BillFitzmaurice.info

I had a conversation with a guy recently that has sparked a few technical question that I have not fully wrapped my head around. I wish to try to articulate it here and see what kind of feedback I can get. In advance, thank you for looking at this and for any supporting content you provide.

Question1
Is it not true that for any given sound pressure level(SPL) there is a specific amount of displacement/volume required?
Like if for example, using arbitrary numbers, a driver with 100cm^2 of Sd moving 1cm in its displacement/excursion has the same SPL output as a driver that has half or 50cm^2 of Sd but is displacing twice as much at 2cm of excursion. The Vd being the same meaning that the SPL is also the same.

Question2
If the above is true than can't we directly associate a Vd value to a dBspl value, then simply add into the equation an efficiency value based off of enclosure topology used, and be able to generate some pretty accurate max output predictions of drivers simply from the Vd and enclosure efficiency?

When I am trying to determine the max potential SPL output of a given driver the thermal and mechanical limitations become the limiting factor as I understand. The higher the sensitivity of a driver the less power will be required to excite it to its maximum. As I understand, the sensitivity spec does little to tell what a driver's max output capabilities are. The Vd is the determining factor for max SPL, so long as the driver is properly chambered/enclosed so that it's not thermally or mechanically inhibited.

Question3-4
If every doubling of Sd gives 6db gain, and Vd is Sd times Xmax, then doesn't that also mean that every doubling of the excursion is 6db in spl gain for a given Sd?
If every doubling of power means 3db spl gain, then to double the excursion it would require 4x the power and yield 6db spl gain?


What I am actually trying to do is fortify an argument about the scale of diminishing returns with regards to driver selection. Below I illustrate two similar sized drivers with very different specs and price points. It would be useful to me to be able to quickly crunch some numbers and identify the value or lack of value in a given configuration. In other words just how much gain can and do you get comparing a budget driver to a more premium driver.

https://sundownaudio.com/index.php/prod ... eries-500w
How do I ballpark the output potential of 4 of these Sundown Audio E-8" V.6 drivers as compared to say the output potential 4 MCM 55-2421 8" drivers in about the same environment/enclosure, either sealed or bass reflex probably.

The Sundown E-8" v.6 driver specs:
$120.00 ea
300w rated
14mm xmax
82.4db@1w/1m
I can double the power to this driver 8 times over to reach the rated 300w spec (256w actually but close enough) for a gain of 24dBspl.
Peak SPL is 106.2db based off of wattage rating.
Add 4 drivers for 106.2+12=118.2dbspl
at $480.00 for the drivers requiring over 1200w, for a yield of 118.2dBspl. The Vd is 57.05l. That is $8.41 per Vdl.

The MCM 55-2421 8" driver specs:
$40.00 ea
120w rated
8mm xmax
87db@1w/1m
I can double the power to this driver 7 times over to reach the rated 120w spec for a gain of 21dBspl.
Peak SPL is 108dBspl based off of wattage rating.
Add four drivers for 108+12=120dbspl
at $160.00 for the drivers requiring around 500w. The Vd is 32.6l. That is $4.90 per Vdl.


If we add power to get the Sundown driver to match output with the MCM of 87db which is almost 6db it would take about 4w to do it. To me that would mean that so long as the Sd is basically the same between the drivers the amount of excursion will be the same.
If we double our excursion ever 6db and it takes 4x the power to do so and with the Sundown driver starting at 4x the power their excursion will match all the way out to the MCM's limit of 120w but will require 480w to the Sundown driver just to be matching the excursion. If the mcm driver is at it limit for travel at 8mm than so would be the Sundown driver be running at 8mm, with 6mm more throw potential you would need almost 4x the 480w to get that sundown to 14mm excursion. my experience is that with drivers like that car audio focused Sundown it more realistically can handle an rms closer to 500-600w and would be dancing between 12-16mm excursion at those power levels.

Question5
Is there an easier way to understand how to factor in the Xmax or Vd spec to help estimate output potential as it corresponds to the sensitivity and wattage ratings?

I see where your mind is at. I've had the same thoughts and curiosities. I don't have an answer, but I'll add this to the pot for additional consideration (and confusion)...

I used to think excursion was linear across all frequencies. However, it's not. For the same voltage input cone travel may be nearly nothing at one frequency and bottoming out the coil at another frequency. AND, the output is more in the higher frequencies when the cone is moving less distance overall, which is a little counter intuitive and confusing.

To consider your questions, I think we'd have to designate a specific frequency.

And it seems that, for a given voltage, Xmax or Xlim is easily reached at the bottom of the target frequency range when the upper end of the frequency range is nowhere near the excursion limit.

Is it not true that for any given sound pressure level(SPL) there is a specific amount of displacement/volume required?

It's not. Vd is only one part of a complicated equation, so you can't just look at it unless all else is equal, which it almost never is. The only time you can be sure that doubling Vd gives a 6dB increase in maximum SPL is when you double the speaker count with identical speakers.

Seth, as far as my thought experiment is going I am happy to focus on a single frequency or hyper narrow band width definitely centered in the lowest useable range say between 15-30hz. I maintain a few car audio enthusiast friends and the majority of content is about making the biggest waves we can as low as we can.

Bill,
For a given Sd, if 1cm of excursion yields say 90dbspl, is it true that increasing the power to achieve 2cm of excursion would yield 96dbspl and be roughly 4x the power?


I am not currently putting personal effort or money into this stuff but I am supporting my friends as well as my kids are getting near driving age and there is still a scene for car audio and I have opportunity to help them and their friends out in this area. The car audio culture is as you know about bling, flare and flash as much as making noise. So often it is more a financial flex than any kind of real technical or engineering accomplishment. I see guys spending hundreds of dollars on heavy inefficient drivers and then spend hundreds more dollars trying to power them. I am in support of getting stupid with sound equipment in a vehicle, but my current understanding has me diverging from the cultural norms, not to mention my wallet. Between the MCM55-2421 8" driver and those GRS 12SW-4HE 12" drivers, a lot of sound can be made for cheap.

ACUA wrote: ↑Fri Jun 09, 2023 9:13 am For a given Sd, if 1cm of excursion yields say 90dbspl, is it true that increasing the power to achieve 2cm of excursion would yield 96dbspl and be roughly 4x the power?

Yes, assuming there is no thermal or mechanical power compression. But at high levels there will be. That's one of the many variables that affect the result.

I see guys spending hundreds of dollars on heavy inefficient drivers and then spend hundreds more dollars trying to power them.

What they should be spending money on is a book or two to learn how speakers work. If they did they'd become aware that the last thing you should believe is advertising as technical documentation.

Bill mentioned this book a while back. I suspect the answers we're seeking are contained within, but I haven't had the level of inspiration required to dive into it. ACUA, your thirst for knowledge seems high at the moment, maybe you can pull some morsels of insight from it?

The entire book as a PDF
Elements Of Acoustical Engineering - By HARRY F. OLSON, E.E., Ph.D

The only things missing from Olson are T/S specs and anything related to SS and digital electronics. On a related note, every now and then I see 'new' speaker technologies appear. For instance, Cubo and Paraflex. Their proponents think them special, but there's nothing special about them. They'd know that if they'd read Olson. Even Danley Tapped Horns aren't new tech. They're rear loaded folded horns. There have been no true innovations in enclosure technology since the 1960s. Everything 'new' since then has been refinement of known tech. That includes my designs.

Bill, are you aware of an alternative comprehensive source of information on the subject that includes T/S specs?

I'm not, other than project oriented books like those from Vance Dickason and Ray Alden.

Bill Fitzmaurice wrote: ↑Fri Jun 09, 2023 11:39 am There have been no true innovations in enclosure technology since the 1960s.

Without asking for specific dates (estimates are just fine), Bill, what would you name as significant new developments in enclosures over the years, and when?

Horns and line arrays (yes, line arrays) through the 1940s. Acoustic suspension in the 1950s, transmission lines in the 1960s, ducted port bass reflex in the 1970s. I know I said nothing since the 1960s, but that's because while T/S specs that led to the dominance of ducted ports came along in the 1960s they weren't widely known about outside of Australia and New Zealand until 1971. Since then the major development was loudspeaker modeling programs, starting with Akabak in 1995. Akabak is a very powerful tool, but the learning curve resembles El Capitan. HornResp incorporates many of its elements and is far more user friendly.

Seth wrote: ↑Fri Jun 09, 2023 10:48 am Bill mentioned this book a while back. I suspect the answers we're seeking are contained within, but I haven't had the level of inspiration required to dive into it. ACUA, your thirst for knowledge seems high at the moment, maybe you can pull some morsels of insight from it?

The entire book as a PDF
Elements Of Acoustical Engineering - By HARRY F. OLSON, E.E., Ph.D

I downloaded the book. It was fascinating to see it dated 1940, over 80 years ago and most of the innovation remains the same. Today there is more evolved materials and manufacturing processes. The advent and deployment of silicone for electronics as well as the advancement of digital computation has dramatically changed the audio world, but the science and math was locked down back then. It was fun to read through the book identifying how relevant certain things still are and also seeing the history and historic engineering challenges expressed that we have overcome today. There is content about the limitations of tube transistors as well as limitations of permanent magnet material. It is fascinating stuff. I really value how well this book lays out the ability to directly correlate an electrical system or circuit to a mechanical system and an acoustic circuit. The fact that you can represent all three equally is so helpful to conceptualize complicated systems. There is more Latin in the mathematical equations than numbers which renders me unable to understand or absorb any of it. Despite it being a highly mathematical engineering piece of literature there is enough explanation and simplicity that I was able to consume it enjoyably in only a few short days. I did skim over the Microphone content which sped up the read.

As far as finding an answer to any of the proposed questions I have put forth in this thread goes, I can remember one specifically that I feel supports my curiosity:
Page 164-165
G. Power Handling Capacity and the Amplitude of the Diaphragm
The maximum allowable amplitude of the diaphragm is another factor
which may determine the maximum allowable power output. The power
output, in watts, of a horn loud speaker in which the diaphragm is terminated
in an acoustic resistance is:
(an equation that does not transfer properly when I copy and paste)
where p = density, in grams per cubic centimeter,
c = velocity of sound, in centimeters per second,
/ = frequency, in cycles per second,
d = maximum amplitude from its mean position, in centimeters,
Ad = area of the diaphragm, in square centimeters, and
Ah = area of the throat of the horn, in square centimeters.
The amplitude of various diameter diaphragms coupled to a horn throat
of one square inch for one acoustic watt output is shown in Fig. 8.14.

From the graph every halfing of the cone/piston area, a doubling of the amplitude is required to maintain the same acoustical output. I believe this is the same as specifying a given Sd and doubling the excursion is the same as keeping the same excursion but doubling the Sd!

The 1940 version is very good, but the 1957 revision is better.
He doesn't talk about Sd and Vd, as those were yet to be invented T/S specs. Today we'd say with each halving of Sd a doubling of excursion would give equal Vd.

It was fun to read that literature and observe the lack of T/S content. It was easier for me to read because I did not get tangled up in acronyms. I want a physical copy of that book that I can be proud of. That is definitely one of the better acoustical engineering works I have read. Not that I have read many mind you. For $31.00 it is going in my Amazon cart today!

I'm wildly impressed you got through the bulk of that book! I get stopped with the equations because I want to figure them out and understand how the numbers work together to create the result. It would probably take me a couple days to figure them out, then I'd "have" to transpose them into an Excel spreadsheet, and a few weeks pouring over the numbers to get myself to an internal level of deep understanding. I just haven't had the juice for it yet. My hat's off to you.