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Old 14th September 2012, 03:18 AM   #1
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Default formula for Q of Helmholtz resonator

Can anyone point me to a formula for the Q of a Helmholtz resonator?
TIA
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Old 14th September 2012, 03:48 AM   #2
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Is it the second formula at (15) p5 in this paper?:

http://www.itwm.fraunhofer.de/filead.../bericht10.pdf
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Old 14th September 2012, 03:52 AM   #3
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found it halfway down this page:
Acoustics/Flow-induced Oscillations of a Helmholtz Resonator - Wikibooks, open books for an open world
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Old 14th September 2012, 05:24 AM   #4
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If the correct formula is Q=2pi SQRT(Vb * ((port length/port area) cubed))
then Q is proportional to port length and inversely proportional to the port cross section area, right?
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Old 14th September 2012, 07:03 AM   #5
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what I'm thinking is that different port length/cross section combinations (for the same freq & box size) will give different Qs, thus having different effects on the bandwidth & level of bass freqs, yet changing the ratios of port length/cross section while keeping everything else constant in box sim programs doesn't have any effect on the freq response shown, what am I missing?
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Old 14th September 2012, 07:27 AM   #6
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I was to say 'group delay' but there are no speakers involved .
Though a certain delay takes place in the process of resonance
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Old 14th September 2012, 12:42 PM   #7
sreten is offline sreten  United Kingdom
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Hi,

The Q of a port treated as a hemholtz resonator has very
little to do with the Q of a vented boxes bass alignment,
as its a coupled resonating system, not one system.

Basically the port "q" simply should be high enough not
to matter much. The main damping in the system comes
from the driver. Damped ports (e.g. drinking straws)
are hard to model AFAIK, best done empirically.

rgds, sreten.
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Old 14th September 2012, 09:37 PM   #8
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Re:'The Q of a port treated as a hemholtz resonator has very
little to do with the Q of a vented boxes bass alignment" - so i guess I'm trying to quantify that 'very little'

re:' the port "q" simply should be high enough' - don't you mean low enough? (I guess that could be a preference thing though, this is part of what I'm trying to explore), and again, it would be good to quantify 'enough'.

(Just to make it clear, I'm not talking about the Q of a port as a resonating pipe, but the Q of the whole box/port combo)
Perhaps I need to wade though those Thele/Small papers again, wish my maths was up to it...
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Last edited by PeteMcK; 14th September 2012 at 09:44 PM.
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Old 14th September 2012, 09:56 PM   #9
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let me put up a hypothesis to be shot down (Subjective language warning): Ignoring the effects of port turbulence & reflections coming through the port, a short port giving a lower helmholtz resonance Q will sound more natural than a long port that results in a higher Q ...???
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Old 18th September 2012, 03:12 PM   #10
sreten is offline sreten  United Kingdom
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Hi,

Again your equation only relates to a port connected to a closed box
with no driver in it and has nothing to do with the Q of a vented boxes
bass alignment. I haven't looked at it in detail as it does not matter.

For a box port to work well its Q has to be high enough so it doesn't
matter much, most of the damping and losses come from the driver.

If you reduce the port Q, by adding port damping of some form most
box sims simply can't handle it, and you'll get a response somewhere
between sealed and "normal" vented. Aperoidic damping is a special
case most sims can't handle either, where no phase inversion takes
place in the port and it can reduce the Q of a sealed alignment,
(by leaking out of phase bass that cancels with driver output).

As you have noted, in Sims changing the port size keeping the same
frequency has no effect on the small signal response / bass alignment.

That is because the Sims assume the port is an undamped resonator,
i.e. infinite Q, in practice port Q just needs to be high enough for the
Sims to be accurate enough for the bass modelling they present.

Port sizes are chosen based on the smallest total volume that
works well with the large signal parameters of the driver, often
port blocking is arranged to coincide with the driver reaching
its excursion limits, compensating for increasing driver Q.

rgds, sreten.
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Last edited by sreten; 18th September 2012 at 03:19 PM.
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