No, octave resonates in two different places. If we talk about octave as of sum of two sines.
The higher tone also excites the sensors for the lower tone.
Wait, does it? I might be spouting bullshit, sorry.
Thinking about it, I'm not so sure it doesn't. I'm not a physicist to know it for sure.
The octave rule definitely has some physical/biological founding, it’s not purely cultural. Although culture also plays a role in its preponderance.