Any rigid driver of very light weight material is prone to "ringing". Think how a cymbal is made...a rigid disc of metal...touch a cymbal even lightly and it will ring for a long time at low levels but audible. In the case of a cymbal it vibrates at many frequencies due to its mottled hammered surface - it "shimmers". In the case of a metal driver then its shape will also influence the kinds of sounds it makes - shape it like a cup or a bell then it will tend to ring at certain frequencies. Manufacturers normally compensate for this with a notch filter.
A woven fabric/silk/paper&pulp type driver will also be light but not as rigid and not as light...it will not resonate like a metal or ceramic driver. This is called "internally damped" it means that when it flexes it quickly stops and it also loses energy more quickly - less efficient and higher frequencies will roll off sooner.
Some hybrid designs use CLD - constrained layer damping - a viscous fluid between two rigid cones. Some use rubber dampers stuck to the cone. Many are coated with a damping fluid.
In any case, if you want to use an internallly damped cone then you forgo frequency bandwidth and efficiency...you may also need to carefully support the less rigid cone in the middle with a larger voice coil (expensive) or carefully shape it (dome) and drive it with a bigger motor and magnet (expensive). The bonus is that the limited bandwidth internally damped driver will have excellent transient response and waterfall plot - it plays a sound without adding coloration.
A woven fabric/silk/paper&pulp type driver will also be light but not as rigid and not as light...it will not resonate like a metal or ceramic driver. This is called "internally damped" it means that when it flexes it quickly stops and it also loses energy more quickly - less efficient and higher frequencies will roll off sooner.
Some hybrid designs use CLD - constrained layer damping - a viscous fluid between two rigid cones. Some use rubber dampers stuck to the cone. Many are coated with a damping fluid.
In any case, if you want to use an internallly damped cone then you forgo frequency bandwidth and efficiency...you may also need to carefully support the less rigid cone in the middle with a larger voice coil (expensive) or carefully shape it (dome) and drive it with a bigger motor and magnet (expensive). The bonus is that the limited bandwidth internally damped driver will have excellent transient response and waterfall plot - it plays a sound without adding coloration.