‘Sound is eternal because it is produced’ refers to which of the following Hetvabhasa?

The correct option is Asiddha.

Detailed Explanation:
In Indian philosophy (specifically Nyaya epistemology), a fallacy of inference is known as a Hetvabhasa, which translates to a "pseudo-reason" or the appearance of a reason. There are five primary types of Hetvabhasa:
1. Savyabhicara (the irregular middle)
2. Viruddha (the contradictory middle)
3. Satpratipaksha (the inferentially contradicted middle)
4. Asiddha (the unproved middle)
5. Badhita (the non-inferentially contradicted middle)

The fallacy of Asiddha (also referred to as Sadhyasama) occurs when the middle term (hetu) is not a proven fact or when its relationship is unestablished. Asiddha is divided into three subtypes:
- Ashrayasiddha: The minor term (paksha) is unreal or unproven.
- Svarupasiddha: The middle term (hetu) is not present in the minor term (paksha).
- Vyapyatvasiddha: The relation of invariable concomitance (vyapti) between the middle term (hetu) and the major term (sadhya) is unproved or conditional.

In the given argument: "Sound is eternal because it is produced":
- Minor Term (Paksha): Sound
- Major Term (Sadhya): Eternal
- Middle Term / Reason (Hetu): Produced

Here, the universal relation (vyapti) between the middle term "produced" and the major term "eternal" cannot be established, because whatever is produced is non-eternal (transient). Since this connection cannot be proved, the argument commits the fallacy of Vyapyatvasiddha, which falls directly under the category of Asiddha Hetvabhasa.