Single sheet TH challenge

[djk]

"You say this like you have a different high SPL rig? Care to share? "

Just more of the same thing. The original build on the dual-15 PPSL was 24 boxes, and 26 of the horn-loaded 12s (one pair of which went with a pair of dual-18 PPSL). I've never run more than 8 of the dual-15 PPSL at any one job.

 

[CRESCENDO]

"Please correct me if this is wrong. "

The 6dB boost is a requirement of the 6th order design using a low Qts woofer, it is not needed per se for a PPSL design.

The PPSL principle may be applied using sealed, vented, dipole or horn configurations; the driver parameters selected according to the type of loading you wish to employ.

Hi djk,

Thank you for the clarification. I'll play with some different designs to see if I can get more realistically useable models.

"D&B and Dub music that can have constant waveforms below 40Hz. "

Does it really?

Depends on the track. There are tons of dubstep tracks that are very mid-range-y, but there are plenty that have a bit more energy down that low.

epa did some scans of a few dubstep tracks a while ago:
Scan session 1
Scan session 2

 

[David McBean]

Hi Art,

The fact that in most respects Hornresp sims are very close to reality is proof that your theory is, for the most part, sound.

Just to clarify - it is not my theory . Hornresp simply uses the standard lumped-element loudspeaker model, similar to AkAbak.

From what I can see of the two William Cowan 60Hz tapped horns connected in parallel, the LF response has increased by about 2 dB compared to the upper response.

In theory, for two speakers connected in parallel compared to one speaker, the difference at high frequencies should be 3 dB and the difference at low frequencies should be 6 dB. When SPL levels are not normalised for comparison purposes, this is exactly what Hornresp shows for the William Cowan 60Hz tapped horn example - see attachment (6 dB difference at 40Hz, 3 dB difference at 400Hz).

The Hornresp sim for the SH15 shows the low corner dropping almost 10 Hz using four cabinets, a much larger spread.

In your example (four speakers compared to one speaker) the difference at high frequencies is 6 dB and the difference at low frequencies is 12 dB - as expected.

Looking at the LF response of one and two of a 2x10" tapped horn with a similar rolloff as the William Cowan horn, I see no difference, in other words, the 2 dB (or so) increase Hornresp predicts does not occur.

It just doesn't make any sense. With two speakers, the horn mouth area is effectively doubled, but the measurements suggest that there has been no change in LF acoustical loading due to the increased mouth "piston" size. I would have thought that there should be some change.

Do you have any real-world measurements that reflect the theoretical dropping of the LF corner in TH that Hornresp predicts?

Unfortunately I don't have any real-world measurements of anything . I am totally reliant on data provided by people such as yourself, to test the validity of the Hornresp models.

Kind regards,

David

 

[weltersys]

Hi Art,
Just to clarify - it is not my theory . Hornresp simply uses the standard lumped-element loudspeaker model, similar to AkAbak.

In theory, for two speakers connected in parallel compared to one speaker, the difference at high frequencies should be 3 dB and the difference at low frequencies should be 6 dB.

With two speakers, the horn mouth area is effectively doubled, but the measurements suggest that there has been no change in LF acoustical loading due to the increased mouth "piston" size. I would have thought that there should be some change.

Unfortunately I don't have any real-world measurements of anything . I am totally reliant on data provided by people such as yourself, to test the validity of the Hornresp models.

Kind regards,

David

David,

After hearing and measuring the 6 dB increase across the frequency range down the center of left /right stacks, commonly referred to as "power alley", I was surprised to hear your model uses a reduced upper response.

To test that "lumped-element loudspeaker model theory", I did some testing using a pair of small horn loaded speakers today.
The small speakers each have a pair of Eminence 6" and APT tweeters on conical horns, the lows are ported.

The tests were done with the mic on axis 2 meters from the speakers, which were on stands elevating the acoustical center to 2 meters, approximating a full space reading.

Tests were done with the speakers together, and also at 2 meters on center spread between them. Speakers were "toed in" to point at the test mic.

In both cases, the average level difference between one and two was uniformly about 6 dB throughout the range of the speakers.

Above 5000 Hz, the gain (or loss) is erratic due to the wavelengths being so small and the speakers , being on unlevel ground were not exactly equidistant to the microphone, causing dips in response (AKA “comb filtering”, or cancellation).
Also of note, because the speakers used are not perfectly matched (as can be seen in the lower two “2x6spread” screen shot) summation is not exactly 6 dB, though quite close.

Real-world measurements of these horn loaded top cabinets and TH low cabinets indicate to me that some of the theory you base the Hornresp model on could perhaps use some adjustment to reality.

That said, most users of Hornresp work indoors, and room reflections make mincemeat of fine frequency response detail.

Most of my work is outdoors, where it is harder to hide a 2-3 dB problem.

Thanks again for sharing Hornresp.

Art

 

[David McBean]

Hi Art,

After hearing and measuring the 6 dB increase across the frequency range down the center of left /right stacks, commonly referred to as "power alley", I was surprised to hear your model uses a reduced upper response.

The Hornresp model doesn't use a 'reduced upper response' - it simply calculates the SPL by applying the following standard formulas and generally-accepted techniques (as documented in Leo Beranek's "Acoustics", for example).

Assuming:

c = 344 metres per second
rho = 1.205 kilograms per cubic metre
Pref = 2 * 10 ^ -5 newtons per square metre

W = acoustical output power in watts
A = spherical surface area in square metres through which the sound radiates

Then:

Sound intensity in watts per square metre I = W / A

Sound pressure in newtons per square metre P = (I * c * rho) ^ 0.5

SPL = 20 * Log10(P / Pref) decibels

CASE 1:

For a single speaker with an output of 1 acoustic watt at high frequencies, where the sound pressure is measured in free space at a distance of 2 metres:

W = 1
A = 4 * Pi * 2 ^ 2

SPL = 20 * Log10(((1 / (4 * Pi * 2 ^ 2) * 344 * 1.205) ^ 0.5) / (2 * 10 ^ -5))

SPL = 103.14 dB

CASE 2:

For two speakers each with an output of 1 acoustic watt at high frequencies, where the total sound pressure is measured in free space at a distance of 2 metres:

W = 1 + 1 = 2

SPL = 20 * Log10(((2 / (4 * Pi * 2 ^ 2) * 344 * 1.205) ^ 0.5) / (2 * 10 ^ -5))

SPL = 106.15 dB

Assuming constant directivity, the theoretical increase in far-field SPL at high frequencies for two speakers compared to one speaker is 3 dB not 6 dB. This is clearly documented in many authoritative reference texts, including the JBL Professional Sound System Design Reference Manual.

To test that "lumped-element loudspeaker model theory", I did some testing using a pair of small horn loaded speakers today.

Thanks for taking the time to conduct the tests, and for advising me of the results.

Real-world measurements of these horn loaded top cabinets and TH low cabinets indicate to me that some of the theory you base the Hornresp model on could perhaps use some adjustment to reality.

I cannot explain your latest measurements - they appear to be defying the laws of physics in that there is twice as much power coming out as is going in. I am reluctant to arbitrarily adjust the Hornresp results to fit your unique reality .

Kind regards,

David

 

[weltersys]

Hi Art,
For two speakers each with an output of 1 acoustic watt at high frequencies, where the total sound pressure is measured in free space at a distance of 2 metres:
W = 1 + 1 = 2
SPL = 20 * Log10(((2 / (4 * Pi * 2 ^ 2) * 344 * 1.205) ^ 0.5) / (2 * 10 ^ -5))
SPL = 106.15 dB
Assuming constant directivity, the theoretical increase in far-field SPL at high frequencies for two speakers compared to one speaker is 3 dB not 6 dB. This is clearly documented in many authoritative reference texts, including the JBL Professional Sound System Design Reference Manual.

Thanks for taking the time to conduct the tests, and for advising me of the results.

I cannot explain your latest measurements - they appear to be defying the laws of physics in that there is twice as much power coming out as is going in. I am reluctant to arbitrarily adjust the Hornresp results to fit your unique reality .

Kind regards,

David

I searched through the JBL Professional Sound System Design Reference Manual and could find no clear documentation that the theoretical increase in far-field SPL at high frequencies for two speakers compared to one speaker is 3 dB not 6 dB.

But a two meter test on a horn speaker is not in the far field anyway.

Perhaps you are referring to figure 1-3 or Figure 2-7 in the JBL Professional’s Sound System Design Reference Manual ( 1999 edition), where two non-correlated noise sources added together sum to only a 3 dB gain .

However, when two coherent (in phase) sources are added, SPL rises by 6.02 dB.

from:
Total dB level adding of two incoherent uncorrelated sound source - combining decibels or SPL sound pressure level add signal noise levels - sengpielaudio Sengpiel Berlin

“Adding of two incoherent sound pressure levels or voltage levels:
Adding of two values of the same level give an increase of the total level of (+)3 dB.

Adding of two coherent sound pressure levels or voltage levels:
Adding of two values of the same level give an increase of the total level of (+)6 dB.
This is obtained by feeding two side-by-side loudspeakers with the same signal.”

At any rate, the results of my test do not defy any laws of physics, they merely demonstrate the predicted 6 dB increase that occurs when a second speaker equally powered is added with a phase coherent summation.

Phase coherent summation of two sources is harder to achieve the higher the frequency because of the progressively shorter wavelengths, indoor reflections and outdoor wind often do result in a net gain (or loss) of less than 6 dB for two coherent sources.

On February 16, 2005, I tested HF horns and small dome tweeters in a line array outdoors.
The results are below.

They are also consistent with the 6 dB increase in level addition of coherent sources, not some “unique reality”.

Anyone doing similar tests outdoors will get similar results .

Art

 

[David McBean]

from:
Total dB level adding of two incoherent uncorrelated sound source - combining decibels or SPL sound pressure level add signal noise levels - sengpielaudio Sengpiel Berlin

Hi Art,

Many thanks for this reference - I will study it closely.

Hornresp is predicting the power response of the two speakers, whereas your measurements are showing the pressure response. From a power perspective, can you see any flaw in the logic of my calculations?

Thanks for initiating this discussion, it is proving to be very interesting .

Kind regards,

David

 

[weltersys]

Hi Art,

Many thanks for this reference - I will study it closely.

Hornresp is predicting the power response of the two speakers, whereas your measurements are showing the pressure response. From a power perspective, can you see any flaw in the logic of my calculations?

Thanks for initiating this discussion, it is proving to be very interesting .

Kind regards,

David

I have a hard time figuring out the logic of your calculations, the only flaw I can see is that they disagree wth actual testing, which is done in dB SPL.

Interestingly, testing indoors, where the sound feild is reverberant, (incoherent) results in a net three dB gain rather than 6 dB doubling a pair of speakers.

Hornresp correctly figures the LF gain as 6 dB (+3dB for doubling radiating surface, +3 dB for doubling power), I don’t understand the reason why the theory used would not allow the same to happen at high frequencies.

Perhaps you are using an omni model, when all horns have directionality?
Art

 

[AndrewT]

Weltersys,
go back to the basic two drivers producing a common mono signal that are close coupled.
Look at the way the pair of drivers set up a beamed wavefront that consists of multiple interference patterns.
Now determine how frequency affects the way the beamed interference patterns spread out.

High frequencies produce a much narrower beam than Lower frequencies.

That's where we get our range of frequency limits when applying the coupled bass drivers. Within the limited frequency range the levels are increased by +6dB, due to +3dB from the doubled power input and +3dB from the doubled efficiency of air coupling to the doubled Sd.

As frequency rises we come outside that range of limiting frequencies and the extra efficiency of the doubled Sd is gradually lost and is replaced with the interference fringes that were mentioned by a few posters earlier in the thread.

 

[David McBean]

I have a hard time figuring out the logic of your calculations, the only flaw I can see is that they disagree wth actual testing, which is done in dB SPL.

Hi Art,

I tried simulating two parallel speakers in AkAbak - the predicted system response is consistent with your test measurement results (+6dB across the entire frequency range).

It would seem there is something in the established theory that I am missing .

I can replicate your results by a simple change to one line of the Hornresp code, but I need to understand what is going on first (not sure how long it will take me). To cover all situations perhaps I should include a "coherent / non-coherent" option in the Multiple Speakers tool.

Thanks again for highlighting this issue - hopefully Hornresp will eventually be a better product as a result of your very valuable feedback.

Kind regards,

David

 

[Kravchenko_Audio]

As a fly on the wall....

Thanks Art for your time and carefully made measurements. They display a great mind at work.

Ans as for David improving Hornesp. I think that's a given. Never have I seen such a commitment to producing so accurate a simulator. All who use it are indebted.

And few have taken the time to verify it's results. The more carefull measurements shared the better.

 

[tb46]

Multiple Speaker SPL

Hi David,

I hope that in evaluating the multiple speaker SPL output level you will not loose the radiator size and frequency dependent relationship of the acoustic radiation resistance.

Regards,

 

[weltersys]

Hi Art,

I tried simulating two parallel speakers in AkAbak - the predicted system response is consistent with your test measurement results (+6dB across the entire frequency range).

It would seem there is something in the established theory that I am missing .

I can replicate your results by a simple change to one line of the Hornresp code, but I need to understand what is going on first (not sure how long it will take me). To cover all situations perhaps I should include a "coherent / non-coherent" option in the Multiple Speakers tool.

Thanks again for highlighting this issue - hopefully Hornresp will eventually be a better product as a result of your very valuable feedback.

Kind regards,

David

Interesting to hear the difference between Akaback and Hornresp, seems in most respects they usually give similar results.

Glad to hear a simple change to one line of the Hornresp code may be a “fix”.

In post #1263 you wrote “In theory, for two speakers connected in parallel compared to one speaker, the difference at high frequencies should be 3 dB and the difference at low frequencies should be 6 dB”.

About the same time, on the full range forum, in the thread ” high efficiency speakers - how much power do they really need?” several people had been observing only a 3 dB gain indoors when doubling speakers.

If it would not have been for both observations disagreeing with my past experience outdoors, I may not have bothered doing the outdoor test with the two way horn speakers that highlighted the inconsistency between Hornresp and measured results (and Akaback results).

If there are any other tests you would like to see done to help in confirmation of any changes you decide to implement in Hornresp, don’t hesitate to PM me.

Art

 

[Wayne Parham]

My outdoor measurements show a pretty uniform 6dB increase as well - when voltage remains constant and drivers are connected in parallel. Of course, if power is made constant, then drive voltage must be reduced as (parallel connected drivers) impedance is reduced. This brings the decibel increase back to 3dB. Also, I do see a smidge of a falloff at higher frequencies, where sound sources are acoustically distant.

Some sample datasets can be seen here:

• Prosound Shootout

Click on the 2006 event, because that year we published charts of some speakers in singles, duals and even quads in some cases. The direct radiators were given a slight advantage, in that we ran them as duals or quads when comparing them to single basshorns. You can look at an individual subwoofer system and see the 2v/10M SPL chart of a single cabinet and compare it with the measurement made using two subs. The charts are 6dB different all the way, until you get up past 100Hz, where the difference falls to maybe 4dB or 5dB. By this point, the basshorns are acoustically large and becoming directional but they are also near mass-rolloff. Summing up high appears to fall off just a smidge, but not by 3dB.

In the 2005 and 2007 events, we focused more on measuring each cabinet at multiple power levels, getting both SPL and distortion charts for each one. So there is useful information there, but we did not have time to do multiple cabinets those years. In 2006, we measured cabinets indidually and in groups, but we did not have time to run them at increasingly higher power levels. So you get a little bit different information each year.

 

[weltersys]

My outdoor measurements show a pretty uniform 6dB increase as well -
-snip-
The charts are 6dB different all the way, until you get up past 100Hz, where the difference falls to maybe 4dB or 5dB. By this point, the basshorns are acoustically large and becoming directional but they are also near mass-rolloff. Summing up high appears to fall off just a smidge, but not by 3dB.

Wayne,

I would bet that if your bass horns were angled in slightly to point exactly at the mic (as in my recent test of the small woofer/tweeter horn cabinet) that "smidge" lower summing up high would also become a full 6 dB increase.

It appears that the 12Pi's 30 Hz response increases by about 1.5 dB over the 6 dB overall response increase going from one to two, how does that compare to the Hornresp LF prediction?

If you have tested four 12Pi's together, that would also be another interesting comparison of measured vs. Hornresp.

Even though to many, a 1.5 dB difference does not amount to much, the fact that your FLH do show a LF increase, and both types of my quite different TH show no LF increase in pairs should be of further interest to David McBean.


Art

 

[David McBean]

I have a hard time figuring out the logic of your calculations, the only flaw I can see is that they disagree wth actual testing, which is done in dB SPL.

Hi Art,

I found the error in my calculations - I was summing the sound powers rather than the pressures . Not sure how I came to do this as I got it right in the Combined Response tool, which operates quite similarly in many respects (apart from having a phase difference between the two signals being combined).

The calculations should have been as follows:

Sound intensity from one speaker I = 1 / (4 * Pi * 2 ^ 2)
Sound pressure from one speaker P = (I * 344* 1.205) ^ 0.5

SINGLE SPEAKER:

SPL = 20 * Log10(1 * P / 0.00002) = 103.14 dB

TWO SPEAKERS:

SPL = 20 * Log10(2 * P / 0.00002) = 109.16 dB

The difference is now +6.02 dB - exactly as it should be .

I will post a message on the Hornresp thread when the error has been corrected and an update is released.

Thanks again for all your help.

Kind regards,

David

 

[Wayne Parham]

I would bet that if your bass horns were angled in slightly to point exactly at the mic (as in my recent test of the small woofer/tweeter horn cabinet) that "smidge" lower summing up high would also become a full 6 dB increase.

Hmm, I dunno. The measurement distance was 10 meters (32.8 feet or 393 inches) and the center-to-center distance between subs standing side-by-side is around two feet, even the largest models. That means each was about 2° off-axis. I'm pretty sure the difference between 0° and 2° is negligible, not even measurable.

 

[weltersys]

Hmm, I dunno. The measurement distance was 10 meters (32.8 feet or 393 inches) and the center-to-center distance between subs standing side-by-side is around two feet, even the largest models. That means each was about 2° off-axis. I'm pretty sure the difference between 0° and 2° is negligible, not even measurable.

One of those things that can't actually be resolved without measurement, so I won't argue the point.

I still am curious about this:

It appears that the 12Pi's 30 Hz measured response increases by about 1.5 dB over the 6 dB overall response increase going from one to two, how does that compare to your Hornresp LF prediction for two cabinets in half space?

 

[weltersys]

Hi Art,

I found the error in my calculations - I was summing the sound powers rather than the pressures . Not sure how I came to do this as I got it right in the Combined Response tool, which operates quite similarly in many respects (apart from having a phase difference between the two signals being combined).

The difference is now +6.02 dB - exactly as it should be .

I will post a message on the Hornresp thread when the error has been corrected and an update is released.

Thanks again for all your help.

Kind regards,

David

Cool, will this have an effect on the simulated LF response of multiple TH ?

 

[David McBean]

I hope that in evaluating the multiple speaker SPL output level you will not loose the radiator size and frequency dependent relationship of the acoustic radiation resistance.

Hi Oliver,

That is the one thing that still puzzles me about Art's test results - and now those also posted by Wayne for dual cabinets.

I would have expected to see an additional 3 dB gain at low frequencies due to the mutual interaction between the two closely-coupled radiating horn mouths - which serve to increase the radiation resistance and therefore the acoustical output power.

I understand why it is not shown in my AkAbak simulations - the program is assuming that the two speakers are separated, not closely coupled.

At this stage I am not exactly sure what to do .

Kind regards,

David