman style subwoofer, but need to adjust the pipe dimensions to better fit a larger driver. I'd like to find out if there are any constraints I'll need to contend with.
Greets!
The basic material Q I'm familiar with is = (SQRT SoS)/net po, so a 1 m long pipe with a 0.1 m dia = (SQRT~342)/((1*(0.1^2*pi/4)*1.21) = ~1946. Then there's a pipe cut-off Q = Fc/F as discussed here: http://mmd.foxtail.com/Archives/Digests/199911/1999.11.05.03.html
GM
The basic material Q I'm familiar with is = (SQRT SoS)/net po, so a 1 m long pipe with a 0.1 m dia = (SQRT~342)/((1*(0.1^2*pi/4)*1.21) = ~1946. Then there's a pipe cut-off Q = Fc/F as discussed here: http://mmd.foxtail.com/Archives/Digests/199911/1999.11.05.03.html
GM
Speed of Sound and depending on who you ask/read, it will vary a bit, but FWIW in case you want to use MJK's TL simming program: 342 m/sec, the one I used in the example
po = weight of air, which varies with temp and humidity, which MJK uses 1.21 kg/m^3
Neither, it's the quality factor of the air mass 'slug', which is what you asked for by description, but I doubt it's what you think you need to accomplish your task. Not knowing the design details of the sub I can't help further beyond saying that scaling rarely works well without knowing how to scale everything, including the driver's specs.
po = weight of air, which varies with temp and humidity, which MJK uses 1.21 kg/m^3
Neither, it's the quality factor of the air mass 'slug', which is what you asked for by description, but I doubt it's what you think you need to accomplish your task. Not knowing the design details of the sub I can't help further beyond saying that scaling rarely works well without knowing how to scale everything, including the driver's specs.
To revive a very old thread because I, too, am interested in experimenting with 1/4 wave tubes...
The OP was asking how to calculate the Q of tubes in order to design a Hegeman Subwoofer: an enclosure that uses a series of tuned 1/4 wave resonators (tubes) to load a woofer. An article in AudioXpress describing said enclosure is attached.
In it, the author says the tubes in a 4-tube design should have a "Q of 2.5 to 3" and the tubes in a 6-tube designs should have "a Q of 4 to 5".
What formula would one use to calculate the Q of tubes for this purpose?
The OP was asking how to calculate the Q of tubes in order to design a Hegeman Subwoofer: an enclosure that uses a series of tuned 1/4 wave resonators (tubes) to load a woofer. An article in AudioXpress describing said enclosure is attached.
In it, the author says the tubes in a 4-tube design should have a "Q of 2.5 to 3" and the tubes in a 6-tube designs should have "a Q of 4 to 5".
What formula would one use to calculate the Q of tubes for this purpose?
OK, then I presume the math behind the link I previously posted:Mechanical Music Digest - Archives
That was my first thought, but it doesn't seem to jive with Morton.
His 21.5Hz tube, which he says achieves a Q of around 3 to 4 when stuffed, is 2.75x3.75 inches. That's a perimeter of 13 inches, corresponding to a wavelength of ~1043 Hz. So, Q when open is:
1043/21.5 = 48.5
Awfully far from the goal, requiring a *lot* more stuffing than Morton used.
Morton also said that:
"The Q values required for [a] six tube design approach the maximum values that are obtained in a tube of this design leaving little room for adjustment..."
Not if we're calculating Q correctly, it doesn't. It leaves vast room for adjustment.
Of course, I say all that assuming the Q=fc/f works the same for a rectangular tube. But circular tubes of the same similar cross-sectional area yields a similar result. They would have to be enormous to get the Q down to something workable.
So I'm stumped.
His 21.5Hz tube, which he says achieves a Q of around 3 to 4 when stuffed, is 2.75x3.75 inches. That's a perimeter of 13 inches, corresponding to a wavelength of ~1043 Hz. So, Q when open is:
1043/21.5 = 48.5
Awfully far from the goal, requiring a *lot* more stuffing than Morton used.
Morton also said that:
"The Q values required for [a] six tube design approach the maximum values that are obtained in a tube of this design leaving little room for adjustment..."
Not if we're calculating Q correctly, it doesn't. It leaves vast room for adjustment.
Of course, I say all that assuming the Q=fc/f works the same for a rectangular tube. But circular tubes of the same similar cross-sectional area yields a similar result. They would have to be enormous to get the Q down to something workable.
So I'm stumped.
Well you can go at it backwards too but, in the end IMO, this stuff is always about the resistance and requires measurement. It's nice to bang-out rough inertances and compliances and have resistance models--and I'm not saying that's not useful--but absent really solid data on the acoustic resistance piece, empiricism would seem ordained to hit final Q targets anyway. Irrespective of the sophistication of modeling all the "air stuff", it's the resistance modeling that's the bugger.
Drat! this is archived link of the one I posted in 2007 since I get a strong message from Avast to use only at great risk.
Here's the design math I thought I posted, but way more intense than I'm willing to tackle, so look forward to any insights and hopefully matches up with the article: Q of pipes
