Standing Wave
Light, Sound and Waves

Standing waves and resonance

for 14-16

Demonstration and class experiments of standing waves provide a key link to musical instruments and to an important principle of engineering design.  
Use a selection from these experiments to illustrate that standing waves are to be found in many situations. The waves are in general more complex than those on a cord, but certain features remain the same:

  • There are definite modes of oscillation, at each of which the response is large (resonance).
  • The patterns depend on the frequency, there being more nodes or nodal lines for high frequencies (short wavelengths).
  • Standing waves have to 'fit' into the system, whether it has one or more dimensions. They are the result of superposition of reflected waves from the boundaries and waves travelling towards the boundaries. As a general rule, wave-carrying systems with edges exhibit standing waves.

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Standing waves

Standing Wave
Light, Sound and Waves

Standing waves

Practical Activity for 14-16

Demonstration

Generating standing waves from transverse waves on a rope and from longitudinal waves on a slinky spring.

Apparatus and Materials

  • Slinky spring
  • Rope, 6 m, soft and flexible
  • Tank, large rectangular transparent

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Tie one end of the rope securely to a fixture on a wall. Pull the other end taut. Move that end up and down, to excite transverse waves. Build up a pattern of standing waves, by feeling for the right resonant frequency, and adjusting the tension.
  2. A more effective method is to drive the motion at a node. Secure the rope firmly at both ends. Mark off the rope into equal segments, such as fifths. Make a loose ring with a finger and thumb round the rope at the nearest marked point. Move your hand up and down, and change the frequency until the 5-loop motion builds up. Different resonances can be produced, of course, by changing the frequency or the tension.
  3. Build up a longitudinal standing wave on a Slinky. Clamp both ends of the well-stretched spring, support it on a trolley runway, and excite it by hand near a node.

Teaching Notes

  • Be clear about the purpose of your demonstration. Depending on the course level and students’ abilities, your purposes in demonstrating standing waves may be any or all of the following:
    • To demonstrate standing wave patterns as a form of vibration.
    • To discuss energies associated with different patterns.
    • To consider the two trains of waves necessary to the production of standing waves.

This experiment was safety-tested in February 2006

Up next

Ring of standing waves

Standing Wave
Light, Sound and Waves

Ring of standing waves

Practical Activity for 14-16

Demonstration

Circular waves on a water surface can produce a standing wave pattern.

Apparatus and Materials

    Using a trough or large bowl:
  • Glass trough, large round
  • Wooden block
  • Using a Petri dish and vibrator-driven dipper:
  • Signal generator
  • Vibrator, with some form of dipper attached
  • 4 mm leads, 2

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.

Read our standard health & safety guidance


Using a trough or large bowl: A trough with diameter 30: 40 cm is adequate. Alternatively use any large plastic bowl.

The driving frequency needs to be high to get a number of wavelengths in the circumference.

It may be better to use a rapid rocking motion.

Using a petri dish and a vibrator-driven dipper: Put a little water in the Petri dish. The dish could be supported, with a screen about 0.1 m below it and a 12V lamp above it, making it a miniature ripple tank. The dipper will produce ring patterns of waves in the dish.

Procedure

  1. Half fill the trough with water.
  2. Place the wooden block in the water surface near the edge. By moving it up and down, excite fairly high frequency ripples and establish a pattern of standing waves.

Teaching Notes

  • This is a tricky experiment to do, and can result in water everywhere. An integral number of half-wavelengths need to fit into the circumference of the trough.
  • You may find that a rapid rocking motion of the hand more effectively produces a standing waves pattern.
  • This is similar to the experiment "Vibrations in a rubber sheet".
  • You may wish to link this demonstration to the wave-mechanical model of the atom, with electron waves fitting into the atom.

This experiment was safety-tested in February 2006

Up next

Vibrations in a rubber sheet

Standing Wave
Light, Sound and Waves

Vibrations in a rubber sheet

Practical Activity for 14-16

Demonstration

In this experiment oscillations are produced in a rubber sheet.

Apparatus and Materials

  • Signal generator
  • Large loudspeaker
  • Xenon stroboscope
  • Sheet of rubber
  • Retort stand base & rod, 3
  • Boss and clamp
  • Large aluminium ring
  • Rubber band(s)
  • 4 mm leads
  • Additional apparatus for a closely-related experiment, Chladni plates...
  • Square or round metal plate
  • Sand

Health & Safety and Technical Notes

Read our standard health & safety guidance


The diagrams above shows how to excite oscillations in a rubber sheet.

Stretch the sheet over the large metal ring, so as to be as evenly stretched as possible. Radial lines drawn on the rubber make the oscillations easier to see. Holding the sheet to the ring by a large rubber band makes it easy to make small adjustments to the evenness of the sheet's tension.

Place the loudspeaker below the ring and rubber sheet. Frequencies in the range 10 to 100 Hz are required, and the larger the power delivered by the loudspeaker, the better.

Safety note: Using the xenon stroboscope, teachers should be aware that frequencies around 7 Hz have been known to cause epileptic fits in certain people. Ask your students if any know that they are susceptible to this response.

Procedure

  1. Try a central position of the speaker first, and a low frequency. Raise the frequency gradually, looking and listening for the lowest resonance mode, in which the centre of the rubber sheet rises and falls, as in diagram (a) below.
  2. The amplitude may be 10 to 20 mm at the centre.
  3. See diagram (b). At a higher frequency, with the speaker off centre, a mode of oscillation can be found in which the rubber surface tilts, one side rising as the other falls, the rim staying fixed of course.
  4. You may be able to produce several other modes of vibration. Is there a simple relationship between the resonant frequencies? Between the patterns obtained?

Teaching Notes

  • The standing waves should be viewed stroboscopically, as well as by eye, to give students a clear understanding of their nature.
  • To show Chladni figures: Attach the metal plate centrally to the vibrator. Before switching the vibrator on, sprinkle sand on the plate to reveal the vibration pattern. Many modes of vibration exist. The resonant oscillations of car door or body panels are of this general kind.
  • Note the resonant frequencies. Are they simply related?

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

Up next

Standing waves along trolleys

Standing Wave
Light, Sound and Waves

Standing waves along trolleys

Practical Activity for 14-16

Demonstration

Standing waves along a line of dynamics trolleys linked by springs make quite a sight: some trolleys stationary while nearby trolleys move quickly.

Apparatus and Materials

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

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

  1. For transverse waves, 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. Oscillate the trolley at the unclamped end continuously, to generate a continuous transverse wave down the line of trolleys. Continue and the reflected wave will build up a standing wave pattern.
  3. For longitudinal waves, 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.
  4. Oscillate the trolley at the unclamped end continuously, to generate a continuous longitudinal wave down the line of trolleys. Continue and the reflected wave will build up a standing wave pattern.

Teaching Notes

  1. These arrangements provide a good 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 these increase whether the material is compressed or extended.
  2. 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.
  3. 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.
  4. Using a simple mathematical wave model for the trolley system you could predict the wave speed, then measure the speed and compare them. You would find that they fit quite closely.
  5. A system like this, with the mass of the wave medium concentrated in discrete lumps with forces between each, does not behave in all respects like a smoothly spread-out medium would do. The system is dispersive: the speed depends upon the wavelength when the wavelength is not much larger than the spacing between parts of the lumped medium. It exhibits 'cut off’: waves of high frequency are not propagated at all.
  6. Try moving an end trolley very rapidly to and fro. The next-door trolley oscillates a little, the next oscillates less, and there is something like an exponential decrease of amplitude along the system. No wave energy propagates down the system. (These problems are discussed in The Berkeley Physics Course, vol. 3 Waves.)

This experiment was safety-checked in February 2006

Up next

Melde's experiment

Standing Wave
Light, Sound and Waves

Melde's experiment

Practical Activity for 14-16

Demonstration

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

Apparatus and Materials

  • Weight hanger with slotted weights
  • Hand stroboscrope


  • Vibration generator
  • Pulley, single, on clamp
  • Thread, 3 metres

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.

Read our standard health & safety guidance


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:

watch video


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

  1. 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.
  2. Put the vibrator near one end, driving the string into resonance at a node.

Teaching Notes

  • 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.
  • 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.
  • 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

Up next

Musical instruments

Standing Wave
Light, Sound and Waves

Musical instruments

Practical Activity for 14-16

Experiment

This experiment could supplement a few demonstrations about standing waves, with students playing their own musical instruments.

Apparatus and Materials

  • Oscilloscope
  • Microphone
  • Ore-amplifier (if necessary)
  • Assorted musical instruments

Health & Safety and Technical Notes

Read our standard health & safety guidance


Connect the microphone to the AC input of the oscilloscope. Initially set the timebase to 1ms/div.

Procedure

Use the oscilloscope to examine the different waveforms of the sounds produced by different instruments.

Teaching Notes

  • Standing waves are set up when musical instruments are either plucked, blown, struck, or stroked. Usually the standing wave pattern is a complex one, and waves of several different frequencies are present.
  • Useful references include the following:
    • Science Enhancement Programme booklet Voicebox: the physics and evolution of speech - available from Mindsets:

      Mindsets


    • Charles Taylor (1992) Exploring Music: The Science and Technology of Tones and Tunes Bristol: Institute of Physics Publishing
    • Scientific American (1978) The Physics of Music San Francisco: W H Freeman and Company

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

Up next

Music from standing waves: monochord

Standing Wave
Light, Sound and Waves

Music from standing waves: monochord

Practical Activity for 14-16

Demonstration

This is a nice simple experiment that enables students to visualize the audible vibrations from a stringed instrument.

Apparatus and Materials

  • Monochord
  • Paper riders
  • Violin bow
  • Rubber hammer
  • Tuning folk

Health & Safety and Technical Notes

Eye protection must be worn. If the wire or cord snaps, it may whip into someone's eye.

Read our standard health & safety guidance


The monochord can be a simple stretched elastic chord or a metal wire attached to a sonometer box specially made for the job.

Violin bow is optional.

Procedure

  1. Stretch the wire taut, and excite it by plucking (or bowing) it near one end. Students listen to the note.
  2. Then pluck (or bow) it again, at the same time touching it very lightly with a finger at its mid-point. Ask students how the note has changed. (The wire will now be vibrating in two loops, with double frequency, an octave higher.)
  3. Repeat with a finger touching lightly at 1/3, 1/4, etc. of the wire's length.
  4. Show the existence of nodes and antinodes by hanging paper riders at appropriate places. Place the finger to suggest a suitable node, and bow gently, briefly. Riders at antinodes will jump off, those at nodes should stay there.
  5. The step 4 procedure needs practice. An easier method is to excite the wire to resonance with a tuning fork. Tune the wire beforehand, by changing the length between bridges, so that it vibrates in, say, three loops with exactly the frequency of the fork.
  6. Let students listen to the fork and to the note of the wire in the chosen harmonic. Place riders on the wire and excite it, by touching the wire at one bridge with the shank of the vibrating fork.

Teaching Notes

  • This demonstration links standing waves with an understanding of musical instruments.
  • If you illuminate the monochord with a stroboscope running at a slightly different frequency, then students will be able to see the motion of the wave in slow motion. If you select the exact frequency, the wave will appear to be stationary. In its ‘fundamental’, or basic, mode of vibration, the length of the string is a half wavelength of the note played.
  • You may want to encourage students to bring in their own musical instruments. They can investigate how the lengths of the string or the lengths of the vibrating air column change while playing.
  • Stringed instruments such as violins and cellos are played with the basic note. The string vibrates in one loop — two or more loops only as a special technique. Yet the motion of the bowed or plucked string is seldom simple harmonic. It is usually compound harmonic, a mixture of the notes of motion in 1 loop, 2 loops, 3 loops, and so on. That mixture gives instruments their characteristic ‘timbre’, or sound quality.
  • A string's motion will depend on whether it is plucked, bowed or excited by a tuning fork.
  • Students who play musical instruments may be familiar with important musical intervals like the octave, perfect fifth and perfect fourth. These correspond to frequency ratios 1:1, 2:3 and 3:4 respectively and can easily be demonstrated on the monochord. Pythagoras made this discovery 2,500 years ago.
  • Flutes, bugles and some whistles are completely different from each other. A flute behaves as a cylinder open at both ends, so the modes have frequencies in the ratios 1:2:3:4 ... A bugle will give frequencies in the ratios 2:3:4:5:6, but it is complicated by the fact that its diameter changes along its length. A clarinet will give modes in the ratios 1:3:5, i.e. as a cylinder closed at one end.

This experiment was safety-tested in July 2004

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Sound waves

Standing Wave
Light, Sound and Waves

Sound waves

Practical Activity for 14-16

Demonstration

A microphone shows the standing wave pattern in the space between a loudspeaker and an acoustically ‘hard’ reflective wall.

Apparatus and Materials

  • Loudspeaker
  • Signal generator, low frequency
  • Oscilloscope


  • Microphone

Health & Safety and Technical Notes

Read our standard health & safety guidance


A video showing the use of an oscilloscope is freely available at the National STEM Centre eLibrary:

watch video


There is also a video showing the use of a signal generator:

signal generator


Procedure

  1. Connect the loudspeaker to the signal generator and drive it at a suitable frequency (2000 to 4000 Hz). Connect the microphone to the input of the oscilloscope by long leads. Set the AC–DC switch to AC, the time-base to l00 micro-seconds per cm and the gain to maximum (or whatever is appropriate for the microphone used).
  2. Slowly move the microphone away from the speaker to show the change in amplitude with distance.
  3. Set the loudspeaker and the microphone facing a ‘hard’ wall, and move the microphone back and forth in the space between the speaker and the wall to show amplitude maxima and minima. You may need to adjust the frequency carefully to produce a standing wave pattern.

Teaching Notes

  • You may need to revise with students the key features of sound waves, or to explain what part each piece of apparatus plays.
  • Reflections from walls and bench tops can be troublesome in a lab. Sound experiments are much better if done in the open.
  • How Science Works Extension: If your students are familiar with standing waves, nodes and anti-nodes, they could be set the task of investigating the pattern of standing waves described above. Can they use it to find the speed of sound? How accurate is their final result?
  • Students will have to move the microphone along the line from the loudspeaker perpendicular to the reflecting surface. They should measure across as many nodes or anti-nodes as possible. Which is easier to detect, a node or an antinode? A microphone is quite a large object, so how can they define its precise position?
  • Measurements of wavelength (= 2 x distance between adjacent nodes) at different frequencies will allow students to calculate the speed of sound (= frequency x wavelength), but a graphical method is better. Discuss how this reduces the uncertainty in the final value.

This experiment was safety-checked in February 2006

Up next

Vibrations of a loudspeaker cone

Standing Wave
Light, Sound and Waves

Vibrations of a loudspeaker cone

Practical Activity for 14-16

Demonstration

This experiment shows how AC oscillations from the generator become sound oscillations at the loudspeaker.

Apparatus and Materials

  • Signal generator
  • Large loudspeaker
  • Xenon stroboscope
  • 4 mm leads
  • Semolina or rice, a small amount

Health & Safety and Technical Notes

Read our standard health & safety guidance


Clamp the loudspeaker so that it faces upwards. Connect the low impedance output of the signal generator to the loudspeaker. Place a few grains of semolina or rice in the cone so that resonances show up clearly, as the generator frequency changes.

Safety note: Using the xenon stroboscope, teachers should be aware that frequencies around 7 Hz have been known to cause epileptic fits in certain people. Ask your students if any know that they are susceptible to this response.

Procedure

  1. Increase the frequency slowly from about 10 Hz to a few 100 Hz.
  2. Watch the resonance of a loudspeaker cone under stroboscopic illumination.

Teaching Notes

The standing waves should be viewed stroboscopically, as well as by eye, to give students a clear understanding of their nature.

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

Up next

Centimetre waves

Standing Wave
Light, Sound and Waves

Centimetre waves

Practical Activity for 14-16

Demonstration

A microwave detector shows the standing wave pattern in the space between a microwave generator and a reflective metal barrier.

Apparatus and Materials

  • Aluminium barrier, plane
  • Amplifier
  • Loudspeaker
  • Microwave transmitter
  • Microwave receiver

Health & Safety and Technical Notes

Modern equipment using a solid-state diode transmitter is safe.

Older equipment using a klystron tube uses hazardous voltages. The connectors on the leads between the transmitter and the power supply MUST be shielded types to minimize the risk of serious electric shock. The ventilation holes in the power supply may also give access to hazardous voltages, so its use MUST be closely supervised.

Read our standard health & safety guidance


The transmitter should produce microwaves of about 3 cm.

The microwaves can be unmodulated, in which case the receiver is connected to a meter. If they are modulated, it is possible to detect them using an amplifier and loudspeaker. A narrow probe receiver will better discriminate between nodes and antinodes than a horn receiver will.

Manufacturers usually supply a full instruction book, including experiments, with their microwave kits.

Procedure

  1. Set the microwave transmitter and receiver facing a metal barrier.
  2. Move the receiver back and forth in the space between the speaker and the wall to show amplitude maxima and minima. You may need to adjust the distances carefully to produce a standing wave pattern.

Teaching Notes

Students find microwaves intriguing because of their invisibility. You may want to discuss how this is similar to other phenomena with which students are familiar; e.g. radio reception interference or mobile phone signal strength, and the way these result from reflections from buildings or geographical contours.

This experiment was safety-tested in February 2006

Up next

Stationary waves in an air column

Standing Wave
Light, Sound and Waves

Stationary waves in an air column

Practical Activity for 14-16

Demonstration

This experiment, using what is often referred to as Kundt's tube, demonstrates vividly how sound waves make air vibrate in a tube.

Apparatus and Materials

  • Loudspeaker
  • Signal generator
  • Polystyrene beads, small
  • Filter funnel
  • Tube, transparent plastic or glass (1.0m to 1.5m long)
  • Rubber bung, or similar, to seal one end of tube

Health & Safety and Technical Notes

Read our standard health & safety guidance


Place a thin layer of polystyrene beads along the length of the tube. Alternatively, you could use lycopodium powder or cork dust. These materials are best inserted by first sprinkling them along a metre rule, placing the rule inside the tube and then tipping them off.

Tape the loudspeaker in place. If the loudspeaker and tube have different diameters, join them with a paper cone or plastic cup.

If you don't have a long tube, use a large measuring cylinder instead.

A video showing how to use a signal generator is available at the National STEM Centre eLibrary:

video


Photographs courtesy of Mike Vetterlein

Procedure

  1. Switch on the signal generator. Vary the frequency of the sound coming out of the loudspeaker, through the range 1 kHz to 10 kHz, keeping the amplitude constant. Ask students to observe what effect this has on the vibrations of the beads.
  2. Vary the amplitude of the sound coming out of the loudspeaker, keeping the frequency constant. Again, ask students to observe what effect this has on the vibrations of the beads.

Teaching Notes

  • At some particular frequencies, a standing wave pattern will be formed, with the beads settling into heaps (piles) at certain positions along the tube. At the simplest level, the experiment demonstrates that sounds from the loudspeaker produce vibrations in air.
  • At more advanced level, you could measure the average distance between adjacent nodes (where the beads settle). This will be half a wavelength.
  • Using wave speed = frequency x wavelength you could go on to make an estimate of the speed of sound in air at the temperature of the room.
  • You could also explore the relationship between frequency and wavelength, for frequencies that produce a standing wave pattern (they should be inversely proportional). Or you could compare the speed of sound in open air with the speed of sound in a tube, then ask whether there an appreciable difference.
  • A version of this experiment, using polystyrene beads, was shown by Pascal Daman on the Luxemburg stand at Physics on Stage 3 in November 2003.

This experiment was safety-tested in February 2006

Up next

Longitudinal standing waves

Standing Wave
Light, Sound and Waves

Longitudinal standing waves

Practical Activity for 14-16

Demonstration

This experiment shows visible longitudinal standing waves in a spring.

Apparatus and Materials

  • Signal generator
  • Vibrator
  • Xenon stroboscope
  • Long spring
  • Metre rule
  • 4mm leads

Health & Safety and Technical Notes

Read our standard health & safety guidance


Put the vibrator on its side, attach one end of the spring to the vibrating element using string or a wire loop. Use the low impedance output of the signal generator, at full amplitude.

Safety note: Using the xenon stroboscope, teachers should be aware that frequencies around 7 Hz have been known to cause epileptic fits in certain people. Ask your students if any know that they are susceptible to this response.

Procedure

  1. Stretch the spring slightly. For example, a spring of length of 0.30 m should be stretched to about 0.50 m (these distances are not critical). Rest the hand holding the spring on a metre rule, the other end of which acts as a stop to prevent the vibrator sliding along the bench.
  2. Increase the frequency of the signal driving the vibrator, from about 20 Hz to several hundred hertz.
  3. What frequencies give standing waves? How are these frequencies related to each other? To the wavelengths produced?

Teaching Notes

  • The standing waves should be viewed stroboscopically, as well as by eye, to give students a clear understanding of their nature.
  • The spring shows standing waves at frequencies in arithmetic progression.
  • When a dozen or so rapid oscillations are sent down a long spring, a standing wave appears briefly where the reflected first few waves travel back through the last few waves which have not yet reached the end.              .
  • The standing wave is so called because it does not look as if it is travelling in either direction along the spring. Yet it is the result of two similar waves travelling along. But they travel in opposite directions.
  • For teaching, a better device than any diagram is the pair of plastic waves laid on top of one another and slid along millimetre by millimetre, or a pair of wave strips used on an overhead projector. With both waves moving, there are fixed places where the waves superpose to give zero effect at all times. There are other fixed places where the waves superpose to give an oscillation having twice the amplitude of either wave alone.

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

Up next

Longitudinal standing waves in rods

Standing Wave
Light, Sound and Waves

Longitudinal standing waves in rods

Practical Activity for 14-16

Demonstration

With this experiment you can show standing waves, either transverse or longitudinal, in a rod or rods.

Apparatus and Materials

  • Glass, steel, or brass rod, about 10 mm diameter and about 1.5 m long
  • G-clamp
  • Wooden blocks
  • Cloth
  • Rosin (for metals)
  • Alcohol (for glass)

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Hold the rod fairly firmly with rosined fingers, or a dampened cloth, and stroke it. What is the wavelength of the standing wave being produced?
  2. If you can find a way of estimating the frequency of the sound emitted, then go on to estimate the speed of sound in the rod.

Teaching Notes

  • In its fundamental mode of oscillation, the rod will have a node at the fixed end and an antinode at its free end. Thus the wavelength will be twice the length of the rod. The standing wave is audible as a sound of pure frequency.
  • By displacing the free end slightly and then releasing it, you might also show an equivalent transverse wave, which is visible.
  • Alternatively, the experiment could be used as one station in a circus of class experiments.
  • A more dramatic version of this demonstration, often called the ‘singing rod’, uses an aluminium rod as much as 2 m in length. See, for example, this video:

    Watch video


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

Up next

Standing waves with a variable wavelength

Standing Wave
Light, Sound and Waves

Standing waves with a variable wavelength

Practical Activity for 14-16

Demonstration

Three different experiments show standing waves having more than a single wavelength. To explain why each system behaves as it does, students need to understand both the factors affecting wave speed in a medium and also the relationship between wave speed and wavelength, for a given frequency.

Apparatus and Materials

  • Signal generator
  • Vibrator
  • Xenon stroboscope
  • 4mm leads
  • rubber cords of different thickness...
  • Rubber cord, 0.5 m long, 3 mm square cross-section
  • Light rubber cord, 0.5 m long (e.g. dressmaking elastic)
  • hanging chain...
  • Length of light chain
  • rubber strip of varying width...
  • V-shaped sheet of rubber, about 0.5 m long, maximum width about 0.1 m
  • G-clamp
  • Wooden blocks to crimp the wider end of the rubber sheet

Health & Safety and Technical Notes

Read our standard health & safety guidance


Rubber cords of different thickness: Tie the thick rubber cord to the thin elastic, and fix one of them to the vibrator. Since the wave velocity depends on the square root of the mass per unit length, an effective demonstration requires cords having a mass ratio of at least four. Good lighting is important.

Hanging chain: Chain sold for securing bath plugs is suitable. It is easiest to swing the top round in a small circle to generate a wave, but it will be clearer that a standing wave is involved if the top is oscillated sideways.

Rubber strip of varying width: Rubber cot sheet is a suitable material. Cut the sheet with a razor blade along previously marked lines, while it is being held down and lightly stretched. A piece 0.5m long, tapering from 100 mm to 10 mm, is about right. A line drawn down the middle helps to make the motion clear, especially as the edges of the strip tend to flap. Stroboscopic illumination along the length of the strip is very effective. Use as large an amplitude of oscillation as can be managed.

Safety note: Using the xenon stroboscope, teachers should be aware that frequencies around 7 Hz have been known to cause epileptic fits in certain people. Ask your students if any know that they are susceptible to this response.

Procedure

    rubber cords of different thickness...
  1. Adjust the frequency of the signal generator until you get standing waves of large amplitude.
  2. Questions for students to answer:
  3. "Do both cords vibrate with the same frequency?"
  4. "In which cord is the wavelength shorter?"
  5. "In which cord does the wave travel more slowly? How do you know? Explain why the wave travels more slowly in that cord.
  6. hanging chain..."
  7. Hold the chain at one end and generate a standing wave.
  8. Questions for students to answer:
  9. "Where is the wavelength large, and where small? Where is the curvature of the chain large and where small, i.e., where does it change direction quickly, and where is it more nearly straight?"
  10. "Where does the wave travel quickly, and where more slowly? How do you know?"
  11. "Explain why the wave speed varies."
  12. rubber strip of varying width....
  13. Clamp the V-shaped sheet of rubber at its wider end and vibrate it at its narrow end. Observe its motion carefully. Where, along the length of the sheet, is the wavelength longest and where is it shortest? Can you explain this pattern in terms of a variable wave speed?
  14. It is worth looking at the lowest frequency of vibration: the standing wave with one single loop, as shown below.
  15. The peak is not in the middle, but near the wide end. Near that end, the rubber curves more sharply than at the other, just as it would have to do if there were many short waves at that end and few longer ones at the other.

Teaching Notes

  • The first experiment shows that wavelength depends on thickness of cord.
  • The second experiment shows that wavelength depends on tension.
  • The top of the hanging chain carries more load than the bottom. Tension and hence velocity and wavelength are therefore greater at the top.
  • The third experiment shows that wavelength depends on the mass per unit length. Where waves travel slowly, on the more massive wide part, the wavelength is short. The wavelength increases slowly along the strip, being long at the narrow end where waves travel fast.
  • In every case, the velocity varies from place to place. The frequency is the same at all places, so the wavelength must vary from place to place. These are standing waves in which a wavelength, adjusted to the proper value for each place, must fit into a finite region.
  • The standing waves should be viewed stroboscopically, as well as by eye, to give students a clear understanding of their nature.

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

Up next

Demonstration or class experiment?

Demonstration or class experiment?

Teaching Guidance for 11-14 14-16

Physics, more than any other science, can be demonstrated principle after principle by direct and simple experiments. In some cases, it is clear that an experiment should be done either as a demonstration or as a class experiment. But many experiments can be done in either way, each having advantages and disadvantages.

Demonstration experiments can clarify a physical principle or show some interesting application of a principle. Make sure that students in the back row, as well as the front row, can see and hear what is going on. The best demonstration experiments avoid unnecessary detail – students can see and understand the whole working arrangement.

Other reasons for demonstrating experiments include safety reasons, and limited apparatus. Demonstrations can also be used as a part of a revision session or when you want to draw quick comparisons, e.g. looking at the behaviour of water waves and comparing that with light or sound. In a short lesson, there may simply not be time for students to carry out their own investigations, after they have set up and dismantled ripple tanks.

Class experiments give students direct experience of physical phenomena. Just as important, they allow students to practise being scientists: discussing, developing hypotheses, designing experiments, predicting outcomes and returning to fresh hypotheses and more experiments. They develop their powers of observation, thinking and problem-solving. Active learning follows the adage ‘hear and forget, see and remember, do and understand’.

Because some students work more quickly than others do, it is a good idea to give students a series of questions to pursue. With a selection of extra equipment set out cafeteria style, students can then proceed at their own pace. That way all remain engaged and faster students accomplish more.

Through class experiments, students can learn:

  • how to devise experiments
  • how to work on their own
  • how to make mistakes
  • how to solve practical problems
  • how to enjoy success
  • and they learn a little theory too.

Up next

Why experiment with waves?

Standing Wave
Light, Sound and Waves

Why experiment with waves?

Teaching Guidance for 14-16

A wide range of mechanical and electromagnetic waves become understandable with a limited number of concepts, e.g. interference.

Practical experience of waves builds familiarity with wave phenomena on which future experience can be based.

Wave phenomena provide many interesting demonstrations and experiments which students can enjoy doing themselves.

Students are able to do the experiments fairly safely, designing their own investigations, provided a supply of equipment is available, on a ‘cafeteria-like’ basis.

Many demonstrations require the development of skills for the effect to be clearly seen, and the acquisition of these skills is a pleasure in itself.

Photograph courtesy of Lucy Hollis

In one of his autobiographical essays, Richard Feynman recounts his experience of finding that degree-level students were unable to connect optics theory with optical effects seen outside the classroom window. Students have many opportunities to observe waves and ripples for themselves. This photo shows diffraction of ripples as they pass an obstruction in a pond.

Up next

Using wave simulations

Interference
Light Sound and Waves

Using wave simulations

Teaching Guidance for 14-16

There are many excellent applets available online that show wave behaviour as if observing a ripple tank or oscilloscope screen.

These cannot substitute for experience of the phenomena themselves but provide a powerful way of helping students to visualize. They provide a valuable complement to experiments by removing extraneous effects.

Up next

The usefulness of the standing wave idea

Standing Wave
Light Sound and Waves

The usefulness of the standing wave idea

Teaching Guidance for 14-16

Anything mechanical that can vibrate and has edges may have a standing wave on it. So the shaft driving a ship's propellers, or turning a turbine, can go into a standing wave oscillation, flexing as it turns. The wings of an aircraft also flex like a springy ruler.

Two-dimensional standing waves are likely wherever flat panels can vibrate, so they matter to the motor and to the building engineer. Three-dimensional standing waves are a problem for acoustic engineers. A good example is a loudspeaker cabinet enclosing a volume of vibrating air.

Electromagnetic waves too can produce standing waves. Radio waves can form standing waves inside metal cavities. Radio waves have been used both to make very accurate measurements of the velocity of the waves, and in the design of powerful high frequency generators of microwaves.

Up next

Standing waves and resonance

Standing Wave
Light Sound and Waves

Standing waves and resonance

Teaching Guidance for 14-16

Standing waves are an example of superposition. They occur when identical waves travelling in opposite directions.

In the diagram below, P and Q represent points along a rope. At the instant shown, two wave trains travelling in opposite directions are just about to overlap at point P. Points L1 to L4, R1 to R4 represent peaks or troughs along the wave train.

Formation of a standing wave

Superposition at point P causes P to oscillate with amplitude 2A, since peaks L1 and R1 arrive there simultaneously, followed half a cycle later by troughs L2 and R2, etc. Careful inspection shows that superposition at Q will result in Q remaining stationary in space all the time.

Standing waves in bounded systems

The edges of any solid object act as boundaries to waves. Superposition of waves travelling towards the boundary with those reflected from it can lead to standing waves, if the object is vibrated at an appropriate frequency (unless the vibrations are damped). In a similar way, standing waves can be set up in fluids if they are contained (air in a trumpet, water in the bath). The same ideas are used to explain the energy levels of atoms.

These more complex standing waves have the following features in common with waves on a string:

  • There is a series of definite modes of oscillation, corresponding to different frequencies, at each of which the response is large (resonance).
  • The patterns developed depend on the frequency, there being more nodes at higher frequencies.
  • The standing waves must fit into the system.

Up next

Some ideas for home experiments: waves

Standing Wave
Light Sound and Waves

Some ideas for home experiments: waves

Practical Activity for 14-16

Students generally enjoy devising their own investigations, using materials readily found at home. From time to time, this can be a good alternative to standard homework, especially when it leads to writing short reports or oral presentations. Home experiments give valuable practise with practical problem-solving and with conceptual thinking.

1 Standing waves in a rectangular tank

It is easy to excite water into a slopping mode, which is why it is hard to carry pans of water. Ask students what they can say about the Q (quality factor) of this system. It may be possible to excite other modes of oscillation using the plunger, for example, by moving it up and down in the middle of a large tank of water, and in other positions.

2 Standing waves under a running tap

Holding a knife-blade about 2 cm below a smoothly running tap, look for standing waves in the water flow. How does the pattern depend on the speed of water flow? On the separation of knife and tap?

3 Step waves under a running tap

Water flowing down from a tap onto a flat surface, such as the under-surface of a baking tray, shows a strange discontinuity: as the water flows away from the impact point, there is a step-like increase in its depth, at a distance r all round the impact point. Find out what factors affect r and try to explain this phenomenon.

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