# Melde's experiment

##### Demonstration

Using a vibration generator to investigate standing waves on a string.

#### Apparatus and materials

Weight hanger with slotted weights

Vibration generator

Pulley, single, on clamp

#### Health & Safety and Technical notes

If a fractional horsepower motor is used, it is essential to connect both field coils and armature as shown, before switching on the power. No changes should be made while the motor is running.

A commercially available vibrator and signal generator can be used for this experiment. Alternatively, the end of the thread can be attached to the vibrating strip in a ticker tape vibrator. A video showing how to use a signal (vibration) generator is available at the National STEM Centre eLibrary.

Another suitable arrangement is to attach a wheel to a small motor: the thread is then attached to an eccentric screw.

Students could observe the thread through hand stroboscopes. Alternatively, the thread can be illuminated intermittently by light.

#### Procedure

Set up the vibrator so that one end of the long thread is excited, whilst the other end passes over the pulley to the weight hanger. Adjust the load until several loops are clearly seen. Alternatively, clamp the thread at both ends.

Put the vibrator near one end, driving the string into resonance at a node.

#### Teaching notes

1 If a vibrator driven by a signal generator is used, you can gradually increase the frequency, showing how the string goes in and out of resonance with an increasing number of loops. Show the pattern of frequencies as the number of loops increases 1, 2, 3, etc.

2 You could use this apparatus to test the relationship between the tension, mass per unit length, frequency, and wavelength. Or you could calculate the speed of the wave by measuring its wavelength and frequency.

3 How Science Works Extension: An electronic stroboscope can be used to illuminate the vibrating string. At resonance, adjust the frequency of the strobe until the string appears stationary. The frequency of the strobe should match the frequency of the signal generator, but this depends on how well they are calibrated. Which is to be believed?

This illustrates the need for a standard of measurement. The mains frequency (50 or 60 Hz, depending on where you are) is very reliable. Ask students how this could be used. (Try driving the vibrator with a low voltage mains supply; adjust the length or tension of the string until it resonates. Take a reading from the stroboscope. Set the signal generator to 50 Hz and see if the string still resonates.)

Students could research the mains frequency. Why might it change? What variation in frequency is permitted?

This experiment was safety-checked in February 2006