Welcome to practical physicsPracticle physics - practical activities designed for use in the classroom with 11 to 19 year olds
 

Standing waves on a rubber cord

Demonstration

An excellent experiment to show standing waves, with its nodes and antinodes. It also enables students to discover the relationship between a fundamental resonance frequency and its harmonics.

Apparatus and materials

  • signal generator
  • vibrator
  • xenon stroboscope
  • rubber cord (0.5 m long, 3 mm square cross-section)
  • retort stand bases, rods, bosses, and clamps, 2 of each
  • metal strips (as jaws), 4
  • G-clamps, large, 2
  • 4 mm leads

Health & Safety and Technical notes


Read our standard health & safety guidance

standing waves on a rubber cord apparatus
The ends of the rubber cord are held by the metal strips in the retort stand clamps.
Clamp the retort stands to the bench so that the rubber cord is stretched to about 1 m length.
Link the vibrator to the cord, a few cm from one end, by a short length of wire (0.71 mm diameter) twisted round the cord and fastened to the vibrator.
It helps to have white bands painted on the cord at regular
intervals along it, and to observe the motion under stroboscopic illumination.

Safety note: Using the xenon stroboscope, teachers should be aware that frequencies around 7 Hz have been known to cause epileptic fits in certain people. Ask your students if any know that they are susceptible to this response.

Procedure


a Set the signal generator on 2 V sine wave output (low impedance), and slowly increase the frequency from 10 Hz to 100 Hz. There should be 4 or 5 resonant frequencies in this range.
b Questions to answer:
Why does the cord show a large response at certain frequencies, but not at other frequencies?
How are the resonant frequencies related to each other and to the length of the cord?
When the vibrator is first switched on a wave travels along the cord. How does this develop into a standing wave?
What factors affect the amplitude of vibration at the antinodes?
Is there an optimum position for the vibrator? Is the vibrator always at a node or an antinode?

Teaching notes


1 Standing waves are an example of superposition. They occur where two similar trains of waves pass through one another, going in opposite directions.
The standing waves should be viewed stroboscopically, as well as by eye, to give students a clear understanding of their nature.

2 The wave produced by the vibrator must take a certain time to travel to one end of the cord and then back to the vibrator again. If this time coincides with the period of the vibrator, we can expect resonance, because the vibrator is just sending off a second wave when the first is about to go on its next trip. But if the vibrator sends off exactly two or exactly three (or any other whole number) of waves in this time, each wave will be reinforced when it passes again travelling in the same direction. So we may expect a fundamental resonant frequency f and other resonant frequencies 2f 3f... nf (called ‘harmonics’).

Readings on the scale of the signal generator should support this. And for, say, the fifth harmonic 5f, the cord vibrates in five sections, separated by four motionless points (nodes), as below.

oscillating motion of a cord

3 The discussion above suggests why the resonating cord responds, but not so clearly why, off resonance, there is practically zero amplitude, despite the motion of the driving force. The point need not be pursued, unless students raise it.

If the distance along the cord and back is not an exact whole number of wavelengths, a wave which has completed a few return trips will be out of phase with the vibrator. If the reflected wave has not lost much energy through damping, destructive superposition occurs. Each new wave is cancelled by an earlier one persisting in the cord.

This experiment has yet to undergo a health and safety check.

 

Related experiments


Standing waves with a variable wavelength
Stationary waves in an air column
Longitudinal standing waves in rods
Vibrations of circular ring wires
Longitudinal standing waves
Vibrations in a rubber sheet
Ring of standing waves

 

 

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