Final answer:
The external laryngeal nerve innervates the cricothyroid muscle, which is responsible for adjusting the tension of the vocal cords to modulate pitch.
Step-by-step explanation:
The muscle innervated by the external laryngeal nerve is the cricothyroid muscle. This muscle is important for tension and lengthening of the vocal cords, which affects pitch during speech. The external laryngeal nerve is a branch of the superior laryngeal nerve, which itself stems from the vagus nerve (cranial nerve X). The innervation allows the cricothyroid muscle to control the position and tension of the vocal cords, which is essential for phonation. However, the information provided here does not directly answer the student's question, as it incorrectly refers to other nerves like the hypoglossal nerve and the accessory nerve, which innervate different muscles. The hypoglossal nerve primarily innervates the muscles of the tongue, and the accessory nerve innervates the sternocleidomastoid and trapezius muscles, which are not connected to the laryngeal function.