I wasn't going to write, because I simply lack knowledge, but since you apparently got a lot of motoring replies instead of information, then I guess I might try and throw in something which could be (perhaps? maybe?) somewhat relevant or at least entertain more knowledgeable people with my foolery.

I don't know if those serrations are like that, but in loudspeakers membrane can be ribbed which is done in order to delay distortion on that specific part. With increase of power membrane will start distorting, but it is not distorting whole, rather certain areas which are responsible for different frequencies start distorting earlier while some later. As such you can increase power handling of the membrane by ribbing it, even just partially. Tonally ribbed membrane is usually darker, while straight/smooth of the same material and dimensions is brighter. However membranes can be made of different materials, for example paper or kapton, and aside size can have different thickness, density, stiffness, they can be soaked or coated in some additional substances, and all will affect both sound as well as power handling properties.

The diagonal angling of those serrations actually look like it might be used to stop the wave from traveling along the membrane, something like wing fences on Mig-15 :P If I recall it right the sound actually travels along the ridge of the speaker and even come to play with the baffle.

Headphone drivers are mystery for me as well, the fight is against the size limitations so there is a lot of witchery like this going on.