Final answer:
The structure described is called the spiral ganglion, and it's closely related to the organ of Corti where the process of converting sound waves into neural signals occurs.
Step-by-step explanation:
The structure containing the cell bodies whose peripheral axons innervate the hair cells of the organ of Corti is called the spiral ganglion. The hair cells within the organ of Corti possess hair-like stereocilia that extend toward the overlying tectorial membrane, which facilitates the transduction of sound waves into neural signals. The basilar membrane underlies the organ of Corti, the tectorial membrane lies above, and the outer hair cells mechanically tune the incoming sound waves, enhancing the hearing process.