Music from standing waves: monochord

Demonstration

This is a nice simple experiment that enables students to visualize the audible vibrations from a stringed instrument.

Apparatus and Materials

• Monochord
• Paper riders
• Violin bow
• Rubber hammer
• Tuning folk

Health & Safety and Technical Notes

Eye protection must be worn. If the wire or cord snaps, it may whip into someone's eye.

Read our standard health & safety guidance

The monochord can be a simple stretched elastic chord or a metal wire attached to a sonometer box specially made for the job.

Violin bow is optional.

Procedure

1. Stretch the wire taut, and excite it by plucking (or bowing) it near one end. Students listen to the note.
2. Then pluck (or bow) it again, at the same time touching it very lightly with a finger at its mid-point. Ask students how the note has changed. (The wire will now be vibrating in two loops, with double frequency, an octave higher.)
3. Repeat with a finger touching lightly at 1/3, 1/4, etc. of the wire's length.

4. Show the existence of nodes and antinodes by hanging paper riders at appropriate places. Place the finger to suggest a suitable node, and bow gently, briefly. Riders at antinodes will jump off, those at nodes should stay there.
5. The step 4 procedure needs practice. An easier method is to excite the wire to resonance with a tuning fork. Tune the wire beforehand, by changing the length between bridges, so that it vibrates in, say, three loops with exactly the frequency of the fork.
6. Let students listen to the fork and to the note of the wire in the chosen harmonic. Place riders on the wire and excite it, by touching the wire at one bridge with the shank of the vibrating fork.

Teaching Notes

• This demonstration links standing waves with an understanding of musical instruments.
• If you illuminate the monochord with a stroboscope running at a slightly different frequency, then students will be able to see the motion of the wave in slow motion. If you select the exact frequency, the wave will appear to be stationary. In its ‘fundamental’, or basic, mode of vibration, the length of the string is a half wavelength of the note played.
• You may want to encourage students to bring in their own musical instruments. They can investigate how the lengths of the string or the lengths of the vibrating air column change while playing.
• Stringed instruments such as violins and cellos are played with the basic note. The string vibrates in one loop — two or more loops only as a special technique. Yet the motion of the bowed or plucked string is seldom simple harmonic. It is usually compound harmonic, a mixture of the notes of motion in 1 loop, 2 loops, 3 loops, and so on. That mixture gives instruments their characteristic ‘timbre’, or sound quality.
• A string's motion will depend on whether it is plucked, bowed or excited by a tuning fork.
• Students who play musical instruments may be familiar with important musical intervals like the octave, perfect fifth and perfect fourth. These correspond to frequency ratios 1:1, 2:3 and 3:4 respectively and can easily be demonstrated on the monochord. Pythagoras made this discovery 2,500 years ago.
• Flutes, bugles and some whistles are completely different from each other. A flute behaves as a cylinder open at both ends, so the modes have frequencies in the ratios 1:2:3:4 ... A bugle will give frequencies in the ratios 2:3:4:5:6, but it is complicated by the fact that its diameter changes along its length. A clarinet will give modes in the ratios 1:3:5, i.e. as a cylinder closed at one end.

This experiment was safety-tested in July 2004