What's the optimal baffle width?

[HwaLF]

I've read several articles, and I'm getting confused about what the best baffle width and design would be. Some conclude that narrow baffles are better for imaging, while others claim that a wide enough baffle (around 45 cm, or depending on the tweeter) could push the diffraction outside the tweeter's bandwidth. I also read a comment stating that if you make a baffle wide enough so it has no significant diffraction at high frequencies, the wide baffle can actually provide better overall imaging due to an improved direct-to-reflected ratio in the low-midrange frequencies.

Would mounting the tweeter on a bottom plate on top of the enclosure be a viable solution?

What would be the optimal design for full sound with great imaging and soundstage? Any advice or insight would be greatly appreciated.

(PS: I'd rather not do an infinite baffle design due to space limitations)

 

[TurtlePaul]

While there is good science on the preference for linearity of flat on-axis frequency response and smooth off-axis response, there is more disagreement regarding if narrow or wide directivity designs are preferred in general if the preference score is the same.

Wide baffles fit right in there with cardioid vents in regards to being a preference thing that some people have. In addition to the high frequency defraction issues, don’t underestimate how good wide baffles (especially when paired with big bass drivers) are at lowering the Schroeder frequency and baffle step frequency in the bass. Look at the difference between small bookshelf speakers which are omnidirectional at 500 hz while big floorstanders generate some directivity at 200 hz.

If you are just looking to reduce diffraction, consider a faceted baffle like the DXT-Mon or Directiva DIY designs.

 

[Keith_W]

I presume you understand what a baffle diffraction step (BDS) is? In case you don't the BDS is a volume loss of about 6dB that occurs over four octaves. If you were to take an omnidirectional driver and mount it on a flat surface (infinite baffle), it radiates into a hemispherical space. On a loudspeaker surface, at some point, it will transition from hemispherical radiation to spherical radiation. The centre frequency f3 can be calculated with the formula f3 = 115824/W (W = baffle width in mm), or f3 = 4560/W (W = baffle width in inches).

The above shows the effect of the BDS on a woofer mounted on a 500mm non-rounded baffle. In green is a simulation measurement at 10cm, in brown at 3m.

The wider W is, the higher the centre frequency. Is it possible to make the baffle so narrow that you can push the BDS above the tweeter's operating range and make it omnidirectional, as you asked? Working backwards, the f3 has to be two octaves above the hearing range of 20kHz, meaning f3 = 80kHz. Rearranging the math, the baffle width would have to be 1.45mm or 0.057". Complicating matters, most tweeters are not omnidirectional. So in theory, the answer should be "no", since the baffle width is an order of magnitude smaller than the tweeter itself. And even if it was, the tweeter itself is directional.

So if we want the smoothest on axis frequency response, the solution is to make the baffle wide enough so that the BDS is too low to matter (as far as the tweeter is concerned), or to implement some kind of BDS compensation in the XO. Suppose you want to high pass the tweeter at 2kHz. Two octaves below that is 500Hz, which means the baffle width has to be 231mm (9") minimum.

The wavy lines in that graph is due to the squared-off baffle. You can reduce this by rounding over the baffle.

However this does not do anything for directivity matching between drivers. That is another long discussion!

As for wider directivity/narrower directivity as a design goal for better imaging, I think the answer is "nobody knows". Wider directivity = more reflections, and that is a huge can of worms on ASR. Some people believe it provides ambience, some people think it worsens imaging. I certainly don't have an opinion either way, and these kinds of discussions have been done to death on ASR. Being able to design a speaker with smooth directivity is said to be a solved problem with modern modelling software. The big question is what your design goal is going to be, and I don't think any of us can help you there.

 

[Duke]

I just now saw this thread; here is the reply I posted in your similar thread on another forum, in case it might be of interest to anyone here:

My understanding is that the edge reflection (diffraction) generates false azimuth (horizontal arrival angle) cues. This is because this reflection arrives later in time by an interval similar to the arrival time difference between the two ears for a sound arriving from somewhat off to either side. These false azimuth cues degrade the imaging precision.

My understanding is that the imaging superiority of a narrow baffle is because said false azimuth cue is not as big of an angular error as would be the case with a wider baffle because the arrival time of the edge reflection is not as late in time as with a wider baffle.

My understanding is that a sufficiently large round-over (or bevel, which is like a first approximation of a round-over) greatly weakens that edge reflection such that cabinet width is no longer a major factor in imaging. The round-over radius should be at least 1/4 wavelength of the lowest frequency you are concerned about.

So if you plan in advance to use a large bevel or large-radius round-over, you can make the cabinet wider for the sake of pushing the baffle step frequency lower without degrading the imaging. The Snell Type A was an imo excellent example of this approach:

http://www.troelsgravesen.dk/SnellA3i.htm

The round-over does reduce the effective baffle width, from a baffle-step standpoint. If you have a 2" round-over on each side of the front baffle, the effective cabinet width is about 2" less than its physical width. So the effective width of the Snell Type A's mid/tweet baffle is a lot less than its actual physical width.

 

[HwaLF]

I presume you understand what a baffle diffraction step (BDS) is? In case you don't the BDS is a volume loss of about 6dB that occurs over four octaves. If you were to take an omnidirectional driver and mount it on a flat surface (infinite baffle), it radiates into a hemispherical space. On a loudspeaker surface, at some point, it will transition from hemispherical radiation to spherical radiation. The centre frequency f3 can be calculated with the formula f3 = 115824/W (W = baffle width in mm), or f3 = 4560/W (W = baffle width in inches).

View attachment 499658

The above shows the effect of the BDS on a woofer mounted on a 500mm non-rounded baffle. In green is a simulation measurement at 10cm, in brown at 3m.

The wider W is, the higher the centre frequency. Is it possible to make the baffle so narrow that you can push the BDS above the tweeter's operating range and make it omnidirectional, as you asked? Working backwards, the f3 has to be two octaves above the hearing range of 20kHz, meaning f3 = 80kHz. Rearranging the math, the baffle width would have to be 1.45mm or 0.057". Complicating matters, most tweeters are not omnidirectional. So in theory, the answer should be "no", since the baffle width is an order of magnitude smaller than the tweeter itself. And even if it was, the tweeter itself is directional.

So if we want the smoothest on axis frequency response, the solution is to make the baffle wide enough so that the BDS is too low to matter (as far as the tweeter is concerned), or to implement some kind of BDS compensation in the XO. Suppose you want to high pass the tweeter at 2kHz. Two octaves below that is 500Hz, which means the baffle width has to be 231mm (9") minimum.

The wavy lines in that graph is due to the squared-off baffle. You can reduce this by rounding over the baffle.

However this does not do anything for directivity matching between drivers. That is another long discussion!

As for wider directivity/narrower directivity as a design goal for better imaging, I think the answer is "nobody knows". Wider directivity = more reflections, and that is a huge can of worms on ASR. Some people believe it provides ambience, some people think it worsens imaging. I certainly don't have an opinion either way, and these kinds of discussions have been done to death on ASR. Being able to design a speaker with smooth directivity is said to be a solved problem with modern modelling software. The big question is what your design goal is going to be, and I don't think any of us can help you there.

I see! Thank you for the response. I really appreciate the info!