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Wave Motion

  • G1-82: PENDULUM WAVES

    G1-82
    Create waves in a very dramatic way using a series of fifteen carefully adjusted independent pendula.
    After the pendula are started into oscillation with the same phase, they pass through a series of various standing wave and traveling wave patterns, finally returning to their initial mode, in which they were all in phase. This is a GREAT demonstration - takes about one minute.

  • G1-83: PENDULUM WAVES - COMMERCIAL VERSION

    G1-83
    Create waves in a very dramatic way using a series of carefully adjusted pendula of various lengths.
    This is a commercial version of our demonstration G1-82: Pendulum Waves. After the pendula are started into oscillation in phase, they pass through a series of various standing wave and traveling wave patterns, finally returning to their initial mode, in which they were all in phase.

  • G3-01 SHIVE WAVE MACHINE - TRAVELING WAVES

    G3-01
    Demonstrates traveling waves

    Make sinusoidal waves by moving the spines at one end of the machine up and down sinusoidally, either with your hand or using the wave generator. Vary the amplitude and the frequency and observe the wavelength. You can show semi-quantitatively that the wave speed is approximately the same for all frequencies.
    Background
    The Shive wave machine illustrates transverse waves - the direction of displacement is perpendicular to the direction of transmission. This can be used as a model of many wave phenomena.
    FS0

  • G3-02: SHIVE WAVE MACHINE - SUPERPOSITION OF PULSES

    G3-02
    Demonstrate constructive and destructive interference using pulses.

    Starting identical pulses from both ends simultaneously, either in or out of phase, they can be observed as they pass. For two identical pulses, move your hand rapidly down and up at the center of the machine with the two ends fixed. The two pulses created will reflect off the ends (left photograph) and interfere constructively as they cross each other on their return (right). Repeat this with one end clamped to get a phase reversal of the pulse which reflects off that end.
    Engagement Suggestion
    • This is a good opportunity to bring up one or two volunteers from the class to participate, rather than trying to reach both ends simultaneously yourself.
    • Encourage the class to predict what will happen when the pulses pass each other.
    Background
    In a linear medium like this, two waves moving in opposite directions can be seen to pass through each other. The principle of superposition states that when two mechanical waves pass each other in a medium, the net displacement at any point is the sum of the individual wave displacements.
    Ofc

  • G3-03: SHIVE WAVE MACHINE - REFLECTION OF PULSES

    G3-03
    Demonstrate reflection of pulses from fixed ends and free ends.

    A pulse generated at the left end (photograph at left) reflects off the right end. The reflecting end can either be fixed (clamped, center photograph) or free (right photograph).
    Engagement Suggestion
    • Encourage students to make a prediction before each combination as to whether the wave will reflect, and whether that reflection will be upright or inverted. • This can be combined with demonstration G3-05, showing that fixed and free end reflections are the extreme cases of partial reflections due to a change in impedance.
    Background
    Like any wave in a transmission medium, when the medium ends the energy in the wave has to go somewhere. The wave is reflected back from the end. With a free end, the wave reflects identically; with the end clamped, it reflects inverted.

    g3-03 g3-03a g3-03b

  • G3-04: SHIVE WAVE MACHINE - STANDING WAVES

    G3-04
    Demonstrate standing waves.

    Standing waves can be generated with either (1) both ends fixed, (2) one end fixed and one end free, or (3) both ends free. You can use either your hand or the motorized drive; your hand possesses better feedback for small adjustments in frequency.
    A metronome is available upon request for comparing the frequencies of various harmonics, or you can time them using the classroom clock or computer.
    Engagement Suggestion
    • Ask students to make predictions before each configuration of the device. Will fixed ends, free ends, or one open and one free end have the longest wavelength fundamental?
    Background
    A standing wave oscillates in time, but the peaks do not travel in space. A standing wave can be created in a mechanical medium of fixed length with an oscillation at that medium's natural frequency, or a multiple thereof.

    g3-04 g3-04b g3-04d

    g3-04a g3-04c g3-04e

  • G3-05: SHIVE WAVE MACHINE - PARTIAL REFLECTIONS

    G3-05
    Show that a wave will be partially reflected at a point where the impedance changes.

    The Shive Wave Machine illustrates transverse waves traveling down a torsional wire. Partial reflection can be produced by
    • • linking the two different segments as shown in the photograph,
    • • adding weights to the end of a central crossarm to produce an impedance glitch, or
    • • attaching the dashpot at a central location and adjusting it for partial absorption of the incoming wave.
    Background
    Changing the arm mass changes the impedance of the medium. This changes the transmission speed; and when a wave passes through the junction, it may be partially reflected. Like a reflection from a free or fixed end (G3-03), this partial reflection can also be upright or inverted. Passing from higher to lower impedance gives an upright partial reflection; passing from lower to higher impedance gives an inverted partial reflection.

  • G3-06: SHIVE WAVE MACHINE - IMPEDANCE MATCHING

    G3-06
    Show that no reflection occurs when the impedance of the load (absorber at right) matches the impedance of the wave machine.
    Adjust the impedance of the absorb-o-matic to eliminate any partial reflection of the incoming wave. The impedance of the absorb-o-matic can be changed by adjusting the string tension.

  • G3-07: SHIVE WAVE MACHINE - TAPERED TRANSFORMER

    G3-07
    Useful for obtaining a reasonably good impedance match between the two large segments of the Shive machine.
    Connect the tapered transformer between the two large wave machine segments. Inserting this reduces the impedance mismatch and allows a continuous sine wave to pass from one medium into the other with minimal reflection, as seen in the photograph at the left. At the right is a close-up of the tapered transformer.

  • G3-08: SHIVE WAVE MACHINE - FABREY-PEROT INTERFEROMETER

    G3-08
    Demonstrate the mechanical analog of the optical Fabrey-Perot interferometer.
    Pairs of small weights are connected to two arms six inches apart in the center of the machine. The dashpot is attached to the end of the machine opposite the wave generator to prevent reflections (It must be adjusted.). Measure the difference in amplitude of the transmitted wave by measuring the amplitude of the oscillation of the dashpot, and compare that with the amplitude of the incoming wave as measured by the amplitude of the generator. The maximum transmitted wave occurs when the reflected wave is minimized, that is, when the two arms with the weights are one-quarter wavelength apart.

  • G3-09: SHIVE WAVE MACHINE - FREQUENCY FILTERING

    G3-09
    Demonstrate frequency filtering through a "filter" consisting of four weighted crossarms and the interference from partial reflections they produce.
    Four sets of weighted small weights are positioned on crossarms at equal intervals along the Shive machine, with the generator at one end and the dashpot at the other end. When the frequency of the generator is adjusted so that the wavelength is twice the spacing of the weights the reflected wave will be minimized and the transmitted wave maximized.

  • G3-10: SHIVE WAVE MACHINE - BRANCHING

    G3-10
    Demonstrate branching and recombining with two wave machines in parallel.
    This is the mechanical equivalent of the Quincke tube interference demonstration for sound (H2-25) or of a parallel LC circuit. At the first connecting point the amplitude and phase are directly coupled (i. e., the same) and waves continue down both machines. Due to the different wave velocities in the two machines, when the transmitted waves arrive at the second coupling they may be out of phase. If they arrive 180 degrees out of phase a node is created and no further energy is transmitted. In analogy with pinching one of the Quincke's tubes, one of the connectors can be removed to allow energy to pass. Crossarm weights are used to counterbalance the alligator crossarm connectors.

  • G3-11: SHIVE WAVE MACHINE - RESONANCE ABSORPTION

    G3-11
    Demonstrate resonance absorption of wave energy by a mass-on-spring system.
    Sending a wave along the machine drives the spring-mass attached to one of the crossarms. The greatest effect will be at the resonant frequency for the mass on the spring. A well chosen driving frequency will result in almost complete absorption of the wave.

  • G3-20: WAVE APPARATUS

    G3-20
    Demonstrate transverse and longitudinal wave motion.
    A number of eccentric disks support a series of metal rods, and when the handle is turned, transverse waves are created. Longitudinal waves are obtained with bent rods running in a metal guide on a metal base. Turn the handle gently. Too hard and the rods might bend.
    G3

  • G3-21 TRANSVERSE WAVES ON A LONG SPRING

    G3-21
    Demonstrates traveling waves

    Clamp the spring to the lecture table and then step back. When you hold the other end with some tension and shake the end with various frequencies, you can illustrate transverse waves traveling along the spring.

    You can move your hand to generate a pulse or wave in the spring. Because of the clamp, the spring acts as a medium with one free end and one fixed end. By changing how far and how fast you move your hand, I can generate different amplitudes and frequencies. If you move my hand farther on each swing, you create a wave with a greater amplitude – the height of each peak is greater. If you move your hand up and down faster, you create a wave with a greater frequency – the number of peaks within a given length is greater.

    With practice, you can also find the natural frequency of the spring and set up standing waves.
    Engagement Suggestion
    • Ask students: “Now that we’ve seen some features of transverse waves, let’s try an experiment. I’m going to send a single upright pulse down the spring. What will happen when it reaches the fixed end? Will it stop entirely, bounce back in the same shape, or bounce back upside-down?”
    • “The pulse returns upside-down!”
    Background
    A transverse wave is one where the direction of oscillation is perpendicular to the direction of propagation. The up-and-down motion of the spring that forms each pulse is at a right angle to the forward movement of the wave. When a transverse pulse reflects off a fixed end, it returns inverted. If instead it had reflected off an open end, it would return upright. We can see this most easily with a single pulse, but this is true of a repeating waveform as well. We see mechanical transverse waves in springs, ropes, and other objects routinely. But another type of transverse wave surrounds us all the time – electromagnetic waves, like light, are transverse waves.
    G3

  • G3-23: TRANSVERSE WAVES ON A LONG SPRING - FREE END

    G3-23
    Show reflections at a free end.
    A string holds one end of the long tight spring to the clamp on the lecture table. Because the string is long, and light compared to the spring, this forms a free end for the spring, allowing the end of the spring moves when a wave approaches.
    G3

  • G3-24: SLINKY ON LECTURE TABLE - TRAVELING WAVES

    G3-24
    Show travelling waves.
    One end of the SLINKY is taped to the lecture table while theother end is free to move for creating waves. For best waves do not overextend the SLINKY.
    G3

  • G3-25: SLINKY ON LECTURE TABLE - IMPEDANCE MISMATCH

    G3-25
    Show partial reflections and dependence of wave speed on density of the medium.
    A string (running inside the SLINKY) connects one end of a SLINKY with a point about 3/4 of the way from that end, with the end taped to one end of the lecture table. When the SLINKY is extended it has regions with two different densities, causing two different wave speeds. A wave started at the free end of the SLINKY (right side in photographs above) will experience an impedance change; it may produce (quickly attenuated) partial reflections at the boundary. The wave moves more slowly in the section at the left, as seen in the photograph at the right.
    G3

    g3-25a

  • G3-26: AIR TRACK - LONGITUDINAL WAVES

    G3-26
    Demonstrate longitudinal waves with a series of spring-coupled air track gliders.
    Several identical gliders are connected by springs, with the two end gliders fixed or attached by springs to the ends of the air track. Longitudinal waves can be created which reflect off the (fixed) ends, and standing waves can be created in the system.

  • G3-27: AIR TABLE - TRANSVERSE AND LONGITUDINAL WAVES

    G3-27
    Demonstrate transverse and longitudinal waves using an air table.
    Identical pucks are attached by light springs diagonally across the air table. Either transverse or longitudinal waves can be created by hand in this system.