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Discussion Starter · #1 ·
Hi,

When discussing subwoofers, it's often mentioned what SPL they can reach at different frequencies. But what about other speakers, such as bookshelf speakers? In reviews of those you mostly see a frequency response graph measured at very low output (e.g. measured at 2.83V input). Something like this:



And the speakers get rated base on that, e.g. 50Hz-22kHz ± 3dB.

But if you have a bookshelf speaker rated at e.g. 50Hz-22kHz ± 3dB, how do you know what SPL the speaker is capable of at the lower frequencies, if the input is increased to higher levels?

Is there any guideline or estimate of what can be expected from such a bookshelf speaker? If playing loud, will the frequency curve look different, so a speaker that is rated at 50Hz-22kHz± 3dB perhaps only is capable of 90Hz-22kHz in actual use at those output levels? :confused:
 

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SPL at a given frequency is determined by volume displacement (Sd x Xmax). You need both of these to make a theoretical calculation, but you really need measurements to determine how loud you can drive them before they are too distorted. Just because a theoretical driver has an Xmax of 6mm, doesn't mean because of poor design that it still be useful at more than say 2mm. Plus, if it's ported, inadequate port area may mean the port is compressing well before the driver is anywhere near Xmax. To give the same SPL at 50Hz as 100Hz, you need 4x the volume displacement, and 1/4 at 200Hz.

I don't have the equation in front of me but I have posted it before. I'll post it at later today.

Most FR measurements are done at 1W or so, and are completely useless for determining max SPL output.
 

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Here you go.

The equation for sound pressure (in pascals) is

p=U*rho0*f / (2*r)

where U is the volume flow in m3/s
rho0=1.2 kg/m3
f is the frequency in Hz
r is the distance

U is also equal to V*2*pi*f, where V is the volume of air displaced in m3.

To get from sound pressure (p) to sound pressure level (SPL)

SPL = 20*log10(p/pref);

where pref=0.00002 Pa

Free space assumed (4 pi).
 

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Discussion Starter · #4 ·
Ok, I see. Thanks!

So for a typical bookshelf speaker rated at 50Hz-20kHz ± 3dB, approximately what actual frequency range can be expected at "loud" volumes? E.g. 60Hz-20kHz, 80Hz-20kHz, 100Hz-20kHz, or something else (all ranges at ±3dB)? Note that I'm not looking for an exact range, just a rough estimate.
 

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Ok, I see. Thanks!

So for a typical bookshelf speaker rated at 50Hz-20kHz ± 3dB, approximately what actual frequency range can be expected at "loud" volumes? E.g. 60Hz-20kHz, 80Hz-20kHz, 100Hz-20kHz, or something else (all ranges at ±3dB)? Note that I'm not looking for an exact range, just a rough estimate.
It depends. See post #2 .
 

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Discussion Starter · #8 ·
Ok, so it could just as well be 1000Hz-20kHz? No way to say anything at all about approximate actual frequency range? I find that hard to believe.

Also, in this case there ought to be a lot of people with bookshelf front speakers and center speakers rated at ~50Hz that will get a frequency dip just above the crossover frequency if used with a subwoofer. That is assuming a typical crossover frequency of 80 Hz, and the front and center speaker actually only being capable of e.g. 100Hz when playing at normal or loud listening levels.
 

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Yeah, I know it depends. That's why I said I'm looking for a rough estimate. Surely it should be possible to say if it's closer to 60Hz-20kHz or 100Hz-20kHz?
If I had this question, and didn't get a good answer, I'd take some measurements on my own.

Measurement mic and REW would do it to my satisfaction.

Start at low level and work your way up the scale, overlay the measurements, and see how long the curves remain 'parallel'.
 

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Ok, so it could just as well be 1000Hz-20kHz? No way to say anything at all about approximate actual frequency range? I find that hard to believe.

Also, in this case there ought to be a lot of people with bookshelf front speakers and center speakers rated at ~50Hz that will get a frequency dip just above the crossover frequency if used with a subwoofer. That is assuming a typical crossover frequency of 80 Hz, and the front and center speaker actually only being capable of e.g. 100Hz when playing at normal or loud listening levels.
Probably not 1 kHz but anything without detailed measurements or very detailed parameters and the ability to do the analysis is a guess. There are far too many variables in speaker design and test conditions. My guess? Someplace between 10 and 1000 Hz.

A "hole" in response around the crossover frequency to a subwoofer is usually because the sub and main speaker are out of phase at the listening position and/or have different crossover slopes. That is a combination of crossover design, speaker design/enclosure type, and distance from each to the MLP.
 

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Basically the woofer (more accurately the mid-woofer) will more of less continue to increase in SPL (roughly 3dB for every doubling of power) until it runs out of excursion or runs into power compression.

What you are asking for must be either measured or modeled for a given driver within a given system and this varies so much there is no way to give any sort of estimate without knowing more about the specific speaker/drivers.

What you want to know can certainly be useful BUT most reviewers don't not measure. You see it in some more exhaustive subwoofer testing (databass for example) but rarely outside that, even in the rather complete Stereophile testing.

Edit: one thing to make note of in the practical world is the crossover area for most sub/speaker combinations is going to be in the modal range of the room. So you may get a lot of help from the room in the area or you may get just the opposite.
 

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I have measured this with my speakers and the graph looks the same each time increasing the volume by 5db. I imagine this will continue until my woffer distorted at the low frequencies.
 

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To OP

Soundstage Network sends some of the speakers they review to Canada's NRC for testing in an anechoic chamber. One of the tests they do there is called Deviation from Linearity It may not be exactly what you're asking for but, its close. I don't have the post count to post links but, its easy enough to find with Google.

Of course they don't test all that many speakers.
 

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To OP

Looks like the graph you posted came from SS. Just scroll down the page to find the Deviation graph. It shows how the frequency response changes as SPL is increased. That's what you want, isn't it?
 

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To OP

Looks like the graph you posted came from SS. Just scroll down the page to find the Deviation graph. It shows how the frequency response changes as SPL is increased. That's what you want, isn't it?
 

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Discussion Starter · #16 · (Edited)
Probably not 1 kHz but anything without detailed measurements or very detailed parameters and the ability to do the analysis is a guess. There are far too many variables in speaker design and test conditions. My guess? Someplace between 10 and 1000 Hz.
Yup, I know it's lots of variables. But again, that's thy I said a rough estimate.

For example, if someone would ask me how lot a typical bookshelf speaker with a 6.5" woofer can play at low levels, I'd say between 45-65 Hz (@ -3 dB). That would be true for most of those speakers, and thus it would be a valid rough estimate.

I think it should be possible to provide a similar estimated range for when the speakers are played at loud levels for someone who has the knowledge. But I'm not sure of that range myself, that's why I asked.
A "hole" in response around the crossover frequency to a subwoofer is usually because the sub and main speaker are out of phase at the listening position and/or have different crossover slopes. That is a combination of crossover design, speaker design/enclosure type, and distance from each to the MLP.
What I meant was this:
-Assume that the speakers are only capable of 200 Hz at loud listening levels.
-The crossover for the speakers is set to 80 Hz.

This would mean:
-The speakers play 200-20kHz.
-The subwoofer plays 0-80 Hz.

=> I.e. there would be a "frequency hole" between 80 and 200 Hz.

If this actually was the case, I think we'd be hearing a lot more complaints from people with bookshelf speakers in their HT systems. Since we do not, I assume bookshelf speakers usually play lower than 200 Hz even at loud volumes. The question is just how much lower.
 

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Discussion Starter · #17 · (Edited)
To OP

Looks like the graph you posted came from SS. Just scroll down the page to find the Deviation graph. It shows how the frequency response changes as SPL is increased. That's what you want, isn't it?
Thanks! I actually just used Google Image search to find the graph in the OP.

Anyway, based on your tip I did some more searching and found the underlying article:

http://www.soundstagenetwork.com/measurements/speakers/paradigm_studio10_v5/

Indeed it did contain graphs from when the same speaker was played at higher input too. Interesting! See for example this when played at 95 dB:



Not that different from what it looks like at lower input levels:



The distortion is higher at louder listening levels though.

No graph from higher listening levels than 95 dB unfortunately. But at least it gives an indication that is can sustain about the same lowest frequency even at louder volumes.
 

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Soundstage Network sends some of the speakers they review to Canada's NRC for testing in an anechoic chamber. One of the tests they do there is called Deviation from Linearity It may not be exactly what you're asking for but, its close. I don't have the post count to post links but, its easy enough to find with Google.

Of course they don't test all that many speakers.
This is an output compression test, it is nice to have it in both freq vs SPL along with magnitude traces which are freq vs deviation which makes it much easier and quicker to interpret at a glance where in the frequency range the greatest compression is occurring.
 

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Discussion Starter · #20 ·
While these are for a subwoofer I think this is what you seek, but you rarely see them published for speakers.

http://www.data-bass.com/data?page=system&id=100&mset=110
Well, from the graphs in my previous post it looks like the frequency graph is more or less the same regardless of SPL on normal speakers. So if a speaker can play down to 60 Hz @-3dB at low volume, it will be able to do that at high volume too. The only difference is that distortion will be a bit higher when playing loud. I suppose that's why frequency graphs at different SPL are not usually published in reviews of such speakers.

As for subwoofers which play very low frequencies it seems to be different though. So a subwoofer may be able to play down to 20 Hz @-3dB at low volume, but at high volume it may only be able to play down to 35 Hz @-3dB.
 
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