classical mechanics - Physics of how the cochlea isolates frequencies along its length?

Can anyone explain the separation of frequencies along the basilar membrane of the cochlea please? (equations would be nice)

I understand it being related to the resistance caused by fluid in the cochlear increasing in proportion to the rate of change at the ear drum versus the stiffness of the basilar membrane decreasing along it's length which somehow creates a condition where the membrane only vibrates in a local region. However all descriptions I have seen so far are always very general and never go into the actual physics of the system.