Resonant Frequency of an enclosure
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 10th December 2001, 12:10 PM #1 AudioFreak   Warp Engineer On Holiday     Join Date: Oct 2001 Location: Queensland, Australia Just wondering if anyone knows the formula to deterimine the resonant frequency of a given volume of air in a sealed enclosure.
 10th December 2001, 06:02 PM #2 kelticwizard   Wizard of Kelts diyAudio Moderator Emeritus   Join Date: Sep 2001 Location: Connecticut, The Nutmeg State AudioFreak: I don't believe that sealed enclosures have a resonant frequency. In ported boxes, the resonance is set up by the combination of the port characteristics-how long, how large-and the size of the air in the box. Without a port or passive radiator, you have no resonance. If you want to know the formula for how a certain size sealed box affects the free air resonance of any speaker, it is as follows: Fs= free air resonance Fc= resonance of speaker in the box Vb= volume of air in box Vas= the volume of air with the same "spring" as the driver suspension. Generally listed with the Thiele-Small parameters. Then: Fc = the square root of: [(Vas/Vb) + 1] So, a speaker with a Vas of 2 cubic feet with an Fs of 30 Hz that is put into a box of 1 cubic foot will have a resonance of 51.9 Hz. Incidentally, the rise in Q uses the same formula. So if that speaker had a Qts of .5, then it's new Q will be .866 when placed in that box. This formula is usually listed with a wavy " = " sign meaning that is a close approximation. But it is generally accepted as being very close. [Edited by kelticwizard on 12-10-2001 at 04:50 PM]
 10th December 2001, 08:29 PM #3 Super   diyAudio Member   Join Date: May 2001 Location: Connecticut I believe Kelticwizard is correct. Any other box resonances would be effected by other factors, such as bracing. __________________ Bryan
 10th December 2001, 08:53 PM #4 Won diyAudio Member   Join Date: Nov 2001 Location: Cambridge, Mass Hm. Intuition suggests that a sealed volume of air is a damped mass-spring system, and therefore might have resonanaces. The boundaries of the box can also generate standing waves, which also count, but I don't think that's what this thread is about. The former, however, simply might not have any affect on speaker design -- I won't venture to guess because I have no quantitative knowledge here. -Won
 10th December 2001, 11:51 PM #5 AudioFreak   Warp Engineer On Holiday     Join Date: Oct 2001 Location: Queensland, Australia thanks for the info.
 11th December 2001, 12:10 AM #6 Petter diyAudio Member   Join Date: Jan 2001 Location: Scandinavia Visual Ears Perhaps you can use the software visual ears to work this out? It is designed to find standing waves in ordinary rooms. A small speaker is an ordinary room. My guess is that you will be more likely to get into a gas resonant frequency in terms of standing waves (geometry) rathern than springiness of the air. Do let us know your results! Petter
 11th December 2001, 01:55 AM #7 AudioFreak   Warp Engineer On Holiday     Join Date: Oct 2001 Location: Queensland, Australia Just read back over everyones posts and kelticwizard gave the exact info i was chasing ..... thanks again.
 4th July 2003, 12:02 AM #8 Jared diyAudio Member   Join Date: Sep 2002 Location: Raleigh NC wow this thread came up in a search.. Of course a sealed box has a resonant frequency. when your Qtc = .707 the f3 and the resonant frequency are the same point. anyways, the resonant frequency, Fcb= Fs * Sqrt( Vas/Vb +1) Vb = box volume.
mikee12345
diyAudio Member

Join Date: Nov 2002
Location: NZ
Quote:
 I don't believe that sealed enclosures have a resonant frequency
i dont beleive that sealed enclosures are a non resonant system

sure it isnt ported,but it is resonant.

?

 4th July 2003, 01:30 AM #10 Ron E   diyAudio Member     Join Date: Jun 2002 Location: USA, MN The box in a sealed box does not have a resonant frequency in the sense that a ported box has a resonant frequency, near the cutoff point of a typical bass driver. A driver has a mass and a stiffness (think of a spring) and this combination resonates at a certain frequency. This resonance is second order because there are two energy storage devices. The mass and the spring. What the box does in a sealed box is isolate the backwave to prevent cancellation and it also acts as a stiffness against which the driver must act in order to move. More stiffness means that the driver resonance moves upward when placed in a sealed box. The bigger the piston, the more stiff an equal volume of air will appear because more air is displaced for the same distance moved - the air is compressed more. There is still only one mass and an equivalent stiffnes made up of the driver stiffness combined with the box stiffness. Kelticwizard has the ideal equation, which is a pretty good approximation for tightly sealed unstuffed boxes. The addition of leaks or damping material affects the resonant system. A port has two resonant systems, the port/box and the driver/box - thus it is 4th order. Passive radiators have a compliant element in series with their mass and are thus 5th order. __________________ Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works. --Carl Sagan Armaments, universal debt, and planned obsolescence--those are the three pillars of Western prosperity. —Aldous Huxley

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