How are two notes the same on different octaves?

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How are two notes the same on different octaves?

In:

They’re not. If you elevate an A3 one octave you get A4. They’re both A because their frquencies “align”.

The frequency of the lower octave note is one half that of the higher octave note, meaning that half of the peaks and valleys of the sounds waves align.

That’s why they sounds alike and are considered the same note.