If the broadcast is live, then it is prescribed to return the salaam, because of the general meaning of the evidence which shows that it is obligatory to return the greeting of salaam. But it is a communal obligation, so if some people do it, it is waived for the rest.
But if it is recorded, it is not obligatory to return the greeting in this case.
Al-Nawawi said in al-Adhkaar (p. 247):
Imam Abu Sa’d al-Mutawalli and others said: If someone calls out to someone else from behind a screen or a wall and says, Peace be upon you, O So and so, or he writes a letter in which he says: Peace be upon you, O So and so, or Peace be upon So and so, or he sends a messenger and says: Give greetings of salaam to So and so, and the letter or messenger conveys that, it is obligatory for him to return the greeting. Similarly, al-Waahidi and others stated that it is obligatory for the one to whom the letter was written to return the salaam when it reaches him. End quote.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked:
If the writer says in his article in a newspaper or magazine, or an author says in his book, or a broadcaster says on the radio or television: Al-salaamu ‘alaykum wa rahmat-Allahi wa barakaatuhu (peace be upon you and the mercy of Allah and His blessings), does the listener have to return the greeting on the basis that returning the greeting is obligatory?
Returning the greeting in cases such as this is a communal obligation, because he is greeting a large audience, so it is sufficient for some of them to return it, although it is better if each Muslim who hears it returns the greeting because of the general meaning of the evidence. End quote.
Majmoo’ Fataawa Ibn Baaz (9/396).
Shaykh Saalih al-Fawzaan was asked:
If the broadcaster on television or radio, or the writer in a magazine, says salaam, is it obligatory to return the greeting in this case?
It is obligatory to return the salaam if one hears it directly or through a letter that is addressed to him, or via media addressed to the listeners, because of the general meaning of the evidence that returning the salaam is obligatory. End quote.
Al-Muntaqa min Fataawa al-Fawzaan, 8/63
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) did not go so far as to say that it is obligatory to return the salaam because the greeter cannot hear the response, but he said: (The greeting) should be returned so as to be on the safe side.
He was asked (may Allah have mercy on him):
What is the ruling if the Muslim hears the broadcaster or Shaykh saying salaam? Does he have to return the salaam?
The Shaykh said: Is it a live broadcast?
Questioner: Yes, he is listening to the Shaykh or broadcaster on the radio.
Shaykh: Sometimes it is recorded; they put it on a tape and broadcast it. If it is recorded, then you do not have to return the greeting, because this is just transmission of sound. But if it is not recorded and it is live, then I may or may not say that it is obligatory. If I say that it is obligatory, the basic principle is that this is a greeting to everyone who hears his words, so they have to respond to it. But if I say that it is not obligatory, that is because the one who gives the greeting cannot hear the response and does not expect it either. The one who says salaam in a broadcast does not expect the people to respond to him. But to be on the safe side, we should return the greeting and say, Wa ‘alayka al-salaam (and upon you be peace).
Questioner: Is that more on the safe side, O Shaykh?
Shaykh: That is more on the safe side, but it is not obligatory. End quote.
Liqa’ al-Baab al-Maftooh, 28/229.