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Wave Motion

  • H2-55: BEATS AND RESONANCE - TUNING BOXES

    H2-55
    Illustrate beats and resonance.
    Adding a small clamp onto one of the tuning bars reduces its frequency. Striking two tuning bars, one with a weight, then produces beats. The frequency of the beats can be adjusted by varying the position of the weight on the bar.
    Without weights on either bar, strike one of the tuning bars, then hold the other adjacent to the struck bar for a few seconds. If the struck bar is then damped, the sound continues. The second bar is in resonance with the struck bar, and some energy is transferred if they are physically near each other.
    This demonstration is similar to demonstration H2-52, except for use of open tuning boxes for resonance. It is a bit louder for use in the lecture halls, but perhaps a bit harder to explain because of the resonant boxes.
    h2

  • H3-01: STANDING SOUND WAVES - TWO SOURCES

    H3-01
    Demonstrate the origin of standing waves from two identical sources.
    Both speakers are driven by the same 3000 Hz sine wave from the audio oscillator, which is shown on the top trace of the oscilloscope. The standing wave pattern, observed by sliding a microphone along the optical rail between the speakers, is displayed on the lower trace.

    Consider showing both this and H3-02, and invite students to speculate about the differences.

  • H3-02: STANDING SOUND WAVES - REFLECTION

    H3-02
    Demonstrate the origin of standing waves from one source and its reflection.
    A loudspeaker is driven at about 3000 Hz by a sine wave oscillation which is displayed on the top trace of the oscilloscope. The standing wave pattern, created by the sound from the speaker and the wave reflected off the flat metal plate, is picked up by a microphone sliding along the optical rail and displayed on the lower trace of the oscilloscope.

    Consider showing both this and H3-01, and invite students to speculate about the differences.

  • H3-03: REFLECTION OF PULSES IN TUBE

    H3-03
    Demonstrate the phase of pulses reflected from open ends and closed ends of a tube.
    A pulse is created by the leading edge of a low-frequency square wave input into a loudspeaker at one end of a long, rigid plastic tube. This pulse travels along the tube and is reflected back and forth at the ends. The phase of the pulse as it reflects back and forth is observed using a microphone inserted into the center of the tube. Several reflections can be observed. It is easy to see the difference between reflection at the open end and reflection at a closed end, obtained by placing a metal plate against the end of the tube opposite the loudspeaker.
    H2, ME2, ME3, OM1, OS0

    h3-03b

  • H3-04: KUNDT'S TUBE - STROKED ROD

    H3-04
    Demonstrate standing waves in an air column.
    This is the classical Kundt's tube standing wave apparatus. A rag covered with violin rosin is used to stroke an aluminum rod which excites standing waves in the air tube. Cork dust in the tube is agitated by the standing wave and deposited on the bottom of the tube such that it shows the basic form of the pattern of air motion. For this system the wavelength is about 11 cm, or one loop about 5.5 cm.

    Note: The modern, oscillator-driven version of this experiment, H3-05, is a more effective demonstration of standing waves for classroom use. We recommend using it primarily, with this traditional version alongside to illustrate the geometry of the original experiment.
    OS5

  • H3-05: KUNDT'S TUBE - OSCILLATOR DRIVEN

    H3-05
    Demonstrate standing waves in an air column.
    An oscillator in the 1000-5000 Hz frequency range drives a loudspeaker at one end of a clear glass tube, with the other end stopped by a moveable plunger. Varying the frequency of the oscillator or the position of the plunger, one can obtain a series of standing wave patterns, which are made visual by the motion of cork dust in the bottom of the tube. The standing wave pattern is shown to large groups by placing the device on an overhead projector. This is a very dramatic demonstration, and is very effective in providing an introduction to standing sound waves. Examples of standing waves as seen using the overhead projector are shown below.

    Be aware that the tube is glass, and must be handled carefully.
    H2, ME3

    h3-05ah3-05b

  • H3-11: TUNING FORKS AND RESONANT TUBE

    H3-11
    Illustrate resonance in an air column.

    This demonstration includes a clear plastic tube and two tuning forks, of slightly different frequencies.

    Strike either tuning fork and hold it to the end of the tube. The sound intensity of the fork at the resonant frequency (480Hz) of the tube increases dramatically, as the second harmonic of the tube is excited; whereas the fork with the non-resonant frequency (384Hz) does not become significantly louder.

    Background

    This illustrates the principle of resonance. One tuning fork's frequency is a multiple of the natural frequency of the air column in the tube, while the other is not.
    H3

  • H3-12: ROARING TUBE - 4 FT

    H3-12
    Demonstrate standing sound waves in air excited by convection currents.
    A switch is held closed, activating a nichrome wire coil in a vertical glass tube, leading to a very loud roar at about 130 Hz, the fundamental frequency of a four-foot air tube. This is the classic Rijke tube demonstration with an electrical heater replacing a gas burner and screen as the source of the convection currents.

    Consider combing this with H3-13, and invite students to make predictions about the differences in pitch and volume.
    FS1

  • H3-13: ROARING TUBE - 8 FT

    H3-13
    Demonstrate standing sound waves in air excited by convection currents.
    A switch is held closed, heating a nichrome wire coil in a vertical four-inch diameter galvanized steel downspout tube, leading to a very loud roar at about 65 Hz, the fundamental frequency of an eight-foot air tube. This is the classic Rijke tube demonstration with an electrical heater replacing a gas burner and screen as the source of the convection currents.

    Consider combing this with H3-12, and invite students to make predictions about the differences in pitch and volume.

    h3-13coilh3-13drawing

  • H3-14 TWIRL-A-TUNE

    H3-14
    Demonstrates standing wave resonances in an open tube
    This popular toy is available in many stores and students may have seen it before, but this is an opportunity for them to explore how it works. To produce resonant frequencies of the tube, hold the tube by one end, keeping that end free for flow of air, and swing it around your head. Increasing the speed of the rotation raises the harmonic produced. Up to seven harmonics can be produced, illustrating the notes of the overtone series. The fundamental can only be produced by blowing gently into one end. SUGGESTIONS: Read Invited talk : Sounds Like Fun, presented by Paul Doherty of the Exploratorium at the 2004 meeting of the AAPT at Sacramento, CA, discussing how the twirl-a-tune works.
    H3

  • H3-15: TWIRL-A-TUNE AND VACUUM CLEANER

    H3-15
    Demonstrate standing wave resonances in an open tube.
    To produce resonant frequencies of the tube, hold the end with the cork up to the input of the vacuum cleaner. As you cover the vacuum input more and more with the cork, more air will be pulled through the Twirl-a-Tune, exciting higher harmonics. Up to around 16 harmonics can be obtained.

    Note that this demonstration is very loud, and should not be used for very long or in a small, enclosed space. For smaller classes or for extended analysis and discussion, consider other demonstrations from this section.
    OS1

  • H3-16: SINGING PIPES

    H3-16
    Show sound resonance created by convection currents in a tube.
    A gas flame is inserted into one end of the tube, heating the wire mesh which has been pre-positioned in the lower half of the tube using the plunger. Holding the tube vertical after the mesh has been heated red hot creates convection currents which enable the tube to resonate. Tilting the tube nearly horizontal limits the convection currents and the sound ceases.

    This can be an exciting demonstration, but requires careful handling for safety. Also consider H3-12 and H3-13.

  • H3-17 FLAME TUBE

    H3-17
    Demonstrates standing waves in a tube
    A loudspeaker in one end of a four-inch diameter galvanized iron tube creates standing waves in propane gas in the tube. The gas emerges out of a series of small holes in the top of the tube, forming a long line of flames when lit. Any sound resonant with the length of the tube can create standing waves in the gas which are readily visible as a pattern in the height of the flames. Both rhythm and frequency response can be seen nicely in music. An oscillator and a cassette deck are provided with the demonstration to be used as simple sources for the loudspeaker. Or, a voice or other music or audio can introduced using a microphone and amplifier or external input jacks, available upon request.
    FS1

  • H3-21: SOUND RESONANCE IN WATER TUBE

    H3-21
    Demonstrate standing waves in a closed tube.
    A tuning fork mounted over the top of the tube is activated by striking it with a rubber hammer. Raising and lowering the reservoir varies the water level in the tube to change the length of the air column. Because the air column is closed on one end (the surface of the water) resonances occur when the length of the tube is approximately 1/4, 3/4 or 5/4 of a wavelength, neglecting the end correction at the top of the tube. Using this apparatus standing waves can be demonstrated and the speed of sound determined to within about one percent.

    h3-21a

  • H3-24 OPEN AND CLOSED PIPES

    H3-24
    Demonstrates open and closed tube standing resonances
    Blow across the open end of the open and closed tubes. The frequency of the closed tube is approximately half that of the open tube, or about one octave lower. (Actually, due to the end correction, which applies to the open end of the closed tube but both ends of the open tube, the frequency ratio is slightly less than one octave to the trained musical ear.)

    For comparison, a half-length tube is also available. Invite students to predict how this one will compare to the open and closed tubes of twice its length
    H3

  • H3-61 BEAKER BREAKER

    H3-61
    Breaks a glass beaker with sound

    An audio oscillator and 100 Watt power amplifier are used to drive a heavy-duty horn driver which is mounted in the back of the plastic beaker cavity with the sound emerging through a hole, which can be seen in the photograph. The beaker is positioned on a foam pedestal in front of the speaker hole. A microphone is mounted at 90 degrees from the position of the speaker.

    The beaker is marked with its primary resonant frequency, found in advance using digital spectrum analysis of a recording of the beaker ringing after being tapped. Most beakers have two possible resonant modes 45 degrees apart, due to the weight of the spout; the most effective technique is to drive the resonance with the spout facing directly away from the speaker. Set the frequency of the oscillator as shown on the beaker, with an amplitude of around 140mVpp. The oscilloscope will show two waveforms, the input signal and the signal picked up by the microphone. You may need to adjust the frequency slightly to account for changes in temperature or age since the beaker was tested; slowly shift the frequency by tenths or hundredths of a Hertz to find the amplitude peak (do not try to tune by watching for a displacement in the phase relationship, as there is a time delay between the signals introduced by the hardware). This done, set the strobe around 3000 cycles per minute, and adjust it until you can see the sides of the beaker flexing.

    This can be used to show the resonance of the beaker. You can also, optionally, shatter it, by increasing the input voltage at resonance. Be careful not to exceed 1Vpp.

    After the resonant frequency is found and the amplitude turned up, the oscillation of the beaker can be caused to exceed its elastic limit and thus to shatter. See the video links below to view a slow-motion video of the beaker at the moment it breaks.

    Engagement Suggestion
    • Show the students that there are two different resonant frequencies, and challenge them to develop theories of why this is.
    • Consider using this in conjunction with H3-62 to illustrate the effects of the beaker's spout in a more obvious (and quieter) manner.
    Background
    This process of driven resonance potentially leading to mechanical failure can be related to many engineering problems. This is an excellent opportunity to discuss how physics applies to real-world problems, like the Tacoma Narrows Bridge collapse.
    Also, be sure to explore our directory of oscillations and waves simulations to show other examples of complex mechanical oscillations.
    FS1, LS2, SU5

  • H3-62: TEACUP STANDING WAVES

    H3-62
    Demonstrate circular standing waves in an interesting way.
    A teacup can be tapped with a spoon to excite standing waves around its rim, exactly like the standing waves in a glass beaker. The standing wave consists of four alternating nodes and antinodes spaced at 90 degrees around the teacup. If the handle is at an antinode, the resonant frequency is lower than if the handle is at a nodal point, because the vibrating mass is greater but the restoring force is the same. Tap the rim of the teacup moving around the rim at intervals of 45 degrees to get alternating higher and lower frequencies This can be used in conjunction with H3-61 to illustrate the effects of the beaker's spout.
    H3

  • H3-71 STROKED ALUMINUM ROD

    H3-71
    Illustrates longitudinal standing waves in an aluminum rod.
    Apply powdered violin rosin to your fingers or wear a rosined glove and stroke the aluminum rod firmly while holding it at a nodal point. Holding it in the center produces the fundamental, holding at 1/4 of the way from one end produces the second harmonic, holding at 1/6 of the way from one end produces the third harmonic, etc. The rod is about 6 ft long, and the speed of sound in aluminum is about 16,700 ft/sec, so the frequency of the fundamental is about 1400 Hz. The sound is very loud and lasts a long time; the Q for this system is around 100,000!
    Alternatively, request an (optional) mallet to use with the rod. Use the mallet to strike the rod on one end; by holding the rod at a node or antinode, all or some modes can be excited or damped.

  • H3-72: TUNING RODS

    H3-72
    Hear longitudinal standing wave resonances in aluminum rods.
    Hold the tuning rod by the center fixture and strike it longitudinally on its end with a rubber mallet to excite the standing wave. The three rods pictured are calibrated: 5000 Hz, 10,000 Hz, and 15,000 Hz.

  • H3-74: TUNING BAR PARADOX - EFFECT OF WIDTH

    H3-74
    Illustrate transverse vibrations of a solid bar struck in the center.
    When struck on top center with a rubber mallet, like a xylophone or marimba, the narrower bar on the right in the photograph above vibrates with a frequency f.

    Q: Will the frequency of the larger bar on the left, which has the same length and thickness as the smaller bar, but twice the width, be greater than, less than, or the same as the frequency of the smaller bar?

    A: The frequency will be the same for transverse vibrations

    H3