I think this one is a little bit of "form follows function" and a lot of "form follows practicality".
I'm curious about the typical speaker and subwoofer design. If sound is caused by vibrations, why are the devices producing those mostly round and slightly concave? Is this optimal for acoustics, or perhaps a compromise of strength, power handling, material cost, etc...
The round shape has many advantages in manufacturing like being able to use a lathe to turn metal parts to size, being able to apply adhesives with a stationary applicator while the speaker spins around on a bearing like a lazy-susan, and not having to control the orientation of many parts since a round magnet mates to a round steel plate and a round basket no matter how you spin them. It is convenient to take a sheet of material and roll it into a round shape like the former of a voice coil, or the copper windings of the voice coil itself.
The motion of the voice coil is also very critical to control, especially since the clearance in the magnetic gap is very tight (often less than a fraction of a millimeter). A round shape for things like the spider and surround apply a uniform force in every direction which keeps the voice coil centered in the magnetic gap really well.
A round shape also has no stress concentrations whereas a square shape would have a stress concentration at each of the four corners. This means the stress or friction or stretching of a material is exaggerated in a few specific spots which will lead those areas to always fail first. Think of a ketchup packet. You can press and pull and squeeze along the smooth edges of those things all you want and they will never open. But if you tear really gently on the edge with ruffles you can rip them apart easily. That is a stress concentration, which is a great thing for ketchup but a bad thing for speakers (like square ones). Actually anything with a "tear here" is a stress concentration on purpose.
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Round shapes are also super easy to cut into cabinets compared to square holes. Sure you can get some more surface area with a square driver but the raw convenience of making round holes is huge.
The acoustic performance off-axis of a round shape is also very easy to predict. Having the same polar pattern up and down vs side to side is not always desired, but it is super predictable and relatively simple methods can be used to design with round speakers.
Chithead, if you mean round vs say the kicker square cones then the issue is boundaries. A round sub has one boundary to keep on the same plane for smooth waves to develop from. If you look at Kicker’s square cones, they have to keep excursion down since it is harder to keep the square cone in the same plane, which would develop the cleanest waves. Plus a square potentially has 4 boundaries corners with each having the opportunity to be slightly out of sync if not perfectly in the same plane, which means a less clean audio wave since it isn’t one clean wave but potentially 4 waves slightly distorted from each other (corners). That’s the audio enthusiast answer and I’d be interested in how Justin can correct me, not that correction is the point. But that is a good question and I’d be interested to know how much further down the deep audio hole Justin could take it.
Interesting idea. I think you're talking about what happens when a cone stops moving as a single rigid body and starts to deform. Or maybe you're asking about how the corners would have a higher stress/pull on them kinda like the stress concentrations I mention above.
A square cone and a circular cone both have standing vibration modes (or breakup modes) at a high enough frequency. They are really neat to visualize and this was the entire subject of my first class at Penn State with Dr. Russell. He has an amazing website with tons of fantastic animated pictures of vibrations: everything from the textbook-style that I'm borrowing below to actual measurements he's made of hockey sticks and baseball bats and acoustic guitars.
If you have a moment, PLEASE go browse the few pages Dr. Russell has. It's mostly like a picture book of really fascinating animations that don't need any science to understand. He's one of the best teachers I've ever seen!
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Image from Dr. Russell at Penn State, at his website:
https://www.acs.psu.edu/drussell/demos.html
https://www.acs.psu.edu/drussell/Demos/MembraneCircle/Circle.html
https://www.acs.psu.edu/drussell/Demos/rect-membrane/rect-mem.html
I would also think the concavity of a speaker is due to space limitations. If it was flat or convex, this would then mean that the speaker needs more space in front of it to be able to move. Ultimately it is about how much air can be pushed/moved and how much space it needs.
I would also think the concavity of a speaker has to be important in some way to the way it is moving the air, concave would mean that all of the air is being sent straight out, convex would send the air out in more drastic angles, and flat would match the in/out angles, but I could be wrong about that reasoning since I am basing that off of more how light works.
The traditional dish style cone shape is a form-follows-function thing where you need a speaker cone to be lightweight and rigid at the same time. If you use a geometric shape that is inherently strong then you can use a little less material and make the cone lighter. Think about a paper water cup that is usually found near water coolers.
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The paper cup is really fragile when you first pick it up because you are holding it from the sides, and pinching it from the sides. When you fill it with water the cup has no problem holding the weight of the water because a cone is stronger in it's axial direction, or up-and-down in this case. When you're done with the cup and it is empty, it takes almost no effort to crush it from the sides and crumple it into the trash, and it weighs nearly nothing because it's essentially a thick sheet of paper with a little glue (much like a paper speaker cone!).
So the shape of the material makes it stronger in this case, but only for the intended use. If a paper cup is intended to hold water, then a paper speaker cone is intended to push and pull air in much the same way. It is a very efficient shape if you need a strong and lightweight shape that only pushes and pulls.
There are many "non traditional" shapes now that we have more exotic materials to play with. There are lots of tradeoffs in the shape of a cone and how it transmits energy to the air. A convex shape like a dome tweeter or a dome midrange has a different off-axis frequency response than a concave shape like a subwoofer cone, and some of that performance difference is due to the frequencies a tweeter plays vs what a subwoofer plays. A concave shape can also have either a straight wall which looks like a simple paper cup, or the wall can be curvlinear which is a fancy way of saying "a constant curve like the edge of a circle". Both have strength and performance tradeoffs too.
The dust cap on a speaker cone can also contribute to its strength in a big way. I'm working on a thin-mount subwoofer design that relies on the presence of the dust cap to make the structure stronger and the design would not work without the dust cap. It is really interesting to be able to model the stresses and how far a material will bend on the computer, and then making changes to see how you can improve the design without ever building a thing.
