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Standing sound-waves in a tube

A tube can resonate when a standing sound wave can be set up within it. For a tube which is open in both ends the ends are anti-nodes for the standing waves and must therefore be separated by a multiple of tex2html_wrap_inline148. The fundamental frequency should be
equation51
Where L=1.19 m is the length of the tube. Putting in numbers we get
equation55
We check to see that indeed the system resonates at that frequency.

As an interesting aside we note that the resonance frequency of such systems depends crucially on the density of gas that is forced to resonate. The density of helium is about 8 times less than that of air so resonance frequencies increase by a factor tex2html_wrap_inline162 if they are based on standing waves in helium rather than in air! We illustrate this by blowing a recorder first with air then with Helium. The recorder has the pitch of a piccolo-flute when the standing waves occur in Helium rather than air all because of the different densities of those two media.



Collin Broholm
Wed Nov 12 13:30:20 EST 1997