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There is a displacement node at the closed end, and an antinode at the
open end. This is just like a string fixed at one end and free at the
other. Let's arbitrarily make the closed end. Then:

(185) 
has a node at for all . To get an antinode at the other end,
we require:

(186) 
or

(187) 
for (odd halfintegral multiples of . This converts
to:

(188) 
and

(189) 
Next: Pipe Open at Both
Up: Standing Waves in Pipes
Previous: Pipe Closed at Both
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Robert G. Brown
20040412