Resonant Frequency of an enclosure - diyAudio
Go Back   Home > Forums > Loudspeakers > Multi-Way
Home Forums Rules Articles diyAudio Store Gallery Wiki Blogs Register Donations FAQ Calendar Search Today's Posts Mark Forums Read

Multi-Way Conventional loudspeakers with crossovers

Please consider donating to help us continue to serve you.

Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving
Thread Tools Search this Thread
Old 10th December 2001, 11:10 AM   #1
Warp Engineer
On Holiday
AudioFreak's Avatar
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.
  Reply With Quote
Old 10th December 2001, 05:02 PM   #2
Wizard of Kelts
diyAudio Moderator Emeritus
Join Date: Sep 2001
Location: Connecticut, The Nutmeg State

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]
  Reply With Quote
Old 10th December 2001, 07:29 PM   #3
Super is offline Super  United States
diyAudio Member
Join Date: May 2001
Location: Connecticut
Send a message via AIM to Super
I believe Kelticwizard is correct. Any other box resonances would be effected by other factors, such as bracing.
  Reply With Quote
Old 10th December 2001, 07:53 PM   #4
Won is offline 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.

  Reply With Quote
Old 10th December 2001, 10:51 PM   #5
Warp Engineer
On Holiday
AudioFreak's Avatar
Join Date: Oct 2001
Location: Queensland, Australia
thanks for the info.
  Reply With Quote
Old 10th December 2001, 11:10 PM   #6
diyAudio Member
Join Date: Jan 2001
Location: Scandinavia
Default 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!

  Reply With Quote
Old 11th December 2001, 12:55 AM   #7
Warp Engineer
On Holiday
AudioFreak's Avatar
Join Date: Oct 2001
Location: Queensland, Australia
Just read back over everyones posts and kelticwizard gave the exact info i was chasing ..... thanks again.
  Reply With Quote
Old 3rd July 2003, 11:02 PM   #8
diyAudio Member
Join Date: Sep 2002
Location: Raleigh NC
Send a message via AIM to Jared
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.
  Reply With Quote
Old 3rd July 2003, 11:35 PM   #9
diyAudio Member
mikee12345's Avatar
Join Date: Nov 2002
Location: NZ
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.

  Reply With Quote
Old 4th July 2003, 12:30 AM   #10
Ron E is offline Ron E  United States
diyAudio Member
Ron E's Avatar
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
  Reply With Quote


Hide this!Advertise here!
Thread Tools Search this Thread
Search this Thread:

Advanced Search

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are Off
Refbacks are Off

Similar Threads
Thread Thread Starter Forum Replies Last Post
speakers operating near their resonant frequency kanguru007 Multi-Way 26 28th March 2009 02:02 PM
Ribbon Tweeter Resonant Frequency DamageG Planars & Exotics 2 14th February 2008 05:30 AM
Reverse engineering resonant frequency jonkun227 Multi-Way 13 12th April 2007 05:33 PM
What about resonant frequency? Javachip Full Range 6 15th June 2006 06:12 AM
how can i figure out the resonant frequency of my room? travis Everything Else 9 17th May 2002 06:17 AM

New To Site? Need Help?

All times are GMT. The time now is 05:03 AM.

vBulletin Optimisation provided by vB Optimise (Pro) - vBulletin Mods & Addons Copyright © 2017 DragonByte Technologies Ltd.
Copyright 1999-2017 diyAudio

Content Relevant URLs by vBSEO 3.3.2