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While playing Fallout 3, New Vegas, Fallout 4, we could listen to radio stations from various frequencies.
In my memory, all songs are from 1930s to 1940s, for example, I do not want to set the world on fire, Geiger Counter, mighty might man and etc.
Do they have a reason for this?
The Fallout series is famous for its Atompunk aesthetics, which is heavily inspired by the aesthetics of post-war America during the period of 1945–1969. Fallout draws its inspiration primarily from the 50s, according to Wikipedia:
The series is set during the 21st, 22nd and 23rd centuries, and its atompunk retrofuturistic setting and art work are influenced by the post-war culture of 1950s United States
This isn't limited to just the music, but also extends to the artwork, the ads, and also the designs of the various machines, such as Mr. Handy, the Robobrains (among many others), and also the cars found all around.
Thus it makes sense for most of its music to come from the 50s or before. After all, there is little music more befitting of a time period, as the music that was available during said time period.
By the way, according to the Fallout Fandom, Fallout 3 and 4 feature music ranging from the 30s to the 60s, while New Vegas has music from all time periods between the 40s and 2000s.
Here is the original producer of Fallout describing the music choices.
As noted in the description of that video, he has a separate video describing the choice of 'The Ink Spots' - a '30s band that led to the style you're describing.
Here is an earlier talk he gave describing the intro music (around 39 mins in)
