Room modes (standing waves) can do weird things. You might get different results by moving the source.

I read this somewhere: "Monaural is like listening to the music through a hole in the wall. Stereo is like listening through two holes in the wall." Even monaural sources sound different when played through the two speakers of a stereo system, because more room modes are excited strongly.

Drawing on your background in music to your advantage, think of two tuning forks of slightly different pitch. When struck they produce a beat note which is the intermediate or difference frequency. In a superhet radio, the same thing happens but at RF frequencies to produce the IF signal (there's also a summed frequency, but forget that. It's not involved or used).

The radio is set up so the local oscillator always tracks at exactly the IF frequency above the received signal, anywhere on the dial.

Herr Helmholtz says hi! (Although if you're standing in front of a Helmholtz resonator you may not hear him...)