Speaker driver beaming frequency formula

[Jim Matthews]

Beaming = speed of sound / driver effective diameter / 2

effective diameter = half surround to half surround

divide by 2 to get half wave

some will divide by 4 but 2 is close enough and makes more sense when talking about CTC spacing.

I said as much in post #2.

I think the OP is just starting out and is looking for someone to agree with him. So far, I haven't seen any support for the (overly complicated) formula he's stuck on. Danny Richie has been at it long enough that he has a grasp of the fundamentals.

I suspect this is yet another case of RTFM.

"Yea, brethren let us turn to page 83, table 6.1 in our hymnal..."

https://meniscusaudio.com/product/loudspeaker-design-cookbook/

 

[Music1969]

I think the OP is just starting out and is looking for someone to agree with him.

Lol how rude of you and no I'm not looking for someone to agree with me.

Just above your post I asked if anyone is familiar with the formula I shared... including the link where it's from.

See post #20

You said the formula may apply to lobing but they use the word beaming as I showed you via screenshot (it's at the link).

 

[Zvu]

How do you define beaming? Is it anything less than omnidirectional? If not is it a specific dispersion angle? If so what is that angle?

We should be practical in my opinion.

Since usual crossover point is at -6dB, i'd define it like frequency where 45 degree response is -6dB relative to on axis response.

Given that there are waveguides with wider/narrower angle of dispersion, it is highly debatable and unusable for a waveguide with 60 degree horizontal dispersion or for 120 degree hor. dispersion. And this all assumes that we have a waveguide that controls the directivity at wanted crossover point. For direct radiators it's just mayhem - no calculations, just measurement would tell.

 

[TimVG]

We should be practical in my opinion.

Since usual crossover point is at -6dB, i'd define it like frequency where 45 degree response is -6dB relative to on axis response.

Given that there are waveguides with wider/narrower angle, it is highly debatable and unusable for a waveguide with 60 degree horizontal dispersion or for 120 degree hor. dispersion. And this all assumes that we have a waveguide that controls the directivity at wanted crossover point. For direct radiators it's just mayhem - no calculations, just measurement would tell.

Agreed!

 

[Tom Danley]

There are a couple simple points on the graph that is easy to remember.
When a simple piston is about 1 wavelength in diameter, the radiation pattern is about 90 degrees.
The point it departs from being an omni source (and reaches the knee in the radiation resistance curve) is when it's diameter is K=1 about 1/3 wl or 1wl in circumference. Complex radiation begins (and produces a narrower lobe with sub lobes and nulls) when the piston is still larger

Examine the polar plots here;

http://www.acousticfrontiers.com/20...kers-open-up-your-acoustic-treatment-options/

 

[Music1969]

I haven't seen any support for the (overly complicated) formula he's stuck on.

It's not even overly different to the other formula shared so no need for dramatic "overly complicated" language here.

After more digging it just appears to be a safety margin on the more general formula (as I already guessed earlier in this thread).

It's basically a 0.64 safety factor.

This guy below also mentions safety margin although not the 2/pi factor. He shows 3 x 8inch drivers start beaming above 1kHz

Using the formula that has (2/pi) factor results in f = 1kHz for 8 inches

https://code-acoustics.blog/2018/08/31/pistonic-motion-speaker-design/

 

[Music1969]

Obviously it's best is to consider individual driver specifics , case by case, rather than blindly applying a formula.

But I imagine here he's trying to show some safety margin is better than no safety margin.

Whether 0.64 is right number or too conservative , I have no idea.

Sometimes too conservative can be impractical.

I guess it shows one of major benefit of 3-way over 2-way design, although there's more challenges too.

 

[Jim Matthews]

It's not even overly different to the other formula shared so no need for dramatic "overly complicated" language here.

After more digging it just appears to be a safety margin on the more general formula (as I already guessed earlier in this thread).

It's basically a 0.64 safety factor.

"As a rule of thumb, speaker drivers will start beaming a frequency having a wavelength equal to the diameter of the radiating cone. Just a few comments here to illustrate the problem as I've had to explain this many times from mails coming in.

Having an 8" driver with a cone diameter of 17 cm, beaming will start at 34400/17 = 2023 Hz (speed of sound in cm/diameter in cm)."

http://www.troelsgravesen.dk/Beaming.htm

One could not have a better guide for DIY than the amazingly generous Mssr. Gravesen. My first successful project was his Quattro design.

http://www.troelsgravesen.dk/QUATTRO_James.htm

 

[Music1969]

Having an 8" driver with a cone diameter of 17 cm, beaming will start at 34400/17 = 2023 Hz (speed of sound in cm/diameter in cm)."

Then he goes on to show beaming starts before this number and recommends 3-way design lol

Just like the blog I linked above shows.

Anyway it's just safety margin. Nothing more complicated than that. Always best to look at case by case driver specifics of course

 

[hardisj]

As I said: use half-wavelength.

speed of sound / effective diameter / 2

 

[Music1969]

As I said: use half-wavelength.

speed of sound / effective diameter / 2

Yes so thats just 0.5 vs 0.64 'safety margin' difference

 

[Music1969]

I said as much in post #2. I think the OP is just starting out and is looking for someone to agree with him.

No this isn't what you said in post #2 by the way... You haven't divided by 2 for half wavelength... so your figure is double what @hardisj suggests to use...

 

[hardisj]

Yes so thats just 0.5 vs 0.64 'safety margin' difference

From personal experience, ignore this safety margin. Use half-wave and call it a day.

The real problem - if you want to split hairs - is making sure the diameter you are using is correct. Just in case you don't follow I'll give you an example. A standard 6.5-inch midwoofer might measure 6.5-inches in overall diameter of the frame, but the actual diameter from half-surround to half-surround might be 5.8-inches instead. Generally, I just use a factor of 0.85*diameter to get a general wag at the beaming frequency. That gets me in the ballpark and is easy enough to do without needing to look up specifications or breaking out calipers (though, I do the latter when I measure T/S using my Klippel, time stamped below).

If you have it from a manufacturer, you can also back the effective diameter out of the Sd as Sd should be provided using effective diameter.

 

[Music1969]

The real problem - if you want to split hairs - is making sure the diameter you are using is correct. Just in case you don't follow I'll give you an example. A standard 6.5-inch midwoofer might measure 6.5-inches in overall diameter of the frame, but the actual diameter from half-surround to half-surround might be 5.8-inches instead.

Yes that was discussed in post #17

To use "effective piston area" given in driver spec sheet shown in the example, to work out the diameter to use

 

[hardisj]

Yes that was discussed in post #17

Hey, man, in my defense, I felt I had addressed everything that needed to be addressed in my initial reply to this thread and the fact that it still lives on is all a bit off to me.


Now, to take it a step further, don't forget to consider non-circular speakers. Rectangular drive units such as AMT or ribbon tweeters, oval shaped woofers... that sort of thing. They have different beaming points for different dimensions.

 

[Music1969]

Hey, man, in my defense, I felt I had addressed everything that needed to be addressed in my initial reply to this thread and the fact that it still lives on is all a bit off to me.


Now, to take it a step further, don't forget to consider non-circular speakers. Rectangular drive units such as AMT or ribbon tweeters, oval shaped woofers... that sort of thing. They have different beaming points for different dimensions.

Lol thanks dude! Your post came later in post #19 haha (cheeky smile)

Shouldn't be a surprise that the thread lives on when there are 3 different formulas discussed. Somebody may still chime in with a 4th lol

Certainly will use your formula as it's most conservative of the 3 but if I use drivers with lots of off axis data provided that is better than using any formula I guess

Thanks again for al your help and info, certainly appreciate it

 

[hardisj]

Certainly will use your formula as it's most conservative of the 3 but if I use drivers with lots of off axis data provided that is better than using any formula I guess

Well, using the 1/4 wave rule (dividing by 4 instead of 2) really is the most conservative but the problem is that it's pretty much impossible to build a modern speaker with less than a 1/4 wavelength between two drive units, even if you modify flanges to make it happen. So, the 1/2 wave "rule" is "close enough".

 

[Music1969]

Well, using the 1/4 wave rule (dividing by 4 instead of 2) really is the most conservative but the problem is that it's pretty much impossible to build a modern speaker with less than a 1/4 wavelength between two drive units, even if you modify flanges to make it happen. So, the 1/2 wave "rule" is "close enough".

Yes noted, I discussed the practical issues of being too conservative earlier and yes what you mention is in one of the links I linked

Thanks again dude, appreciate the insight

 

[fluid]

Instead of using a formula you could use VituixCAD to simulate the directivity based on the piston area or diameter for both circular and rectangular drivers.

Then you can see it in either a line chart or a polar map whichever suits. This is pretty accurate and you can also include the baffle shape to see the effects of diffraction at the same time. This is a 15" driver normalized.

 

[Rick Sykora]

Instead of using a formula you could use VituixCAD to simulate the directivity based on the piston area or diameter for both circular and rectangular drivers.

View attachment 132878

Then you can see it in either a line chart or a polar map whichever suits. This is pretty accurate and you can also include the baffle shape to see the effects of diffraction at the same time. This is a 15" driver normalized.

View attachment 132876

View attachment 132877

Instead of using a formula you could use VituixCAD to simulate the directivity based on the piston area or diameter for both circular and rectangular drivers.

View attachment 132878

Then you can see it in either a line chart or a polar map whichever suits. This is pretty accurate and you can also include the baffle shape to see the effects of diffraction at the same time. This is a 15" driver normalized.

View attachment 132876

View attachment 132877

Thanks for sharing!

Still discovering all that VituixCAD does. When you do not have measurements, this is a way better representation than the simple formula yields!