Given below are some examples of wave motion.
Is the ear particularly sensitive to such a frequency? Four times length of the tube, and on the bottom it's only the odd integers.
What are the frequencies of the fundamental and the first two overtones? There are other points along the medium that perform vibrations between a large positive and large negative displacement.
So the basis for drawing the standing wave patterns for air columns is that vibrational antinodes will be present at any open end and vibrational nodes will be present at any closed end.
This mix is what gives various musical instruments and human voices their distinctive characteristics, whether they have air columns, strings, sounding boxes, or drumheads.