Speaker driver beaming frequency formula

[MZKM]

I live in

BTW, took me all of 2min to find your house (what’s up with the weird cage around your neighbors pool?).
Not sure if you care or not. I’m for sure more on the reserved side (one reason why I don't use my real name).

_______
Back to speakers, would be awesome to see Tom’s speakers measured once supply has been worked out.

 

[hardisj]

BTW, took me all of 2min to find your house (what’s up with the weird cage around your neighbors pool?).

I think it's kind of weird that you went looking, whether it was to make a point or not. Just sayin'.

 

[tomtoo]

@hardisj
Lucky you! Speakers for the big boys.
Lift some jericho horns there, no need for sportstudio any more.

Man...

...J5-4015 “Caleb” is the most accurate powerful High Q loudspeaker ever created. A single cabinet can produce quality audio well beyond 1,000 feet from a true full range Synergy Horn housing twelve x 18” drivers, thirty-two x 8” mid-range drivers and 64 x 1” high frequency compression drivers...

Thats so far away from home hifi like a saturn5 engine from a fireworksrocket

 

[Rick Sykora]

For a very rough classification of the different chassis sizes, such a loudspeaker cabinet-independent formula is useful, especially if you have no other option.

So let's apply all formulas for a 6.5'' woofer. Specifically, it should be the 6.5'' Purifi driver, with about 0.131m effective diameter.
Besides this formula, other formulas were mentioned. Here is an overview of all formulas:

c = speed of sound
dia = effective driver diameter

f-beam < c/N*dia = 2600Hz / 1700Hz / 1300Hz (N = 1, 1.5, 2)
f-beam = 2*c/pi*dia = 1700Hz
f-beam = 2*c/dia = 1300Hz
f-beam = c/dia = 2600Hz



Exactly, nowadays, unlike 40 years ago, every developer has tools at his disposal that more or less accurately predict the radiation behavior.

For very accurate predictions the effort is quite high (because the behavior of the whole driver has to be simulated), for good predictions (around +-1 or +-1.5dB) simulations are relatively easy to set up.

In addition to the obvious influences such as cone shape and driver surround, the shape and dimensions of the loudspeaker cabinet also have a major impact on the radiation pattern of the driver (as already mentioned by others) - the depth of the cabinet also plays a role, which is often not taken into account during preliminary considerations.

So let's take our driver from above and put it into different speaker enclosures.
1) a very narrow cabinet with 17cm width
2) a wide cabinet with 30cm width
3) a very narrow cabinet of 17cm width and shallow depth
4) an asymmetrical cabinet with a width of 8cm at the top and 33cm at the bottom

View attachment 133291 View attachment 133292 View attachment 133293 View attachment 133294

As a measure of beaming, we consider the -6dB point (sound pressure level is lowered by 6dB) relative to the normalized axis frequency response, for each enclosure shape:
View attachment 133302

After the transition from full-space to half-space, the loudspeaker cabinet significantly determines the radiation pattern.

- Wide cabinets show a significantly different radiation pattern than very narrow ones (green and cyan curves).
- The cabinet depth also has a significant influence on the radiation pattern (cyan and red curves).

Only above 2.2 - 2.6 kHz the driver itself determines the radiation.

For all those who think it would change fundamentally, if one does not normalize to the axial frequency response, here the same analysis normalized to the 30° frequency response:
View attachment 133303

For all those who can't do anything with the upper diagram, here are the simulations of the frequency responses 0-180deg

To summarize, for a minimal baffle, driver effective diameter times the speed of sound is a workable rule of thumb.

For applications where the baffle is more of an influence, half the effective diameter times the speed of sound is more appropriate as a rough estimate.

Otherwise, for more accurate prediction, better to model. For basic baffle shapes, modeling could be done with VituixCAD diffraction tool. For more complex cabinet and baffle interactions, need more sophisticated BEM/FEM/FEA tools to simulate.

 

[Andysu]

okay , there is so many speaker parameters to understand . okay , beaming from what i can see in the graphs for each frequency wavelength and the on-axis looking directly at the speaker and the off-axis looking at the speaker from the side angle , yes i wouldn't notice a certain frequency very clearly as i (or anyone else) at that certain angle . yeah , i think i understand a bit more about this . okay going to pet my cat now as he needs some on/off axis petting otherwise he gets grumpy and they do this to my JBL speakers , so this JBL G12 won't be doing much beaming now .



i know Danny may not be everyone flavour here, but he seemed to explain it

 

[bert stoltenborg]

Hi all

I saw this below formula for calculating speaker driver beaming frequency for driver diameter but when I saw this video by Danny, his numbers for various driver sizes don't match my spreadsheet.

Watch Danny from 7 minutes to 8 minutes. Can anyone help with the correct formula?

Thanks!

View attachment 132699

2*C ? WTF?

 

[Rick Sykora]

This thread already recommends best practices for determining beaming. None support what Danny posted.

Simply ignore him.

p.s.

Realized what I wrote about may seem overly dismissive, but we have better tools and many driver measurements show more off-axis behavior than in the past. Anyone doing serious speaker design work will use this information and the integrate measurements with modern simulation tools. A rule of thumb (ROT) is only really useful as long as you understand the assumptions it is based upon. One can spend time trying to characterize the ROT assumptions or apply newer tech for a more comprehensive result. I prefer the latter.

 

[bert stoltenborg]

This thread already recommends best practices for determining beaming. None support what Danny posted.

Simply ignore him.

p.s.

Realized what I wrote about may seem overly dismissive, but we have better tools and many driver measurements show more off-axis behavior than in the past. Anyone doing serious speaker design work will use this information and the integrate measurements with modern simulation tools. A rule of thumb (ROT) is only really useful as long as you understand the assumptions it is based upon. One can spend time trying to characterize the ROT assumptions or apply newer tech for a more comprehensive result. I prefer the latter.

To write simulation software you of course need to understand the physics and know the formula

 

[Music1969]

2*C ? WTF?

In later posts on page 1 you see the explanation for this formula

 

[bert stoltenborg]

In later posts on page 1 you see the explanation for this formula

I see a load of opinions

 

[Music1969]

I see a load of opinions

Feel free to add value to this thread and share your opinion ?

 

[Rick Sykora]

To write simulation software you of course need to understand the physics and know the formula

Agree, though there may be different math depending on how sophisticated the solution is. As this thread reveals, the cone shape and baffle size and shape play a role in how much beaming and at a broader set of frequencies. This is much more key for integrating drivers to create a speaker that has good directivity.

A rule of thumb can be a useful start, but is rather crude compared to the broader solution that simulation software supports.

 

[bert stoltenborg]

Agree, though there may be different math depending on how sophisticated the solution is. As this thread reveals, the cone shape and baffle size and shape play a role in how much beaming and at a broader set of frequencies. This is much more key for integrating drivers to create a speaker that has good directivity.

A rule of thumb can be a useful start, but is rather crude compared to the broader solution that simulation software supports.

You can make stuff as complicated as you want, but the second law of newton is in essence F=ma and a circular piston (not sure if this is a pleonasm ) is beaming from c/pi d.

 

[fpitas]

Not to take all the fun out of it, but most good drivers' datasheets show off-axis response. The cabinet will affect it, but that gives you a real good idea going in.

 

[bert stoltenborg]

Not to take all the fun out of it, but most good drivers' datasheets show off-axis response. The cabinet will affect it, but that gives you a real good idea going in.

True, but this topic is about the beaming formula for a piston and not about all the off topic bullshit . The formula is totally valid like the laws of Newton. Or it is a next reason we should skip the word 'science' in the forum name.

 

[Rick Sykora]

Cannot speak for the OP, but this all really comes down to what problem do you want to solve?

If the goal is a simple characterization of beaming, a simple formula may suffice. If the goal is designing a good speaker, than getting fixated over one aspect of the system (like one simple formula) is shortsighted. The OP cited a GR post and (not surprisingly considering the source), it comes up shy.

From personal experience, am very confident that most people could care less about speaker beaming. It may be more interesting to a casual audiophile, but it really matters to a good speaker designer. In my opinion, beaming can be explained without needing the math. For anything beyond a simple understanding, applying the math requires a more comprehensive view.

 

[fpitas]

True, but this topic is about the beaming formula for a piston and not about all the off topic bullshit . The formula is totally valid like the laws of Newton. Or it is a next reason we should skip the word 'science' in the forum name.

Yet many actual drivers do not act purely pistonic. If the object here is to only study theory, that doesn't matter. But if the object is useful knowledge for speaker design, that matters.

 

[fpitas]

I had always been taught that cone drivers started to beam at a frequency corresponding to the speed of sound in inches (roughly 13,500) divided by the diameter of the cone (which is always less than the frame diameter). For a six-and-a-half inch driver, that would be approximately 2.250 cycles.

What I found interesting was the use of the word "started". I believe that word is somewhat mis-used. From what I have found, narrowing starts at half that frequency, but the effect is so subtle to human ears that it is almost unnoticeable. The frequency derived from the simplistic formula above is the point at which the beaming becomes noticeable, and one more octave defines the frequency where the beaming becomes, for lack of a better word, obnoxious (approximately 4,500 cycles).

So .... a question:

Is the formula for beaming based on absolute physics, or is it based on our rough human perceptions?

Jim

Physics. But as I said above, the reality is that a lot of drivers don't start beaming until well past where theory says they should. The cone does not act as a simple piston.

 

[617]

In my experience, there is definitely a diameter related trend influencing directivity, but baffle size has an effect, and at a certain point the motion of the cone becomes non pistonic. This essentially means the cone is divided into smaller sub regions moving independently which, due to their smaller size, create wider dispersion, but due to their number, this dispersion is chaotic.

I believe cone geometry and phase plugs make a difference as well.

BmR drivers control this breakup, which is why they don't beam.

I never thought 'beaming' was a useful way of looking at speaker radiation unless you can specify a threshold where it is significant . An eight inch woofer will produce some 10khz energy at 180 degrees, it's just a matter of how much. The transition from omni to hypercardioid is totally continuous.

 

[fpitas]

FWIW, with horns beamwidth is usually quoted as -6dB re on-axis. I'm not sure such a standard exists for cone drivers.