"In
non-electronic instrument, the stable, controlled vibration
is produced by a standing wave."
http://newt.phys.unsw.edu.au/music/
Since
the ends of a flute are open, they are close to atmospheric
pressure. The standing wave is sketched below.

http://newt.phys.unsw.edu.au/music/
The Vibration
in pressure is the bold line, the fine line represents
the displacement of the air molecules. Air molecules are
free to move in and out at the open ends.

The above picture is a harmonic series and notes with pitches
shown.
Since the flute is open to
the air at the ends the total pressure is close to atmospheric
pressure. So the acoustic pressure is close to zero. In
order for a wave to satisfy this condition the longest
standing wave is one in which it's wavelength is twice
as long as the flute!
The pressure inside the tube does not have to be atmospheric.
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http://newt.phys.unsw.edu.au/music/
The
sketch at above represents a cross section of the flute at the
embouchure.
The university of New South Wales,
Sydney, Australia reports on the natural
variation of the air due to pressure:
"And
indeed the
maximum
variation
in
pressure
(the
pressure
anti-node)
occurs
at
the middle."
http://newt.phys.unsw.edu.au/music/
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