This is a question of damage caused by resonance.
Hypothetical scenario – a glass resonates at Middle C, and if subjected to prolonged exposure to this note shatters.
If you raise the note an octave to the C above middle C, will the glass still resonate and shatter after prolonged exposure?
Or any C either below or above Middle C for that matter?
This glass shattering is a bit of a 'urban myth' possible in theory but very unlikely in reality. But if a glass resonated at a particular note it is only that one exact note it would not be affected by a note an octave higher (or lower)
It isn't an urban myth but it does need a fine glass.
Objects rarely resonate at a single frequency. Almost all sound is made up of harmonics and it wold be unusual for something to resonate at a frequency without having some response to a sound at an octave higher (double the fundamental frequency).