New trends in physics teaching, v.4; The ... - unesdoc - Unesco

New Trends in Physics Teaching IV
of a pipe closed at one end has a wavelength four times the length of the pipe. When the pitch
falls an octave, the number of oscillations per second or the frequency, halves. In this mode, air
rushes in and out of the open end, the motion diminishing towards the closed end, where it is
zero, as shown in figure 11. Listen to the timbre of an open straw, and one which is half as long
closed at one end. Although they have the same pitch, their sound is quite different. The open
straw can vibrate with all the harmonics of the fundamental, but the closed straw possesses only
the odd harmonics (i.e. three, five, seven times the frequency of the fundamental, etc.).
Amplitude of
vi brations
t
Figure 11.
One can make a pitch pipe from a straw, since its frequency depends only on its length, and
the velocity of sound, which is 344 m s-l at sea level and room temperature. The top string of a
guitar is tuned to E4 (329.6 Hz) which would be given by an open ended straw 52.5 cm long. It
is more convenient to use a straw 12.5 cm long, which, with one end closed, gives the octave of
this note. A correction should be made for the finite width of the straw. One should add 0.82 of
the radius for each open end, so this amount should be subtracted from the length of the straw
given above.
Vibrations in pipes open at both ends are represented musically by such instruments as the
flute family, and the open flute pipe in an organ, often called the open diapason. However, most
wind instruments employ reeds to provide vibrations, and these act effectively to close the end
of the pipe. We can make simple reed devices with paper and straws with which to experiment.
Take a 15-20 cm square of paper and fold along one diagonal, Then open it out and proceed
to roll the paper tightly around a pencil from one end of the diagonal crease to the other end, so
that the diagonal rolls along itself as shown in figure 12. If a six-sided pencil is used, do not wrap
it too tightly, or the pencil wil not come out. When completely rolled, it should resemble the
lower figure. Push the pencil out and glue the last fold at A, or hold it in place with a rubber
band or strip of sticky tape.
Now from the point marked b in figure 13, at one end cut away on each side, in the direction
indicated by the small arrows, until the end piece may be opened out into a triangular shape c.
The cuts must be at right angles to the main roll and are each a trifle over one-third of the
circumference of the rolled tube. Fold the triangular piece at right angles to the tube SO that it
forms a little cover over the end. Now place the other end of the tube in your mouth, and instead
of blowing, draw in your breath. This action wil cause the little triangular paper lid to vibrate
and the instrument wil give a bleating sound. The noise can be made louder by poking the tube
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