Longitudinal standing waves

Demonstration

This experiment shows visible longitudinal standing waves in a spring.

Apparatus and Materials

• Signal generator
• Vibrator
• Xenon stroboscope
• Long spring
• Metre rule
• 4mm leads

Health & Safety and Technical Notes

Read our standard health & safety guidance

Put the vibrator on its side, attach one end of the spring to the vibrating element using string or a wire loop. Use the low impedance output of the signal generator, at full amplitude.

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

1. Stretch the spring slightly. For example, a spring of length of 0.30 m should be stretched to about 0.50 m (these distances are not critical). Rest the hand holding the spring on a metre rule, the other end of which acts as a stop to prevent the vibrator sliding along the bench.
2. Increase the frequency of the signal driving the vibrator, from about 20 Hz to several hundred hertz.
3. What frequencies give standing waves? How are these frequencies related to each other? To the wavelengths produced?

Teaching Notes

• The standing waves should be viewed stroboscopically, as well as by eye, to give students a clear understanding of their nature.
• The spring shows standing waves at frequencies in arithmetic progression.
• When a dozen or so rapid oscillations are sent down a long spring, a standing wave appears briefly where the reflected first few waves travel back through the last few waves which have not yet reached the end.              .
• The standing wave is so called because it does not look as if it is travelling in either direction along the spring. Yet it is the result of two similar waves travelling along. But they travel in opposite directions.
• For teaching, a better device than any diagram is the pair of plastic waves laid on top of one another and slid along millimetre by millimetre, or a pair of wave strips used on an overhead projector. With both waves moving, there are fixed places where the waves superpose to give zero effect at all times. There are other fixed places where the waves superpose to give an oscillation having twice the amplitude of either wave alone.

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