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A pan flute is based on standing wave resonance in a tube that is open where the
musician blows and closed at the bottom end with bee’s wax.
(a) Describe the standing wave pattern of air displacement in such a tube when a tone
is played.
(b) Determine the length of the tube needed to produce a 440 Hz fundamental
frequency.
(c) Determine the sequence of harmonic frequencies that are supported as standing
waves in that tube.
(d) A given tube is found to be slightly out of tune producing a frequency of 445 Hz
rather than 440 Hz. By what distance should the bee’s wax be moved and in what
direction?
(e) Will the pan flute sound out of tune playing alone on a cold day? What about if
the pan flute plays along with an electronic piano on a cold day?
(f) What happens to the frequency and the set of harmonics of the 440 Hz tube if the
bee’s wax were to completely fall out of a tube so that the bottom of the tube is
now open.
1 answer