The simple theory using the method of equivalent circuits, which we have just derived, is not valid above some frequency between 300 and 1000
Hz. In the higher frequency range, the cone, diaphragm mass M
, and also the radiation impedance change no longer move as a single unit. These changes may occur with great rapidity as a function of frequency. As a result, no exact mathematical treatment is available by which the performance of a loudspeaker can be predicted in the higher frequency range, unless the geometry is very simple, as in the case of a shallow spherical shell 
. Cones are often approximated by concentric rings 
or finite element models. Modern finite element models include the magnetic path ...