**Core Concept:** The sensory supply of the vocal cords is crucial for their sensitivity and function. The vocal cords are essential for speech production and play a significant role in airway protection.

**Why the Correct Answer is Right:** The correct answer is C: The recurrent laryngeal nerve (RLN) supplies the sensory innervation to the vocal cords. The RLN is a branch of the vagus nerve (CN X) and plays a vital role in the sensory input to the vocal cords.

**Why Each Wrong Option is Incorrect:**

A. The glossopharyngeal nerve (CN IX) is incorrect because it supplies the posterior third of the tongue, not the vocal cords.
B. The hypoglossal nerve (CN XII) is incorrect because it supplies the muscles of the tongue, not the sensory innervation to the vocal cords.
D. The superior laryngeal nerve (a branch of CN X) is incorrect because it primarily supplies the superior larynx and does not innervate the vocal cords directly.

**Clinical Pearl / High-Yield Fact:** A thorough knowledge of the sensory supply to the vocal cords is essential for understanding the function of the vocal cords, their potential injury, and the resulting symptoms. Injury to the RLN can lead to hoarseness or loss of voice, which is often referred to as Recurrent Laryngeal Nerve Palsy (RLNP). This clinical scenario should prompt a thorough evaluation of the patient's airway and voice production, allowing for early intervention and rehabilitation.