Final answer:
The basilar membrane is the membrane within the cochlea that houses receptor cells for hearing, known as hair cells. When sound waves cause vibrations in the basilar membrane, the hair cells respond by generating electrical signals.
Step-by-step explanation:
The membrane within the cochlea responsible for housing receptor cells for hearing is called the basilar membrane. These receptor cells, known as hair cells, are located above the basilar membrane and have hair-like stereocilia that come in contact with the tectorial membrane. When sound waves cause vibrations in the basilar membrane, the hair cells respond by opening gated ion channels and depolarizing, leading to the generation of electrical signals.