The basilar membrane will vibrate when the fluid in the upper and in the lower scala's vibrate. But the basilar membrane is not the same (homogeneous) along its length. Rather, it contains fibers that are short and stiff in the base and long and slender in the apex. Therefore, the basilar membrane will vibrate more at the base when the sound has a high frequency. Lower frequencies are better detected in the basilar membrane in the apex.
So, in short:
high frequencies are best detected at the base
medium frequencies are best detected in the middle
low frequencies are best detected close to the apex
This has really become a frequency analyzer! (just like the led's in your radio or music player)
C. Organ of Corti :
The organ of Corti is located on the basilar membrane. So, if the basilar membrane vibrates, then the organ of Corti will also vibrate and at the same frequency (remember; at high frequencies at the base and at low frequencies at the apex).
The organ of Corti consists of hair cells which stand on the basilar membrane. The hairs of the cells are connected and fixed to the tectorial membrane. From the hair cells, axons emerge that run along to form the cochlear nerve.
If the basilar membrane vibrates, the hair cells on top of this part of the membrane will be pushed and pulled against the tectorial membrane. This will make the hairs bend. This 'bending' will affect the behaviour of neighbouring channels. As the channels open and close in rhythm with the vibrations, potentials will be generated inside the cells. This may lead to action potentials in the axons that connect these hair cells. This process is called "mechanical transduction".
Sometimes, in accidents, especially when high speeds are involved, the connections between the hairs and the tectorial membrane gets broken. Then, the haircells are no longer stimulated by the vibrations. Essentially, the person has become deaf to the frequencies affecting this part of the membrane. This can also happen when a person is subjected to loud noises at a particular frequencies. (see "gun shot deafness" later).