Let's compare the impulse response of two drivers. They are identical apart from the cone material, one has a plastic cone. The plastic is homogeneous; in other words the mechanical properties are the same on all directions. The second driver has a cone of woven Kevlar®, treated with a resin to control the stiffness and a PVA compound to add damping and seal the fabric. Being woven, the Kevlar® cone's mechanical properties are different depending on the angle to the direction of the fibres. Both cones are terminated at the outer edge in the usual way by a half-roll rubber surround. If we look at laser scans of the two different cones at different points in time after an impulse signal has been applied the conical shape of the diaphragm is lost in the process.
At the time just after a signal has been applied, just the centre of the cone has started to move in both cases. With the plastic cone a circular bending wave starts to spread out from the centre of the cone. However, with the Kevlar® cone the wave front begins to assume a square shape, imposed by the weave. When these bending waves reach the joint between the cone and surround, some of the energy is reflected back into the cone and some passes into the surround. This is because the two materials have different mechanical properties. It's similar to the situation when you look out of a window. As well as the view from outside, you can see a reflection from inside the room. In that case it's because glass and air have different optical properties.
Further reflection occurs where the surround is attached to the chassis or basket of the driver. When these reflected waves reach the centre of the cone, they are reflected back out again and so on, until damping in the materials eventually dissipates the energy. Because the wave front in the plastic cone is circular, these repeatedly reflected waves set up a pattern of concentric rings which radiate delayed sound to the listener that adds to and colours the initial sound received. Although reflections do occur with the Kevlar®, they happen at different times around the edge and the movement pattern of the cone is more random. The total area of the cone moving forward at any given time is more balanced by the total area moving backwards and far less of this delayed energy is actually radiated as sound to the listener; the air just shuffles across the surface of the cone.