Radio is not an audio recording technology it is an audio transmission technology, There is no storage of the sound required.
The first feature film with synchronized sound is [https://en.wikipedia.org/wiki/The_Jazz_Singer](https://en.wikipedia.org/wiki/The_Jazz_Singer) from 1927. The majority of studio moves used sound in 1929, Half of all cinemas in the US had sound systems in 1930.
The first feature film is from 1900 +- 3 years depending on your definition.
When you get radio the first transmitted human voice was in 1900 and the first commercial radio station started in 1920
So even if the radio was relevant in only exist conversely for 1/3 of the time that silent moves were the norm.
The problem with sound is movies is synchronized. The first audio recording is on phonograph disc record and even tubes with a scratched gove that many would today just call LP even if that is just one variant. Music starts to be sold that way around 1890
The Jazz singer used discs and they manage to synchronize them. That syncopation was the key, The required technology is not directly related to radio transmission.
A magnetic tape that you might think of as old audio storage is later the sound in film. Practical plastic tape for sound was demonstrated in 1935 and metal tapes had been existed from 1924.
So movies started to use sound as soon at it was technically possible and it is quite soon after you have comersial radio broadcast.
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