The song is broadcast from an FM broadcast radio station. The FM broadcast band falls within the VHF (very high frequency) part of the radio spectrum. VHF radio waves propagate mainly by line-of-sight which means waves travel in a direct path from the source to the receiver. Thus, radio wave propagation is affected by atmospheric conditions and obstructions in the terrain like mountains.
The range can be great between mountaintop to mountaintop, but it will be limited valley to valley. The signals won't reach if you are down in the valley and the broadcast is from a station on the opposite side of the mountains or in another valley. The radio signal may not be able to penetrate the mountains.
The song originates from the radio station in the island. Abbott family and some other families (including Emmett and his family) were living in a valley in the mainland. There are mountains in between. Thus, the mountains were blocking the radio signals. When Emmett moves to an abandoned steel foundry, he begins to hear the music as the place is not in the valley.
Here is the relevant part from the transcript of A Quiet Place Part II:
♪ Somewhere ♪
♪ beyond the sea ♪
What is it?
What is
it?
Music.
♪ Stands on golden sand and watching ♪
It’s
a…
Beyond the Sea.
Have you heard this?
Ah. Yes.
No. Dad would’ve heard this.
It’s the same song that has been
playing over and over the last four months.
You’re lying!
My Dad used the radio every day!
What she’s saying?
She
thinks he would have heard it.
Who?
Lee.
It’s the
valley.
It’s the valley, I tried the radio, from our house too.
But…
We never heard anything until we got up here.
Your dad
was never gonna make it work.
https://scrapsfromtheloft.com/movies/a-quiet-place-part-ii-2021-transcript/