If you're 10 feet away from one radio and 5 feet from another, will turning one on (through a remote control) affect the intensity of the other radio?

Are you assuming that the other radio is in fact already turn on?

 

Anyway, based on what I know, it should not affect the intensity of the other radio much, even though the radio you are turning on is activated through remote control. The radio frequency that the remote control is using a frequency band that is quite far away from the spectrum of the actual radio signals from the radio station.

This is an interesting question. Can the intensity of the sound the person actually hears be affected by the sound waves interferring with each other?