**Core Concept**
The stereocilia of hair cells are specialized sensory structures that play a crucial role in sound and balance perception. They are embedded in a gelatinous structure that helps to transmit mechanical vibrations to the hair cells, allowing for the conversion of these vibrations into electrical signals that can be interpreted by the brain.

**Why the Correct Answer is Right**
The stereocilia of hair cells are indeed embedded in the tectorial membrane, a gelatinous structure that overlays the hair cells in the cochlea of the inner ear. The tectorial membrane is rich in lipids and proteins, and its surface is covered with the stereocilia of the hair cells. As sound vibrations reach the cochlea, the tectorial membrane moves in response, bending the stereocilia and triggering the opening of mechanically gated ion channels in the hair cells. This leads to a depolarization of the hair cells, which sends electrical signals to the auditory nerve and ultimately to the brain.

**Why Each Wrong Option is Incorrect**
**Option A:** The basilar membrane is a critical structure in the cochlea, but it is not the membrane that the stereocilia of hair cells are embedded in. Instead, the basilar membrane provides the mechanical support for the hair cells and helps to transmit sound vibrations to the tectorial membrane.
**Option B:** Reissner's membrane is a thin, semi-permeable membrane that separates the scala media from the scala vestibuli in the cochlea. While it plays a role in the transmission of sound vibrations, it is not the membrane that the stereocilia of hair cells are embedded in.
**Option D:** The tympanic membrane, also known as the eardrum, is a thin membrane that separates the external ear from the middle ear. It is not related to the stereocilia of hair cells or the tectorial membrane.

**Clinical Pearl / High-Yield Fact**
It's worth noting that the tectorial membrane is a critical structure for sound perception, and damage to it or the stereocilia of hair cells can lead to hearing loss or other auditory disorders. The tectorial membrane is also an important target for research into new treatments for hearing loss and other ear-related disorders.

**✓ Correct Answer: C. Tectorial**