Anyone knows minimum Xmax values needed in order to achieve a 20Hz target for a 15",12" ,10" and 8" drivers respectively?Thanks in advance!
XMax doesn't tell you how low a driver can go. What it does give you is another limit on how much power it can take at low frequency's.
It roughly measures not power but potential cone displacement, which is not the same thing. But it's quite true that Xmax has no bearing on the frequency that a driver will go to, just how much air it can move.
I second that excursion tell us nothing about the frequency only the pressure level, as cone area and excursion are the limiting factor in the output volume.
For low frequencies max SPL is
20*log10(Sd*Xmax*rho0*pi*f^2/(r*sqrt(2)))
Where
Sd is the equivalent piston area in m2 of the driver
Xmax is the peak (one way) max excursion in metres
rho0 is the density of air (1.2 kg/m3)
f is frequency in Hz
r is the source-listener distance in metres
assuming low frequencies and free space. For half space add 6 dB.
Xmax says nothing about the cut-off frequency.
20*log10(Sd*Xmax*rho0*pi*f^2/(r*sqrt(2)))
Where
Sd is the equivalent piston area in m2 of the driver
Xmax is the peak (one way) max excursion in metres
rho0 is the density of air (1.2 kg/m3)
f is frequency in Hz
r is the source-listener distance in metres
assuming low frequencies and free space. For half space add 6 dB.
Xmax says nothing about the cut-off frequency.
454Casull said:
The equation Svante posted is essentially only for sealed enclosures. It is the sound produced by a piston of a certain diameter (mounted in an infinite baffle) moving a certain distance back and forth. The equation also says nothing about the power needed to achieve that SPL.
Deriving such an equation for a vented box is not too difficult, but it is a lot harder to write down. There is one at www.diysubwoofers.org that assumes a max piston excursion of 1.15 times Xmax. BTW, in the model used there, inserting Fb=0 makes the equations apply to a closed box.....
This link may gve you the answers you are looking for.
Linkwitz Labs Excersion calculator
Enjoy
Doug
Linkwitz Labs Excersion calculator
Enjoy
Doug
Here is the list of cone areas, (Sd), for the various size drivers you listed:
15 in: 132 sq in
12 in: 86 sq in
10 in: 56 sq in
8 in: 32 sq in
Here is a link to the thread I started that deals specifically with this issue.
http://www.diyaudio.com/forums/showthread.php?threadid=5668&highlight=
Post #2 contains the link to the volume of air necessary to produce certain bass notes at a certain SPL. It is in regular measurements.
Post #3 contains the link to the same chart, but it is in Metric measurements.
Richard Small, of Thiele-Small fame, is the one who made the charts. They appeared in the Journal Of The Audio Engineering Society in 1971.
These are for Closed Box only. Ported Box would require much less air being displaced.
For Closed Box, for instance, if you want to produce 97 dB SPL @ 20 Hz, you need to move 32 cu in of air.
If you want to produce 103 dB SPL @ 20 Hz, you need to move 64 cu in of air.
So, if you want to produce 103 dB SPL @ 20 Hz and you have 15" driver in a Closed Box, you look at the chart and see you need to move 64 cu inches of air.
A 15" driver has 132 sq inches of area.
So the necessary excursion is:
(64 cu in) / (132 sq in) = 0.48 inches excursion.
That is one-way excursion, incidentally. That is, the 15 in woofer must start from the center, move 0.48 in forward, come back to center, and move 0.48 inches back, and return to the center. It is not 0.48 in front-to-back. This is important.
For a 12 in speaker to produce the same, (103 dB SPL @ 20 Hz), it goes like this:
(64 cu in) / (86 sq in) = 0.74 in. Which is quite an excursion.
Like I said, post #3 has the Metric measurements if you want to do it that way.
If you have any more questions, ask on the forum or Email.
15 in: 132 sq in
12 in: 86 sq in
10 in: 56 sq in
8 in: 32 sq in
Here is a link to the thread I started that deals specifically with this issue.
http://www.diyaudio.com/forums/showthread.php?threadid=5668&highlight=
Post #2 contains the link to the volume of air necessary to produce certain bass notes at a certain SPL. It is in regular measurements.
Post #3 contains the link to the same chart, but it is in Metric measurements.
Richard Small, of Thiele-Small fame, is the one who made the charts. They appeared in the Journal Of The Audio Engineering Society in 1971.
These are for Closed Box only. Ported Box would require much less air being displaced.
For Closed Box, for instance, if you want to produce 97 dB SPL @ 20 Hz, you need to move 32 cu in of air.
If you want to produce 103 dB SPL @ 20 Hz, you need to move 64 cu in of air.
So, if you want to produce 103 dB SPL @ 20 Hz and you have 15" driver in a Closed Box, you look at the chart and see you need to move 64 cu inches of air.
A 15" driver has 132 sq inches of area.
So the necessary excursion is:
(64 cu in) / (132 sq in) = 0.48 inches excursion.
That is one-way excursion, incidentally. That is, the 15 in woofer must start from the center, move 0.48 in forward, come back to center, and move 0.48 inches back, and return to the center. It is not 0.48 in front-to-back. This is important.
For a 12 in speaker to produce the same, (103 dB SPL @ 20 Hz), it goes like this:
(64 cu in) / (86 sq in) = 0.74 in. Which is quite an excursion.
Like I said, post #3 has the Metric measurements if you want to do it that way.
If you have any more questions, ask on the forum or Email.
Great stuff kelticwizard. I assume that information pertains to free air, i.e. no bolstering by half-space loading (as you would get in a real room)?
Looks like I will be able to easily hit 100dB @ 20Hz with my new sub then 😀
Looks like I will be able to easily hit 100dB @ 20Hz with my new sub then 😀
when its nearing 120db-130db the fun begins and your clothing and hair starts moving =basshorns
😎
Cool indeed, but my box is only 14 inches cubed externally and sealed, so fantastic group delay and transient response 😀
richie00boy said:
It's for 2 pi steradians, which meand half space. For the SPL rating, mention is also made of "normally reverberant room".
However, the chart is very conservative, and most charts I see that include "room response" give SPL's at 20 Hz far greater than this. So for all intents and purposes, I think you can say this doesn't include "room response".
Here is the quote from Small's 1971 article.
I can send you or anyone reading this the whole article if you want, if you are technically minded. I have both parts on my hard drive. 🙂
Attachments
kelticwizard said:
I just figured out that this chart does not include room response for sure.
http://www.diyaudio.com/forums/attachment.php?postid=55867
How do I know?
Try this. Take a look at 101 dB SPL, and notice the volume of air that must be displaced as you go down octave by octave.
The displaced air volume is:
80 Hz: 3.2 cu in
40 Hz: 12.8 cu in
20 Hz: 52 cu in, (approximating from chart).
In each case, when you maintain the same SPL but go down an octave, the amount of air you must displace increases four times.
That agrees with the general rule, for outdoors or anywhere-going down an octave in frequency while maintaining the same SPL requires four times the volume of air to be displaced.
If you included room gain in this chart, this would not be so. If you maintained SPL and moved down an octave, you would only have to displace 3 times or two times the air. The room gain would supply the rest of the SPL.
But that does not happen in this chart. Therefore, this chart does not reflect room gain.
As a result, you can count on your output in a real life room as being above the SPLs listed here, especially the lower you go. Just about every real life room you encounter is bound to have room gain.
Svante said:
Ahh, well, this equation was written from the top of my head, and obviously it produces silly results. It should read:
20*log10(Sd*Xmax*rho0*pi*f^2/(r*sqrt(2))/Pref)
where Sd is the equivalent piston area in m2 of the driver
Xmax is the peak (one way) max excursion in metres
rho0 is the density of air (1.2 kg/m3)
f is frequency in Hz
r is the source-listener distance in metres
Pref is the reference pressure (20 uPa)
...or you could try an excel sheet I just put together at
http://www.tolvan.com/max_SPL_calculator.xls
20 hz
its also good to know the resonant frequency of the room because below this frequency there will be a steady increase in base response as the wavelength is bigger than the room. So in small listening rooms 20 hz usualy compreses the air as a whole and helps spl out. Thats why in the car audio world its easy to get 140+ db with 2 12" subwoofers because the boost starts a 60hz somtimes because of how small the listening area is.
Also when using ported boxes at the port frequncy the xmax drops significantly as the port takes over producing most of the bass. this affect continues to drop above port frequency until the box acts sealed. that is why subwoofers designed for ported boxes have a smaller xmax which is traded usually for efficiency
its also good to know the resonant frequency of the room because below this frequency there will be a steady increase in base response as the wavelength is bigger than the room. So in small listening rooms 20 hz usualy compreses the air as a whole and helps spl out. Thats why in the car audio world its easy to get 140+ db with 2 12" subwoofers because the boost starts a 60hz somtimes because of how small the listening area is.
Also when using ported boxes at the port frequncy the xmax drops significantly as the port takes over producing most of the bass. this affect continues to drop above port frequency until the box acts sealed. that is why subwoofers designed for ported boxes have a smaller xmax which is traded usually for efficiency
interesting stuff..
so to get an actual handle on some real figures.. what is a typical good value for xmax?
would 5mm for a 15" subwoofer be good or bad at ~88dB sensitivity?
so to get an actual handle on some real figures.. what is a typical good value for xmax?
would 5mm for a 15" subwoofer be good or bad at ~88dB sensitivity?
5 mm would not be a good linear Xmax for a 15" subwoofer.
By the way, there are two numbers which sometimes get labelled "Xmax".
The first is linear Xmax. It is how far back and forth a speaker can travel before running into large amounts of distortion. For the typical speaker, it is generally pretty close to:
[(length of voice coil winding) - (height of magnetic gap or air gap)] / 2
So a speaker with a voice coil winding of one inch, (25mm) and a magnetic gap, (air gap), of 6 mm equals:
[(25mm) - (6mm)] / 2 = 9.5 mm.
The other number sometimes written as Xmax is the excursion a speaker can go before physicial damage occurs to the speaker. It is always longer than the linear Xmax. This is also sometimes labelled Xmech.
For hifi speakers, Xmech is usually 1.5 to 2 times longer than linear Xmax. For PA speakers, Xmech can be 3 times longer than linear Xmax.
Generally, any speaker with a linear Xmax longer than 1/4 in, (6mm) is considered having a long excursion. Lately, quite a few subs have come out with linear Xmax of 0.5 in, (12 mm), or more. And there are even some subwoofers with linear excursions of 1", (25mm), and even 1.5".
So the short answer to your question is: For subwoofers, 9 mm is okay, 12 mm or above is really long excursion. Make sure that is linear Xmax, not Xmech.
By the way, there are two numbers which sometimes get labelled "Xmax".
The first is linear Xmax. It is how far back and forth a speaker can travel before running into large amounts of distortion. For the typical speaker, it is generally pretty close to:
[(length of voice coil winding) - (height of magnetic gap or air gap)] / 2
So a speaker with a voice coil winding of one inch, (25mm) and a magnetic gap, (air gap), of 6 mm equals:
[(25mm) - (6mm)] / 2 = 9.5 mm.
The other number sometimes written as Xmax is the excursion a speaker can go before physicial damage occurs to the speaker. It is always longer than the linear Xmax. This is also sometimes labelled Xmech.
For hifi speakers, Xmech is usually 1.5 to 2 times longer than linear Xmax. For PA speakers, Xmech can be 3 times longer than linear Xmax.
Generally, any speaker with a linear Xmax longer than 1/4 in, (6mm) is considered having a long excursion. Lately, quite a few subs have come out with linear Xmax of 0.5 in, (12 mm), or more. And there are even some subwoofers with linear excursions of 1", (25mm), and even 1.5".
So the short answer to your question is: For subwoofers, 9 mm is okay, 12 mm or above is really long excursion. Make sure that is linear Xmax, not Xmech.
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