# Standing Waves

#### Abstract

An AC electric current is used to excite standing waves in a wire passed over a magnet.

Yes

#### Principles Illustrated

The standing waves are the ones that “fit” on the wire of length L with nodes at both ends, having wavelengths given by

where n=1,2,3… While one can observe quite a few standing waves with the apparatus, the n=1 and the n=2 standing waves are the most visible.

The apparatus allows students to explore the effects of changing the length of the wire, the linear mass density of the wire, and the tension in the wire. Note changing the tension and/or linear mass density changes the speed of waves on the wire as where

is the linear mass density of the wire and T is the tension.

SinceĀ

either the frequency or wavelength must change. Since the wavelength is fixed by the condition above it must be the frequency that changes.

We use this as a demonstration apparatus and as a laboratory exercise apparatus. Guided enquiry works well with this experiment. For example, get students to find the first standing wave (n=1) and get them to predict the frequency of the n=2 standing wave. Ask them to predict the effect of doubling the mass used to tension to wire, and so on.

This is essentially an update of an ages old demonstration in which a mass is hung over a pulley on the end of a table, with the wire passing through a horseshoe magnet. See for example PIRA 3B.22.10.

PHYS 3.3

#### Instructions

If you want to build this yourself it is not difficult. You just need a sig gen, a rare earth magnet, some varnish insulated wire, and a few other bits. The standing wave resonances are quite sharp so adjust the frequency slowly. A stronger magnet works better, but they become dangerous.

This experiment works much better with a signal generator with 0.1 Hz resolution. They are readily available now.

#### Safety

Rare earth magnets can break fingers and do worse. Handle them carefully, particularly larger ones. They are also quite toxic if ingested.

Individual teachers are responsible for safety in their own classes. Even familiar demonstrations should be practised and safety-checked by individual teachers before they are used in a classroom.

#### Notes

It is worth explaining to students that this is essentially an electric guitar in reverse.

PIRA 3B.22.10