It's about the period of the resulting wave. If you play a root note and its fifth dropped by one octave (i.e., a perfect fourth below, e.g., a C with a G below) then the frequencies are
f denotes the frequency of the C note. The question is now what the frequency of the resulting wave will be. We know that periodic waves can be represented by a weighted sum of (phase-shifted) sinusoids with integer multiples of the fundamental frequency (Fourier series). So we just have to figure out if there's some fundamental frequency
f0 that results in the two frequencies
f as integer multiples of
f0=f/4. So the fundamental frequency
f0 of the resulting wave corresponds to a C that is actually two octaves below the C that was played. Even if that low C is not actually played, it is, and can be perceived as, the fundamental frequency of the resulting wave.