Demonstration

A close look at interference between two, random wave pulses in a ripple tank.

Apparatus and Materials

For the class

• Ripple tank and accessories

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.

Read our standard health & safety guidance

Procedure

1. Make one ripple (pulse} with a finger, and start another ripple from another place some distance away. Watch the two ripples carefully as they pass through each other.
2. What happens when one ripple crosses another? Do they upset each other? Are they changed by the encounter?

Teaching Notes

• The fact that two waves continue on their way when they have passed through each other as if there had never been an encounter will come as no surprise to students who have:
• Closely observed raindrops falling in a puddle, or
• Thought about the fact that signal-carrying microwaves and radio waves pass through each other constantly, particularly in cities dense with communications.
• Still it is remarkable.
• Of course, this only happens for linear systems which obey Hooke’s Law. In non-linear systems, where energy from the passing disturbance is partially absorbed by the medium, waves will permanently affect each other when they pass.

This experiment was safety-tested in February 2006

Class Practical

Using a ripple tank to observe interference between two wave pulses that are in phase may be suitable for intermediate or advanced level students.

Apparatus and Materials

• Light source, compact

• Hand stroboscope

• Ripple tank and accessories

• 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.

Read our standard health & safety guidance

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

Procedure

1. Use two fingers of one hand to make a pair of single pulses, at the same time.
2. Now make two streams of continuous ripples. Take turns observing with a hand stroboscope the pattern this produces. Can you see any pattern? Can you explain what you see?

Teaching Notes

• This method will not produce a pattern that is very regular or easily seen, but it should give a feel for interference from two sources.
• The exercise could lead on to the use of the vibrator with two point dippers attached to it to act instead of the fingers.
• Where the two waves overlap, they simply give the sum of their two separate effects. If those effects are both in the same direction the sum is large, called ‘constructive interference’. If the effects are in opposite directions then the sum may be small or even zero, called ‘destructive interference’.
• The explanation that you give will depend on student’s prior knowledge. A useful discussion with students might run like this:
• here one ripple arrives that makes the water go up and down
• flip-flap, flip-flap.....
• and the other ripple also arrives making the water go up and down
• flip-flap, flip-flap.....
• The two wave signals add up, FLIP-FLAP, FLIP-FLAP
• But here, where the wave from one source has travelled a little further than the wave from the second source, the two waves do not arrive in step.
• One makes the water go up and down flip-flap
• and the other makes the water go flap-flip
• Or you may prefer to use more conventional terms, identifying crests and troughs - or simply up and down. You could also use plastic wave models to explain what is happening. These are described in Collection 8.
• The most important thing is to draw students attention to places where each of these happen.
• With more advanced students, you may also want to draw attention to distances from the two sources at various locations, and the way that different path lengths affect the relative phases of the waves from each source.

This experiment was safety-tested in February 2006

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

• Ripple tank and accessories

• Hand stroboscope

• 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.

Read our standard health & safety guidance

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

1. 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.
2. Turn on the motor and run the vibrator as slowly as possible.
3. Look for lines where the water surface appears not to be disturbed. How many are there?
4. 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.
5. Ask: How does the pattern change as you make the wavelengths shorter?

Teaching Notes

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

Class Practical

Using strips of plastic to model what happens to at different positions in terms of changing phase relationships.

Apparatus and Materials

• Plastic waves, 2
• Nails, 15-cm, 2
• Retort stand
• Bosses, 2

Health & Safety and Technical Notes

Read our standard health & safety guidance

Procedure

1. You can illustrate interference from two point sources by crossing the ends of the plastic waves supported from a retort stand, as shown.
2. Move the crossover point up and down to show that light and dark bands will be produced on a screen.

Teaching Notes

• This apparatus can be used to explain Young's experiment, with light producing fringes.
• With more able students, you could increase the spacing of the clamps to get more lines of nodes. It is not advisable to start with wide spacing as the waves then cross at quite large angles in some cases and the addition and subtraction are not so obvious.
• If you prefer to work in the horizontal plane, you could place the two vertical rods about 25 cm apart to represent the slits. Support the plastic waves from them in a sling so that they can be moved horizontally backwards and forwards.
• An alternative to plastic waves is corrugated cardboard. Cut two strips about 20 cm long and about 1/4 cm wide, and place them on their sides on a drawing board. Pin each strip to the board by a pin through a wave hump near one end. These anchored ends represent the two sources, a few centimetres apart on the board.

This experiment was safety-checked in February 2006

Class experiment

Students, working in pairs, observe and try to explain what happens to wave pulses on a long narrow spring. This could be just one station in a circus of wave experiments.

Apparatus and Materials

For each student pair:
• Long narrow spring (if not available, use a Slinky spring)
• Metre rule
optional
• String
• Curtain ring, large nylon
• Retort stand base, rod

Health & Safety and Technical Notes

Long narrow springs do not become entangled as easily as Slinky springs do. Because the spring is narrow and closely wound, the shape of pulses is easy to see.

Each pair of students needs a long narrow space to work in, such as a corridor. It is usually best to work on the floor rather than on a bench.

A complementary experiment involves sending waves and ripples along a long shallow trough of water. This requires about 2 metres of flat-bottomed guttering (resting directly on a bench), with both ends closed by end stops. Because waves of many sorts can be made, and they travel slowly, the device is good for observing how wave pulses superpose and pass through one another without being affected.

Read our standard health & safety guidance

Procedure

You will need to produce pulses in the spring. It is easier to see what is happening if you make single hump-like pulses, by giving the end of the spring a single sideways flick.

1. Observe the pulse as it travels, with a view to answering questions
such as:
• Does the speed depend on the shape of the pulse - its height or length?
• Does the speed depend on how rapidly you flick the end of the spring?
• Does the speed depend on the spring - how could the speed be made larger or smaller?
• Does friction make any difference to the speed of the pulse? to its shape?
• What decides the shape of a pulse?
• What happens when pulses, starting from opposite ends of the spring, meet?
• What happens when the pulse reaches the far end of the spring, and that end is not free to move?
2. If you have time, try the following:
• Attach a large nylon curtain ring to the end of the spring and slide the ring onto a retort stand rod. When the pulse reaches this end, the end is free to move. What happens to the pulse?
• Tie a piece of thick string or cord onto the end of the spring. What happens to the pulse as it moves from the spring to the string or vice versa? Can you explain this?

Teaching Notes

• You may need to revise some basic terms before students begin this investigation, through class questioning:
• Define the terms wavelength , frequency , and amplitude for a wave profile (e.g. the one above).
• What is meant by the equilibrium position and the displacement of a point such as P?
• What determines the frequency of the wave, and what unit is frequency measured in?
• How are wave speed, wavelength, and frequency related? How does P move as the wave travels along?
• After carrying out these investigations, a plenary might usefully consolidate the following conclusions:
• The shape of a pulse on a spring is determined by the nature of the flick creating it: a quick flick gives a short pulse, whereas a slow flick gives a long pulse.
• Friction makes a pulse grow smaller in amplitude as it travels – its energy spreads out to its surroundings.
• The speed of a pulse is not determined by its shape, nor on how you flick the spring to create it.
• The speed does depend on the spring - and on the tension with which it is held. The speed increases as the tension is increased.
• When pulses meet they superpose - the displacements that each pulse alone would cause on the spring add together; but when the pulses pass beyond each other they continue with their original shape - see below.

• When a series of pulses is reflected, the returning pulses form a stationary pattern as they superpose with those pulses still moving outward (see below).

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

Class experiment

Waves and ripples are sent along water in a long shallow trough. This could be one station in a circus of wave experiments.

Apparatus and Materials

• Plastic guttering, 2 m long, 100 mm wide
• End stop for guttering, 2
• Bucket

Health & Safety and Technical Notes

The guttering, both ends closed by end stops, rests on the bench. The sort of guttering that has a flat bottom needs no side supports to prevent it rolling over.

Read our standard health & safety guidance

Procedure

1. Because waves of many sorts can be made, and they travel slowly, the device is good for observing how wave pulses superpose and pass through one another without being affected.
2. Alternatively students could compare a measured pulse speed with a calculation based on theory.

Teaching Notes

Speed of long waves in deep water

g is the acceleration of gravity, for gravity is the force moving these waves along.

In deep water, surface tension forces, s, are too small to matter. The density, r, does not appear because if it rises, the force acting and the mass to be moved both increase by the same factor, with no net effect on the response time of water ahead of a wave front.

Speed of waves in shallow water

(λ >> h, amplitude << h)

h is simply the depth of the water.

In water whose depth is large compared to the wavelength, l, the wave speed expression contains two terms, one for gravity effects and one for surface tension effects. It is

where the symbols have the meaning given above.

For short wavelength (ripples), the second term predominates, and the speed is approximately

For long waves, the first term predominates, and the speed is approximately

Interested students may be referred to Tricker, Bores, breakers, waves and wakes or Barber, Water waves. Bores are a special case of shallow water waves v =

A bore can easily be made in the water trough by sweeping water along at a steady rate using a wide paddle.

Speed of tiny ripples on water

if wavelength is small.

These waves have a speed which depends also on the wavelength A. Surface tension forces move these waves along. There are gravitational forces on the tiny humps of water, but they are too small to matter.

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

Demonstration

Lines of dynamics trolleys connected by springs make good models for both longitudinal and transverse waves. They are best used at advanced level, when investigating factors affecting wave speed.

Apparatus and Materials

• Spring holders, 20
• Springs, 20
• Dynamics trolleys, 11

Health & Safety and Technical Notes

Read our standard health & safety guidance

If the model is set up on a table with no raised edge, it is easy for part of it to run off the side of the table. The rest of the model inexorably follows! So it is best set up on a smooth floor, or on a surface provided with barriers along its edges.

Use fairly long dowels and keep the springs down at the bottom of them. Otherwise the springs have a tendency to fly off and the trolleys scatter.

Procedure

Transverse waves

1. Clamp a trolley to one end of a smooth bench and connect the others side by side with springs, as shown. The trolleys are separated so that they can move without hitting each other.
2. Give the trolley at the unclamped end a sudden deflection to one side and back, to show a pulse wave travelling along the line of trolleys.

Longitudinal waves

1. Connect the trolleys end to end, as shown. (Some trolleys have a projecting front wheel. Such trolleys may have to be linked between their towing pegs with springs.) The springs snap shut when released, so you will need to hold the whole model in tension.
2. Roll the trolley at the unclamped end a short distance and back, suddenly, to show a pulse traveling along the line of trolleys.

Teaching Notes

• Unless the bench is very rough, if you try to produce continuous waves you will get reflections from the clamped end. These are likely to cause standing waves. This may be a distraction worth avoiding.
• Longitudinal pulses can be produced much more successfully if the trolleys are connected with compressive springs (available as trolley accessories), rather than the extension springs shown in the diagram. One end of the line of trolleys can be left free and a pulse sent down the trolleys from the other end. The reflected pulse from this ‘open reflection’ can be compared with the reflected pulse when the end of the line of trolleys is firmly fixed, a ‘closed reflection’.
• You could investigate how the wave speed is affected by changes in mass and in tension. The mass of each trolley can be doubled by adding loads, and the tension can be doubled by adding extra springs. Doubling the mass of each trolley reduces the wave speed; doubling the tension raises it. Both modifications change the speed by the same factor, actually √ 2 . and both made together will restore the speed to its original value.
• Clearly, the wave speed depends upon how long it takes each part of the model to acquire some speed when forces act upon it, as the wave front arrives.
• A system like this, with the mass of the wave medium concentrated in discrete lumps with forces between each, behaves differently than a smoothly spread-out medium would do. This system is dispersive: when the wavelength is not much larger than the spacing between parts of the lumped medium, wave speed depends on wavelength. It also exhibits cut off: waves of high frequency are not propagated at all.
• Try moving an end trolley rapidly to and fro. The neighbouring trolley will oscillate a little, the next trolley oscillates less, and there is something like an exponential decrease in amplitude along the system. Wave energy cannot be propagated through the line of trolleys.
• These arrangements provide a reasonable physical model of a pulse travelling through a medium in which masses are connected together by spring-like connections. Atoms, at an equilibrium distance, are ‘connected’ by electrical forces, though of course inter-atomic forces increase with distance whether the material is compressed or extended.

This experiment was safety-tested in February 2006

• Another way to model transverse waves is using a wave machine (cheap and simple to construct):