Episode 309: Generating waves

This episode introduces the idea that vibrations can give rise to disturbances travelling outwards, i.e. to progressive waves. It shows some of the basic properties of waves.

Lesson Summary

• Demonstration and discussion: Transverse waves on spring (15 minutes)
• Student experiment: Transverse waves on springs (15 minutes)
• Demonstration: Longitudinal waves on spring (10 minutes)
• Student experiment: Longitudinal waves on springs (15 minutes)
• Demonstration: Waves along a row of students (10 minutes)
• Demonstration: Ripple tank (10 minutes)
• Demonstration (optional): Waves along linked trolleys (15 minutes)
• Summary: Discussion of common wave properties (10 minutes)

Discussion and demonstrations: Transverse waves on spring

Here you are trying to establish these points:

• a wave is caused by a vibrating source, and travels outwards from the source
• the particles of the medium through which a wave travels move about their equilibrium positions; they do not move along with the wave
• energy is transferred from place to place by a wave i.e. a change at A can cause at change at B with nothing materially passing between A and B.
• you can demonstrate these points by showing waves on a stretched spring – there are two types of spring used in activities of this sort:
• The slinky type, diameter about 9 cm, can also be used to show longitudinal waves. It is easily damaged if it is let go when stretched, not stored carefully or allowed to fall on the floor. Keep a good one out of students’ reach for your demonstrations, as the slightest kink spoils the motion
• The long narrow, tightly coiled spring, about 3 cm diameter shows transverse waves well and is relatively robust. Alternatively, use a rope or rubber tubing.

Fix one end of the slinky using a retort stand and large weight, keep it on the floor or bench, and keep hold of the other end yourself. Demonstrate how a pulse travels along the spring when you move the end from side to side. (You will have to move your hand sharply to get a good pulse.) Repeated pulses make up a continuous wave.

Mark one coil with a white sticky label so that the motion can be seen. Remind your audience that the coils represent particles of a medium such as water or air as they move to and fro giving rise to the wave. A little ball of crumpled paper hit by a transverse pulse moves convincingly at right angles to the motion of the pulse. This is a transverse wave.

Use questioning to draw out the points listed above.

Student experiment: Transverse waves on springs

Pulses and continuous waves with a Slinky spring

Transverse waves along a rope

Safety

• Insist that springs are kept on the floor
• Use eye protection
• Beware of the spring whipping back
• if it someone lets it go when stretched
• Do not lean over the stretched spring

Undirected activity here can lead to chaos! So discuss a list of things to look for with the transverse pulses:

• Does the size of a pulse change as it travels along the spring? (Single pulses lose energy and so height but they don’t slow down.) What if there was no friction? (Pulses would stay the same height, i.e. no energy lost.)
• What happens when a pulse reflects at the fixed end? (It flicks over to the other side – there is a 180 ° phase change, but this doesn’t happen at a free end.)
• How does the speed change if you change the tension? (This is not easy to show with spring. In fact it always takes the same length of time for a pulse to travel the length of the spring, as the speed increases to compensate for the greater distance travelled.) It is easier to show with a stretched rope.
• What happens if pulses set off from opposite ends at the same time? (If students at both ends each make a pulse on opposite sides they will be seen to travel through one another.) Students may think that pulses bounce off one another and return. You may wish to demonstrate pulses passing through one another. Time lapse photography or frame by frame video might be used here or make sure one pulse has a larger amplitude than the other
• They should also draw the sudden change in phase upon reflection at a fixed end. This lets you check that phenomena have been observed correctly.

Demonstration: Longitudinal waves on spring.

Now use the slinky spring to show longitudinal pulses. Fix one end to a retort stand, and quickly push the free end back and forth, along the length of the spring. Watch the motion of the marked coil. It moves to and fro as the disturbance is passed along.

Identify compressions and rarefactions. Point out that rarefaction is not the same as refraction!

Student experiment: Longitudinal waves on springs.

Students can now find out whether longitudinal waves show the same behaviours as transverse waves; in this case, they send longitudinal waves along a stretched spring by pushing the end back and forth, along the length of the spring (rather than from side to side).

They should find that the crumpled paper ball is left untouched at the side when a pulse travels down. There is the same increase in velocity with tension.

Demonstration: Waves along a row of students

To emphasise the two types of waves, try simulating both types of wave using a row of students.

This can work well if students are cooperative. It is best to practise e.g. two steps forward, four back, then two forward brings them back to their equilibrium position. (You could use the Mexican wave for the transverse wave.)

Two points to bring out here:

• The meanings of displacement and amplitude
• Individuals in the wave are out-of-step with each other; this is useful for developing the idea of phase

This motion can then be compared with a standing wave later on.

Waves along a line of students

Demonstration: Ripple tank

In everyday life, waves are something we see on water. In physics, the idea of waves has been greatly extended. Show some simple water wave effects using a ripple tank.

You may find it simplest to work as follows:

Place the ripple tank on an overhead projector, so that students see the waves projected on the screen. If this proves difficult, place the lamp under the tank and project onto the ceiling.

Do not use a motor to generate ripples; make short bursts of ripples by hand (by dipping into the water), or by dripping water into the tank.

Use a minute piece of paper to show that it just bobs up and down when a ripple goes past.

Submerge a flat glass plate, and show the change of wavelength when ripples arrive head on to the shallower water.

Omit curved barriers at this stage.

Safety

Be very careful not to spill any water as you are using electrical equipment. If possible, have the low voltage power unit at least 1m away from the tank.

Practical Physics experiments:

Simple circular pulses in ripple tanks

Simple straight pulses

Reflection of a straight pulse by a barrier

Reflection of a circular pulse by a barrier

You should be able to make these points:

• A disturbance travels outwards from a vibrating source
• Ripples pass through one another and carry on
• The ripples would not be circles if the wave speed was not the same in all directions. Extend to 3D and spheres with the inverse square law in mind
• Wave speed changes (and hence wavelength changes) when in shallower water above a glass plate. (Don’t show change in direction here, refraction proper comes later.)

c=    g h

(Wave speed in shallow water so if h is smaller, (due to the smaller depth due to the shape), and then the waves go slower.)

Refraction of ripples entering shallow water

Demonstration: Waves along linked trolleys

Waves travel through matter; each particle interacts with its neighbours, and so the wave is passed along. With this demonstration, you can show that the speed depends on the strength of the links between the oscillating particles.

A row of trolleys is linked by springs and the trolley at one end moved back and forth.

This takes a while to set up so will have to be done beforehand. You will need several trolleys and a lot of space if you want to do both types of wave at the same time. Double the number of springs on each link to change the interaction. The mass of each particle is also easily doubled using trolley masses. Relate this to the speed of sound in solids which is much faster than in gases.

This demonstration may best be done on the floor to avoid having the trolleys fall off the bench.

Waves with trolleys

Summary discussion: Discussion of common wave properties

Summarise the common properties seen with mechanical waves:

• Vibrating source
• Disturbance travels outwards from a vibrating source
• Transport of energy (but not matter)
• Reflection
• Waves pass through one another and carry on.
• Dependence of speed on conditions.