I'm making an instrument from an open-ended tube that produces sound when the top (opening) is struck. To find the lengths corresponding to pitches, I used
$$ V = \lambda f \tag{1} \label{1} $$
and combined it with the fundamental frequency of an open-open system. However, I've found that I am one octave below my desired pitch in testing.
If I were to treat it as an open-closed system where the length equals 1/4 of the wavelength, my calculations would work out.
Why is this? Is it a coincidence?