Speaker baffle design, diffraction and baffle step
Does speaker box shape matter ? Is baffle design important ?
Baffle design and cabinet shape is important for a hi-fi loudspeaker build. But let’s dive into the subject, by observing what most of the speaker manufacturers are doing. They are producing rectangular shaped cabinets. Does that mean that the best shape is a rectangle ? Not quite. Making a rectangular box has the advantage of being easier to build, both for the mass producer and for the hobbyist. It is easier to integrate in your living room as a furniture. They have to make sense in terms of size and visual appeal.
Of course, making sure the you got the right volume for the box is paramount, but taking care of the small details will ensure a great result. Lets split the shape of the box into 2 categories :
- The inner shape. Parallel surfaces encourage standing waves. Making a cabinet more angular, will minimize this drawback. However, other solutions like sound deadening material, will work wonders. The proportions of the box are important as well. Make sure if you divide the dimensions of the box between each other (height / width or width / length etc), you don’t get a whole number. A cube would be a worst choice, for example. This is to minimize resonances.
- The outer shape. This has to do with diffraction from the edges of the cabinet, also known as edge diffraction, which we will discuss in depth.
Diffraction happens when a sound wave meets an obstacle. When this happens, the sound wave is distorted or its direction is modified. This happens differently, depending on the frequency of the sound. Different frequencies have different wavelengths. If the wavelength is bigger than the size of the obstacle, it passes through it like it’s not even there. So for woofers, diffraction is not much of an issue. For higher frequencies, which have a short corresponding wavelength, diffraction can and will happen.
Edge diffraction – We can see in this drawn explanation of diffraction, that the speaker is generating sound waves, and the waves are expanding in a hemispherical fashion. When the waves reach the edge of the speaker baffle, the pressure drops, because the waves expand from half space to full space. This pressure difference creates another sound wave, which originates from the edge of the cabinet and moves forward. This wave will have phase mismatches with the original wave, and it will alternately reinforce or diminish it, causing ripples in the frequency response.
The sound is radiated in all directions, so when it reaches the edge of the baffle, it traveled a shorter or a longer distance, depending on which part of the edge it arrived. This is important, because each frequency has its own wavelength, and when it will diffract from the edge, it will have different phase relationships with the original wave.
Phase and edge diffraction
- half of wavelength of a particular frequency, when it diffracts, it will be 180° out of phase with the original wave and cancellation will occur. The cancellation is not perfect though, but it will translate into a dip in the frequency response, at that particular frequency. This also happens if the distance is a wave and a half, 2 waves and a half etc
- one wavelength of a particular frequency, when it diffracts it will be 360° out of phase with the original wave and that is basically in phase. Which means it will reinforce the original wave, for an up to +3 db. This happens if the distance is 2 wavelengths, 3 wavelengths etc.
Imagine how many lines can you draw from the center of the speaker to the edges of the baffle (lines of different lengths). Now imagine how many different frequencies the speaker will play. These frequencies have corresponding wavelengths. The possibilities are endless for the wavelengths to match the speaker-edge distances in half and full multipliers. This will create multiple dips and peaks in the frequency response, also referred to as ripples.
Shape of the box
The shape of the cabinet has a major impact on diffraction intensity. Diffraction has to be minimized as much as possible, because it has a detrimental effect on the frequency response. To review our cabinet shape options, we can analyse a study, made several decades ago, by Mr. Harry Olson. The study features 12 different enclosure shapes, with speaker mounted in more than one location for some of the enclosures. Then, he measured the on-axis frequency response, to see if there are any SPL variations. Indeed there are, starting from almost flat response to ± 5 db variations.
Cabinet and baffle design
The study included very odd shapes, like a double pyramid and we are going to list the shapes and SPL variations that make sense in the real world :
- Sphere ± 0.5 db.
- Rectangle ± 3 db.
- Beveled rectangle ± 1.5 db.
- Cube ± 5 db.
- Beveled cube ± 1.5 db.
- Cylinder ± 2 db.
As you can see, the sphere is the shape with the least amount of diffraction. Manufacturing process is quite challenging to create a sphere shaped speaker cabinet. You encounter them rarely, but there are manufacturers who take advantage of reduce diffraction and make speakers like Morel Soundspot. As expected, the cube is the worst shape you can go for.
Interestingly enough, beveling creates a significant drop in SPL variation (therefore less diffraction), even for the cube. This doesn’t excuse the fact the cube will have terrible panel resonances. Because they are the same distance, one panel from another, at a certain frequency, the resonance will reinforce each other and will make the enclosure “ring”. And now we are back the the old rectangle. As you can see there is a good diffraction drop to be achieved by rounding the edges of the enclosure. While the sphere is still king, when it comes to diffraction issues, the beveled rectangle is not far behind, and considering the other building advantages of rectangle cabinets, makes it a very popular choice.
Driver placement on the baffle
Where should I place my speaker drivers on the baffle? First of all, is that even an issue worth considering in your baffle design? Driver placement does create some SPL variations in the frequency response. If you look at what most manufacturers are doing, you are going to observe that they are placing the drivers in the center, on the horizontal axis, and vertically they place the tweeter at the top, the midrange in the middle and the woofer at the bottom. Sometimes the woofer is at the top, in woofer – tweeter – woofer combination.
All of the speakers are kept as close to each other as possible, to minimize the vertical acoustical center misalignment. Some of these decisions are taken to make the production process easier. If you center the speakers horizontally, the baffle design will be the same for both the right and left speaker. If you place the tweeter offset to the right, you have to place it offset the left on the other speaker. This is to keep it look symmetrical and it is called mirror-imaged speakers.
Here is a table showing the SPL variation of a tweeter and a 4.5″ midrange speaker, in different locations on the baffle :
As you can see, placing the speaker into different locations on the baffle can yield better or worse results. Another thing we can conclude is that offsetting the speaker to the left or to the right, can improve the linearity of the frequency response. Offsetting a midrange speaker placed on the middle of the baffle (vertical wise), can have a pretty significant improvement (2 db variation). Other locations will have a negligible improvement from offsetting, so that is why you don’t see this practice that often.
When a source (the speaker) is emitting sound, it is radiating in all directions equally, like a sphere that is growing in size. Because the baffle itself is an obstacle, the sound can’t expand similar to a growing sphere. One half of the sphere (in front of the speaker) is expanding normally, but the other half meets the baffle and bounces from it. 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.
OK, great ! This means the baffle design will actually increase the efficiency of the speaker. Not quite. Not all frequencies benefit from this effect. Like we talked before, every frequency has it own wavelength. Low frequency (bass) have long wavelengths, while high frequencies have shorter wavelengths. An obstacle has to be sufficiently large compared to the wavelength, to diffract the wave.
- If the object (baffle in our case) is at least half of the wavelength of that particular frequency, full diffraction will occur.
- If the object (baffle in our case) is 10 times smaller than the wavelength of that particular frequency, the wave passes through like there is no obstacle.
- This means that for bass notes, with long wavelengths, the baffle is insignificant in size, and the sphere grows unhindered, therefore the +6 db doesn’t happen.
- If the size of the object (baffle in our case) is somewhere between the previous 2 sizes, partial diffraction will occur (more or less, depending on the baffle design).
Imagine a speaker with a baffle width of 10″.
- The wavelength of 10″ corresponds to the frequency 1360 Hz (see online converters).
- For diffraction to occur, the baffle needs to be the equivalent to half of wavelength (or larger).
- Half of wavelength at 10″ <=> Full wavelength at 20″ <=> Frequency of 680 Hz <— This is the Baffle Step.
- All the frequencies above the 680 Hz mark will gain a boost in output (+6 db).
- All frequencies below the 680 Hz mark will gain partial or no output boost.
Diffraction, edge diffraction and baffle step are important issues, that need to be considered for cabinet and speaker baffle design. While some aspects of diffraction are more important than others, it is good to know them and act accordingly, depending on your project. Furthermore, for the ending of this article, I want to make a list, on how to reduce the effects of diffraction. Some were mentioned before, but i want to group them in a list.
- Best way to eliminate diffraction is to use an infinite baffle. Or a finite baffle design, which extends 17 m in all directions (this eliminates diffraction up to 20 Hz). Highly impractical.
- Choosing a different shape for the cabinet (sphere is the best one).
- Rounding the edges of the cabinet.
- Offsetting the speaker.
- Baffle step is addressed in the crossover design. It is called baffle step compensation (BSC) and lowers the output of the frequencies above the baffle step.
- Countersinking the speakers. Picture to the right showing a M-Audio BX5 with a countersunk tweeter.
- Lining the speaker cabinet with felt (while not the most appealing looking, it has considerable effect on reducing diffraction).
- Loudspeaker Design Cookbook 7th Edition by Vance Dickason (Audio Amateur Pubns, 2005).
- Master Handbook of Acoustics by F. Alton Everest, Ken Pohlmann (McGraw Hill Professional, 2009).
- Image source : link.