# Interference with two sources, using vibrators

##### Class Practical

This demonstration of interference can be spectacular. Intermediate or advanced level students certainly find it helpful to observe interference patterns produced by continuous waves from two point sources that are in phase.

#### Apparatus and materials

Motor mounted on beam, with beam support

Dippers, 2

Light source, compact

Paper, white

#### Health & Safety and Technical notes

Beware of water on the laboratory floor. Make sure you have a sponge and bucket handy to mop up spills immediately.

Place the power supply for the lamp on a bench, not on the floor by the tank.

Photo-induced epilepsy
In all work with flashing lights, teachers must be aware of any student suffering from photo-induced epilepsy. This condition is very rare. However, make sensitive inquiry of any known epileptic to see whether an attack has ever been associated with flashing lights. If so, the student could be invited to leave the lab or shield his/her eyes as deemed advisable. It is impracticable to avoid the hazardous frequency range (7 to 15 Hz) in these experiments.

The white paper is used as a screen on the floor.

The ripple tank should be set up so that there is a balance between the water being deep enough to produce good ripples and shallow enough to prevent too many reflections coming from its sides. The water in the tank should be about 1 cm deep.

#### Procedure

a Place two point dippers on the beam, about 3 cm apart. Adjust their height so they just raise the surface of the water up to them.

b Turn on the motor and run the vibrator as slowly as possible.

c Look for lines where the water surface appears not to be disturbed. How many are there?

d Gradually increase the speed of the vibrator. At each frequency, count the lines where the water surface is undisturbed. At high speeds you are likely to need a stroboscope to see the pattern.

Ask: How does the pattern change as you make the wavelengths shorter?

#### Teaching notes

1 Slow wave interference can be seen clearly without a stroboscope or by blinking, but a stroboscope is needed for higher frequencies.

2 Point out that the nodal lines in the tank, places where there is no displacement of the water, are not straight lines but curve away from the line of symmetry (perpendicular to, and midway along, the line between the sources).

Increasing the frequency produces more nodal lines, reducing their separation.

Students might also increase the spacing of the dippers. They should find that this increases the number of nodal lines and makes them closer. The effect is most obvious with the vibrator running slowly; at high speeds the pattern is very beautiful, but the lines of minimum displacement are very close together.

3 If there is time, students could also measure the path difference from the two sources for
positions where ‘maxima and minima’ wave trains (antinodes) from positions where there is no displacement (nodes).

They will find that nodal lines occur where path differences are an odd number of half wavelengths, and that antinodes occur where path differences are an even number of half wavelengths.

A simple variation on the experiment

a Place a ripple tank or a Petri dish or any other flat-bottomed transparent container over a pale surface and illuminate from above. Put some water in the container.

b Touch the surface with a vibrating tuning fork. The prongs are coherent wave sources and so produce an interference pattern.

c Observe the maxima and minima.

d By averaging over many, measure the spacing of the shadows between the prongs to deduce the wavelength. Frequency is printed on the tuning fork. Multiply together to find the wave speed.

e It could be interesting to explore the variation of wave-speed with depth of water. (At what point does depth become irrelevant?) If you have tuning forks of several different frequencies, investigate dispersion – how does wave speed depend on frequency?

This experiment was safety-checked in February 2006