This is related to another question I just asked, but they are different enough I thought it deserved its own spot. Speaker elements seem to always be shaped like a cone with a portion of a sphere at the center. What is the physics reasoning behind this shape being so standard? Is it a precise shape that all speaker elements share (e.g. parabaloid + sphere), or just kind of a general shape that "works well"? Does it work just as well for any light solid, or is it actually tuned to the speed at which sound propogates through the speaker element?
[Physics] The shape of speaker cones
acousticswaves
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Yes, the cone will produce sound waves if you move it to and fro by hand. The speaker produces sound by moving the cone, and it doesn't matter whether it's the moved by current in the coil or you moving it by hand. The sound waves will have whatever frequency you're moving the cone at, and I doubt you could manually move the cone at more than a few Hz, so the sound will have far too low a freequency for you to hear.
Also note that the efficiency of the sound generation falls off at low frequencies because it's hard for a small object to produce a sound wave with a large wavelength. Wiggling the cone by hand will produce a sound wave, but that wave will have a very low amplitude.
To radiate sound effectively, you require the radiating object to present a good impedance match to the air surrounding it. In so doing, you will maximize the radiation resistance of the sound source. In practical terms this means the physical dimensions of the object should be approximately the same as the wavelength of the radiated sound. For example, to radiate well at 1000Hz (wavelength ~1 foot), the radiator should be about 1 foot in size- so a 12" loudspeaker will be well-coupled to the air surrounding it at 1000Hz; a 6" speaker will be well-coupled at 2000Hz, 3" at 4000Hz, 1.5" at 8000Hz, and so on. This is why the tweeters in your hi-fi speaker system have a cone diameter of about 1", the midrange will be 4", and the bass will be 12"- or as big as you can fit into the enclosure of your choice.
This rule extends to low frequencies too, but here the practicality of the scaling law breaks down: To radiate well at 100Hz requires a speaker 10 feet in diameter, and a pair of these will not fit in your living room. Instead, you make up for the poor impedance match with more cone excursion: You drive the speaker cone farther back and forth so as to pump the same volume of air that the big speaker would, only with a smaller speaker.
This is an inefficient way to get good low-frequency response, and requires the power amp that is driving the woofer cone to feed a lot more juice to it- but at the present time, power amplification is inexpensive compared to the cost of (for example) an 18" diameter loudspeaker, which needs to be mounted in an enclosure the size of a refrigerator in order to engage the air properly.
Best Answer
I believe it's to do with the fact that the speaker's function is to propagate pressure waves through the medium (air).
So, it's mainly a mechanical concern: you want something to push air, and you do not wish to expend much energy. So it has to be light and rigid, which the cone manages to fulfil due to its shape. A plane sheet, for instance would undergo buckling. [1]
The size of the cone depends on the wavelength you wish the speaker to transmit. Deep cone for low frequencies, shallow ones for higher frequencies, and curvilinear to cover a range [2].
As for the spherical portion, it's just a dust cap, and I have never come across literature claiming a 'significant' effect due to its shape.
Note: alls of this applies to dynamic speakers. Others, such as electrostatic speakers use different principles.
[1] http://www.vias.org/crowhurstba/crowhurst_basic_audio_vol1_044.html
[2] http://www.ewp.rpi.edu/hartford/~ernesto/SPR/Miller-FinalReport.pdf