Musical octaves are wired into physics. If a note is at frequency X Hz, then the note one octave above it is 2X Hz. Of course due to the harmonics of the string

Musical octaves are wired into physics. If a note is at frequency X Hz, then the note one octave above it is 2X Hz. Of course due to the harmonics of the string, a string vibrating at X is also vibrating at 2X, so when you play a note at X Hz, then you are also hearing the note one octave above at the same time. So... it doesn't need to be learned... When you hear a middle A, you're also hearing the A above for sure. And when you hear the A above by itself, you're hearing one part of the A below. Of course, understanding that what you're hearing is a called an octave is almost certainly learned. But in my experience, any one who is not tone deaf will naturally lower or raise their voice by an octave if you ask them to sing a song 'lower'.