Peace be upon you.
Ayatollah Khamenei (may Allah protect him):
There are conditions for the permissibility of the slaughtered animal, which are:
- The slaughterer must be a Muslim and must say the name of Allah at the time of slaughter.
- The slaughter must be done with a sharp instrument, preferably iron; otherwise, it is permissible with other materials like wood or glass.
- The four main veins must be cut: the esophagus, the trachea, and the two jugular veins surrounding them.
- The place of slaughter must be under the throat, aligned with the head.
- The slaughter must be done from the front, not from the back.
- The animal must be facing the Qibla (the direction of prayer).
- There must be some movement from the animal after slaughtering, indicating it was alive.
If these conditions are met, the slaughtered animal is permissible to eat. If by 'the sound of the radio' you mean that the name of Allah is recited through a recording and not directly by a Muslim during the slaughter, this is not sufficient for the permissibility of the meat.
Source: Fiqh al-Wali - Hunting and Slaughtering + Special Inquiry.
Ayatollah Sistani (may Allah protect him):
There are conditions for the permissibility of the slaughtered animal, which are:
- The slaughterer must be a Muslim or someone in a similar status.
- The slaughter must be done with a sharp instrument if possible; if not, it is not permissible even if done with other metals.
- The intention must be to slaughter by cutting the main veins; if the knife accidentally cuts the animal without intention, it is not permissible.
- The animal must be facing the Qibla during slaughter; if this is neglected knowingly, it is forbidden.
- The slaughterer must say the name of Allah at the beginning of the slaughter or in a way that is connected to it; the name of someone else is not sufficient.
- The four main veins must be cut: the esophagus, the trachea, and the two jugular veins.
- There must be a significant amount of blood that flows out during slaughter; if not, it is not permissible.
- The animal must show some movement after slaughter, indicating it was alive.
If by 'the sound of the radio' you mean that the name of Allah is recited through a recording and not directly by a Muslim during the slaughter, this is not sufficient for the permissibility of the meat.
Source: Minhaj al-Salihin - Vol. 3 - Slaughtering + Official Website
May you be successful in all good.