PM DIY Baffle Step

Andre Vergison

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After reading articles such as https://sound-au.com/bafflestep.htm and https://trueaudio.com/st_diff1.htm it seems to me that the PM DIY would loose 6 dB due to the baffle step whenever used in open air, that is when there is no back wave reflection. Assuming a box width of 40 cm then a 6 dB drop would occur at F3 = 115 / .4 = 287 Hz.
Is that really happening in practice?

How about mounting a simple solid baffle around the pole-mounted box? This pic below shows two half baffles (in red) which could be mounted both sides of the box (blue).
A total width of one meter would already move the step F3 downwards to below 115 Hz.

1574764925050.png

In fact that's what the old Altec (and other brand) cinema speakers did:
1574765143258.png

Also, putting multiple boxes together will also cause a similar effect. Line array units probably also do.

I agree that adding flaps around a pole mounted speaker may not always be practical (wind shield!) but you still can easily obtain more lower frequency SPL with the same power.

BTW, having written this I still wonder how we should interpret the "6 dB" figure. In https://trueaudio.com/st_diff1.htm I read:
Most loudspeaker modeling is performed based on the assumption of radiation into half space. A speaker radiating into half space plays 6 dB louder than the same speaker radiating into full space. This is the crux of the diffraction loss. A full range speaker finds itself radiating into half space at the upper frequencies but radiating into full space at lower frequencies. As a result, there is a gradual shift of -6dB from the highs to the lows. This is what is called the "6 dB baffle step" or the enclosure’s "diffraction loss".
Here "6 dB louder" sure kind of implies 6 dB SPL. However I understand that when the same power emitted into full space is directed into half space you'll experience twice as much power whenever you are located in that very half space. Assuming no directivity that means that the SPL will increase by 3 dB, and not 6 dB. I still agree that the sound POWER level (SWL) will increase by 6 dB (and 6 dB after all is a ratio of about 2) but not the sound PRESSURE level (SPL).
For instance, it's not the first time that I'm reading that adding a second subwoofer will increase the SPL by 6 dB. Wow, that would be wonderful indeed: if a speaker produces 100dB SPL with 1 watt, then add another one and you get 106 dB. Add another two speakers (4 watts in total) to get 112 dB. Eight watts yields 118 dB. And so on. Then a set of speakers good for 1024 watts would then produce a whopping 160 dB! Hmm.

Hence the baffle step would be 3 dB SPL, not 6.
Or did I miss something?

Andre
 

Peter Morris

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Firstly the PM DIY was designed to be relatively small and pole mount. This meant there were compromises made, especially in the low frequency area.

The trick was using a horn and compression driver that could go low enough to be used a 12” bent horn and a box design that had no wasted space to keep the size and weight down.

While I expect there would be an increase in SPL at the low frequencies by adding a baffle, I think you would be much better off increasing the size of the horn – longer path and bigger mouth, but then the concept has changed :)

The gain from the baffle occurs because you are effectively radiating into ½ space instead of whole space, but where the directivity is already controlled by the horn there is nothing to be gained.

When you talk about getting 6 dB of additional output by putting 2 speakers together - you get 3 dB more output because you have doubled the power input, and 3 dB because of the increase in efficiency. The area of 2 cones provides a better impedance match (coupling) to the air and the efficiency goes up. There are limits to this, and when the array size becomes large compared to the wavelength of what its producing other problems occur ...

Put two compression drivers on more or less the same horn you will only get 3 dB increase in output. There will not be an increase in efficiency as the horn has already increased the efficiency of the system by matching the acoustical impedance of diaphragm to the air.
 
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Andre Vergison

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When you talk about getting 6 dB of additional output by putting 2 speakers together - you get 3 dB more output because you have doubled the power input, and 3 dB because of the increase in efficiency. The area of 2 cones provides a better impedance match (coupling) to the air and the efficiency goes up. There are limits to this, and when the array size becomes large compared to the wavelength of what its producing other problems occur ...
True. I tried this out using two 6" drivers close to each other and an SPL meter somewhere in the room, and feeding the drivers with 400 Hz. In parallel I get 6 dB gain when adding the second driver, and power has doubled. When wired in series then shunting one of the drivers (half impedance -> double power on a single driver) yields about equal SPL.

So replacing one driver by two will buy me +3 dB for the same amount of power.

Now, if I replace a single 6" by four drivers in a tight square (let's not consider lobing effects etc.) and connect them in series and parallel to get a same input impedance then I would get +6 dB with the same input power, right?

Via http://techtalk.parts-express.com/forum/tech-talk-forum/44566-added-spl-by-doubling-drivers?p=628587#post628587 and going to the said book, I read on page 78 that the frequency below which mutual coupling (causing an increase of radiation impedance) becomes effective is given by

F = sqrt(N) * c / d

N is the number of coupled drivers
c is the speed of sound (m/s)
d is the nominal spacing between drivers (m)

A figure on the same page confirms that 4 units may add up to 6 dB given a same input power.

So my four squared 6" drivers would then be 6 dB more efficient up to some 2500 Hz.

A more impressive example is two rows of four adjacent subwoofers (8 in total) which would gain 9 dB efficiency in their typical subwoofer range. If one subwoofer gets 1,000 watts then the equivalent power for the whole group would become 8 * 1,000 * 8 = 64,000 watts. I.o.w. if there were no coupling then you'd need 64 subwoofers to get the same SPL.

Crazy.

The gain from the baffle occurs because you are effectively radiating into ½ space instead of whole space, but where the directivity is already controlled by the horn there is nothing to be gained.
Of course. But do you have an idea of the directivity of the DIY mid horn both horizontally and vertically? Did you also mean that at lower frequencies (say 100 Hz) the box is not omnidirectional at all?
 
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Peter Morris

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Yes we do have a good idea of its vertical and horizontal directivity. In fact the dipole arrangement and crossover point was designed with that in mind - to control the vertical directivity down to quite a low frequency. Lots and lots of off axis responses were measured.

Below is the directivity plot of a box that should be similar down to about 700Hz after which the DIY vertical directivity is is estimated (red line)

As I said above, if you want more SPL in the low frequencies then I believe you are better to make the horn bigger rather than adding a baffle.

You get the advantage of better directivity in the low frequencies AND the longer horn which will give you better horn loading of the lower frequencies .... model it in HornResp and you will see what I mean ... may be as much as 6 - 10 dB at 100Hz by increasing the horn length by 30cm, BUT the box becomes much bigger and not pole mountable.

Also don't forget that the DIY was designed to be crossed at 100Hz, at which point the directivity of the sub / bass bin comes into play.

You talked about putting 6" driver together .... yes they will sum but you need to have a look at what happens to the polar's as the frequency goes up beyond about 1000 - 1500 Hz :cautious:
 

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Andre Vergison

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Summarizing a bit:

adding a second subwoofer will increase the SPL by 6 dB
That's true indeed, discussed above.

Hence the baffle step would be 3 dB SPL, not 6.
6 dB it is, and http://audiojudgement.com/speaker-baffle-design-and-diffraction/ explains it nicely:
What actually happens is, that the sound which should be going backwards, reflects from the baffle and goes forward. These waves will merge with the waves that normally expand forwards, to combine for a +6 db in output.

Looks equivalent to the following: we take the speaker, without baffle, let it radiate forward and add a second forward radiating speaker generating the lost backward waves (the other half space, hence same energy). We get twice same output, hence again +6 dB. However, in this scenario we'd have to supply double power. With the baffle we don't need it, the baffle increases the efficiency.
All of that within frequency range limits, of course.