The Harmonics of a whirly

A physicist's view

by Paul Doherty

A corrugated plastic tube, known as a whirly, will sing a sequence of harmonics when swung overhead.
The higher the rate of rotation the higher the harmonic.

In this image the shading represents the density of the air.

Dark orange is highest density.
yellow is atmospheric average density.
white is lowest density.

Notice that the density of the air in the tube at the open ends is at atmospheric density.

The sinusoidal lines going up and down within the tube represent the displacement of air from its equilibrium position. Where these lines pass through the center of the tube the air is not displaced from its equilibrium position. When the lines are at the top or bottom of the tube the air has maximum displacement.

Notice that the ends are positions of maximum displacement.

Short vertical lines mark the positions of the nodes of displacement. The positions in the tube where the air does not move away from its equilibrium position.

See also the Movie of Air motion in a Whirly

Scientific Explorations with Paul Doherty

© 2001

21 Feb 2001