Step 1: Understanding the Concept:
The question provides a quote describing the psycho-physiological process of speech production, from the soul's intention to the exhalation of breath. It asks to identify the source text for this description. This subject matter belongs to the field of \textit{Śikṣā} (phonetics and phonology), one of the six Vedāṅgas.
Step 2: Detailed Explanation:
The quote "ātmā buddhyā sametyārthān mano yuṅkte vivakṣayā..." is a famous verse from the Pāṇinīya Śikṣā. This is a foundational text on Sanskrit phonetics, traditionally attributed to Pāṇini or his school.
The verse outlines the stages of speech production:
1. Ātmā (the self/soul): Perceives objects/meanings with the intellect (buddhi).
2. Manaḥ (the mind): Is yoked with the desire to speak (vivakṣā).
3. The mind then gives an impulse to the bodily fire (kāyāgni).
4. This fire, in turn, drives out the breath (māruta or prāṇa).
This breath, as it ascends and is articulated in various places in the mouth, produces the different speech sounds. This description is a cornerstone of ancient Indian phonetic science.
Step 3: Final Answer:
The text that describes the process of articulation in this specific manner is the Pāṇinīya Śikṣā. Therefore, option (3) is correct.