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]
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.
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.
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.
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.