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3 - Oscillations and Waves

Oscillations
Wave Motion
Acoustics
Instruments
Sound Reproduction

3A - Oscillations

3A10 - Pendula

Simple Pendulum (3A10.10)
A single simple pendulum with a length of 1 meter.

Simple Pendulums of Various Lengths and Masses (3A10.14)
Simple pendulums with differing lengths (1 m or 0.25 m) and/or differing masses (wood or metal). For comparing the mass and length to the period.

Inverted Pendulum (3A10.20)
A vertical bar with a sliding weight is clamped at the bottom and free to oscillate at the top. The period of oscillation depends upon the position of the weight.

Metronome as a Pendulum (3A10.21)
A metronome is used as an adjustable pendulum.

Torsion Pendulum (3A10.30)
A heavy disc at the end of a limber vertical rod can be set into torsional oscillation. Mass can be added to the disc to show the effect on the period of oscillation.

Variable Angle (Variable g) Pendulum (3A10.40)
A physical pendulum is mounted on a bearing so the angle of the plane of oscillation can be changed.

3A15 - Physical Pendula

Physical Pendulum (3A15.20)
Compare the period of a bar supported at the end with a simple pendulum that is 2/3 the length of the bar.

Hoops and Arcs (3A15.40)
A full circular hoop and portions of a hoop of the same diameter pivot from a hole at the center of the periphery of each. Though they vary greatly in size, each will swing on the pivot with the same frequency of oscillation.

Kater Pendulum (3A15.70)
A pendulum used for a highly precise measurement of g. Analysis requires moments of inertia, for which we have no precise data.

3A20 - Springs and Oscillators

Oscillating Mass on a Spring (3A20.10)
A mass is hung on a spring mounted in front of the blackboard, then pulled down and released to show simple harmonic motion.

Air Track - Oscillating Glider (3A20.35)
A single air track glider of variable mass oscillates between two springs.

Water in U-Tube (3A20.55)
Colored water oscillates between two legs of a glass U-tube. Motion can be frozen at any point by corking one leg of the tube.

Ball in Plastic Bowl (3A20.60)
A rubber ball rolls in a large hemispherical plastic bowl.

3A40 - Simple Harmonic Motion

Circular vs. Simple Harmonic Motion (Spring) (3A40.10)
The shadow of a pin moving uniformly around a circle in the vertical plane is superimposed over that of an oscillating spring and weight. The shadows of the pin and the weight are synchronized so that the shadows move in unison on the screen.

Circular vs. Simple Harmonic Motion (Pendulum) (3A40.20)
The shadow of a pin moving uniformly around a circle in the horizontal plane is superimposed over that of a swinging pendulum. The shadows of the rotating pin and pendulum are synchronized so that the shadows move in unison on the screen.

Tuning Fork with Light (3A40.41)
Tuning Fork with Light (3A40.41) -- a large tuning fork with a low frequency has a small light bulb on one tine. The tuning fork is set into vertical oscillation and then moved horizontally in a dark room. The light bulb traces out a sine curve.

Phase Shift (3A40.65)
A vertical disc has two balls mounted at its edge which may be moved to different angular positions. As the disc is rotated, the balls are shadow projected so that their circular motion appears as SHM. By moving the balls to different relative positions on the disc (in multiples of 45 degrees), their motion on the screen will be 90 degrees out of phase, 135 degrees out of phase, etc.

3A50 - Damped Oscillators

Water Damped Spring and Weight (3A50.10)
A weight on the end of a hand held spring is set oscillating in a water column and quickly damps out.

3A60 - Driven Mechanical Resonance

Tacoma Narrows Bridge Collapse (3A60.10)
A film showing the collapse of the original Tacoma Narrows Bridge due to resonance. Also available at archive.org

Resonant Driven Pendula (3A60.31)
Three simple pendula of different lengths are hung from a horizontal bar with an attached driver pendulum. The driver pendulum is a stiff rod with an adjustable bob so that its frequency can be changed. The driver pendulum is set to the natural frequency of each pendulum in turn, and only that one pendulum oscillates.

Bowling Ball Pendulum and Hammer (3A60.35)
A heavy bowling ball hangs from the ceiling on a long cord. A rubber mallet is used to strike the ball and build up oscilations. If the striking frequency equals the natural frequency of the pendulum, the oscillations build up to large amplitudes.

Driven Spring and Weight (3A60.43)
A mass on a spring is driven at an adjustable frequency. Damping the motion in a cylinder of water shows a small shift in the resonant frequency of the oscillator.

Driven Spring and Weight with Display (3A60.43)
A newer version of the above demo (Driven Spring and Weight) but also has a marker for increased visibility.

Reed Tachometer (3A60.50)
A set of metal reeds of descending natural frequencies is attached to a gyroscope. The gyroscope is slightly off balance so that it vibrates as it spins, and as its rotational frequency passes through the frequencies of the reeds each reed vibrates in turn.

3A70 - Coupled Oscillations

Wilberforce Pendulum (3A70.10)
A spring with a weight which has a natural rotational frequency equal to its vertical oscillation frequency. Start the weight oscillating, and energy will transfer back and forth between the rotational and translational modes. Large bright dots on the weight improve visibility.

Spontaneous Synchronization in Metronomes (3A70.23)
Five small metronomes on a lightweight board are set to the same frequency and started oscillating out of phase. At first the board sits on the table and the metronomes will oscillate independently. The board is then placed on two empty aluminum cans (on their sides) to provide some light coupling between the metronomes. The metronomes will phase lock with each other within a minute or two and their 'tick-tocks' will all be in unison.

Coupled Pendula (3A70.25)
Two identical massive bobs at the ends of two pendulum rods are coupled by a spring and set swinging. Alternately each one stops oscillating as its energy is transferred to the other, then begins swinging again as the energy is transferred back. Different springs change the amount of coupling and the time required for total energy transfer.

3A75 - Normal Modes

Air Track - Multiple Coupled Gliders (3A75.10)
Two or three gliders are hooked together with springs to form a coupled oscillator system. Different modes of oscillation may be set up easily by hand.

Air Track - Two Gliders with Spring Steel
Two gliders are attached with a long piece of spring steel. With the air track turned off, the gliders are brought close together (compressing the spring) and the gliders are tied with a loop of string. When the string is burned, the gliders oscillate about the midpoint of the spring steel. Can also be set in motion before burning the string.

Phonon Modes (Periodic Boundary Conditions)
The Pasco Longitudinal Wave Model (3B20.30) is driven by a mechanical oscillator to set up standing waves. The two rods on the ends are rigidly connected to the driver while the other rods are coupled together by springs. Cutoff frequency: ~6.4 Hz.

3A80 - Lissajous Figures

Lissajous Patterns (3A80.20)
Two audio oscillators, one connected to the vertical input of a large oscilloscope and the other to the horizontal input. A change of pattern is observed with a change in amplitude, frequency ratio, or phase.

3A95 - Non-Linear Systems

Lockable Double Pendulum
A chaotic double pendulum that has a locking bolt to turn it into a simple nonchaotic physical pendulum.

Periodic but not SHM (3A95.38)
A pendulum with a massive bob at the end has a long limber wire projecting out of the top. The pendulum exhibits simple harmonic motion, but the wire is constrained by a loop encircling it and exhibits periodic but non-simple harmonic motion.

Pump Pendulum (3A95.70)
A pendulum swings on the end of a string which passes over a pulley. If the string is pulled to lift the weight at the right frequency and phase, the amplitude of the pendulum gradually increases.

3B - Wave Motion

3B10 - Transverse Pulses and Waves

Wave on a Rope (3B10.10)
A long rope is attached to the wall. Shake the loose end to show a travelling transverse wave.

Tension Dependence of Wave Speed (3B10.15)
Waves plucked on a length of stretched rubber tubing shows a strong dependence on tension.

Spring on Table (3B10.20)
A long brass spring is stretched out on the lecture table and shaken at one end. Transverse waves of large amplitude and low velocity will propagate along the spring. The far end can be fixed or free.

Pulse on a Moving Chain (3B10.26)
A chain loop is hung loosely across two wheels, one free and one motor driven. Motor speed and chain tension can be adjusted so that a pulse wave produced by a sharp blow from a stick will propagate at the same speed as the chain motion and thus appear motionless. Practice to avoid knocking the chain off with too heavy a blow.

Transverse Waves (Bell Labs Wave Machine) (3B10.30)
Rods are arranged like ribs along a square wire "spine." A torsional wave can be sent down the spine by sharply displacing the tip of the first rod. As the wave propagates along the spine, each rod is tipped in turn by the passage of the wave, and the displacement of the ends of the rods is visible to the class, appearing as a transverse wave (visibility can be increased by illuminating the fluorescent tips of the rods with UV).

3B20 - Longitudinal Pulses and Waves

Longitudinal Waves (Hanging Slinky) (3B20.10)
Longitudinal waves propagate slowly on a large plastic slinky suspended horizontally. The slinky is hand driven and can be used to show single pulses or standing waves. Paper markers hang on the coils to increase visibility of compression and rarefaction. The far end can be free or fixed. Note: This is on the same setup as Transverse Waves (Bell Labs Wave Machine) (3B10.30).

Pasco Longitudinal Wave Model (3B20.30)
The Pasco Longitudinal Wave Model is a series of vertical rods, the pivot at their centers, and are connected by springs.

3B22 - Standing Waves

Standing Transverse Waves (Driven Waves in Rubber Tubing) (3B22.10)
A long piece of rubber tubing is stretched out horizontally and run over a pulley at one end, then tensioned with a hanging weight. At the other end a revolving bar strikes the tubing at a frequency which can be adjusted with a motor speed controller. Transverse waves of various frequency can thus be sent along the tubing, and when the right frequencies are reached the tubing vibrates in various standing wave modes. 1 kg and 0.25 kg masses can be used to vary the tension.

Standing Waves in Hanging Slinky (3B22.50)
Drive a hanging slinky by hand to produce standing longitudinal waves.

Standing Longitudinal Waves and Ultrasonic Levitation (3B22.60)
A 28 kHz ultrasonic transducer with an adjustable reflector plate. The plate can be positioned to produce a standing wave pattern with enough pressure to levitate styrofoam beads. Visible with the Schlieren Optics System (6A40.60)

Standing Wave Model (3B22.90)
A sine wave is drawn on a loop of acetate that moves between two rollers. The students see two sine waves, one moving to the left and one to the right at the same velocity. At some points (nodes) the amplitudes of the two waves will always be equal and opposite, so they cancel. At points in between (antinodes), the two waves will always be moving together, so they will reinforce at those points to create greater amplitudes. A grid can be inserted that marks the nodes and antinodes for easy viewing.

3B25 - Impedance and Dispersion

Bell Labs Machine - Impedance Matching (3B25.10)
The long and short rod sections of the wave machine can either be connected abruptly (unmatched coupling) or with a section of gradually lengthening rods (matched coupling).

Bell Labs Wave Machine - Reflection (3B25.20)
The Bell Labs Wave Machine with the end fixed, damped, or free to show the affect on the reflected wave.

Spring on Table Reflection (3B25.25)
Reflections in a long horizontal brass spring (3B10.20) with fixed and free ends.

Acoustic Coupling with a Speaker (3B25.35)
A small speaker has a coupling horn which may be removed. With the horn on, the sound is much louder than with the horn off.

3B27 - Compound Waves

Bell Labs Wave Machine - Superposition (3B27.15)
Start positive pulses from each end of the Bell Labs Wave Machine.

3B30 - Wave Properties of Sound

Phonodeik
Status: Unavailable
Shows the deflection of a light beam which is reflected from a delicate mirror on the diaphragm of a mechanical microphone during oscillation. An "oscilloscope" from the pre-electronic era of candle flames, levers, and ingenuity. Note: For show and tell only right now.

Light and Siren in Vacuum (3B30.3)
A buzzer and a LED are mounted inside a bell jar. The air is then evacuated from the jar, and although the LED can still be seen, no sound can be heard from the siren. Also listed as 6A02.10.

Sound in Helium (3B30.50)
Helium can be blown through a variety of resonant music makers to demonstrate the higher notes that are created with a lower density gas. Choices include organ pipes, a jug or ocarina instrument, and (most popular) an inhaled lungful by the instructor.

3B40 - Doppler Effect

Doppler Effect (3B40.10)
The pitch from a siren rises and falls as it is swung around overhead.

Doppler Reed (3B40.25)
A reed mounted on the end of a rotating arm produces a tone whose pitch wobbles up and down as the arm rotates.

3B50 - Interference and Diffraction

Ripple Tank - Single Slit Diffraction (3B50.10)
Diffraction from plane waves passing through a single slit.

Ripple Tank - Double Source Interference (3B50.20)
Two point sources in phase show interference.

Ripple Tank - Double Slit Interference (3B50.25)
Interference from plane waves passing through two slits.

Ripple Tank - Multiple Slits
Plane waves passing through multiple slits.

Moire Pattern (3B50.40)
Two identical patterns of concentric circles are superimposed on an overhead projector or under the document camera. The separation between their centers changes by sliding one across the other and prodcues interference patterns.

3B55 - Interference and Diffraction of Sound

Two Speaker Interference (3B55.10)
Two speakers driven from a common source are mounted at the ends of a long horizontal bar. The bar can be rotated to sweep the nodes and antinodes through the class.

Acoustical Interferometer (Quincke's Tube) (3B55.40)
A function generator drives a speaker that is connected to two U shaped tubes, one of which has a variable length. The two tubes recombine and a microphone and oscilloscope show how the amplitude changes with the path length difference.

3B60 - Beats

Beats from Tuning Forks (3B60.11)
Two matched tuning forks are used, one of which has an adjustable weight on one tine. By adjusting the weight, the forks can be set to either equal frequencies or slightly different frequencies to produce beats.

Beats from Organ Pipes (3B60.13)
Two large metal pipes mounted vertically on the lecture table will resonate at low frequencies when a source of "white noise" (a Fisher burner) is placed at the bottom end. If both pipes are excited they will produce beats.

Beats from Singing Glass Tubes (3B60.16)
Two small glass Rijke tubes (3D30.70) have electrically heated wire grids and moveable tubes. Move a tube so that the grid is at the 1/4 point and the tube will "sing." Put it anywhere else, and it won’t. Since the tubes are slightly different lengths, running them both together produces beats.

Beats from Two Speakers
Two speakers with separate audio oscillators produce beats.

Beats on Oscilloscope (3B60.20)
Status: Unavailable
The outputs of two function generators are mixed and fed into an amplifier, then the amplifier output is fed into a speaker as well as an oscilloscope. Note: Needs work right now.

3B70 - Coupled Resonators

Coupled Tuning Forks (Sympathetic Vibrations) (3B70.10)
Two matched tuning forks are mounted on resonance boxes. Hit one and the other vibrates too.

Ames Tube Resonating Cavity
A hollow metal cavity is made to resonate with a tuning fork. Can also show sympathetic vibration, beat phenomena, and mechanical coupling.

3C - Acoustics

3C10 - The Ear

Model of the Ear (3C10.10)
A model of the human ear.

3C20 - Pitch

Range of Hearing (3C20.10)
An audio oscillator, speaker, and an oscilloscope. Sweep the frequency up and down, announcing the value as the class gets a feel for the audible range and the relationship between frequency and pitch. Can also display subsonic and ultrasonic frequencies that cannot be heard.

Galton Whistle (3C20.15)
A small ultrasonic whistle produces high intensity sounds at frequencies that are essentially inaudible to humans.

Siren Disc (3C20.30)
A disc with eight rings of uniformly spaced holes and a ninth ring of randomly spaced holes. The disc is spun by a motor and an air jet is directed at the holes. Puffs of air through the disc as a hole passes the air jet produce pressure variations, and thus sound. Different musical notes are heard from different rings of regularly spaced holes but noise is heard from the ring of randomly spaced holes.

Gear with Vibrating Card (3C20.40)
Similar to a playing card in the spokes of a bike wheel. Rotation of the gear can be varied to produce everything from a rapid clicking (under 20 Hz) to full-fledged sounds.

3C30 - Intensity and Attenuation

Decibel Meter (3C30.22)
A sound level meter with output measured in decibels. Try it with your voice, a buzzer, or various instruments. Used under the document camera.

3C50 - Wave Analysis and Synthesis

Pasco Fourier Synthesizer (3C50.10)
The Pasco Fourier Synthesizer is connected to a speaker and an oscilloscope. The synthesizer can generate two fundamentals of 440 Hz and eight higher harmonics, each with amplitude and phase control. The synthesizer can produce either sine, square or triangular wave forms. Note: While it works fine, there are several nice java applets available.

3C55 - Music Perception and the Voice

Tuning Forks on Resonant Boxes (3C55.55)
Two tuning forks and two resonant boxes. Shows that the box needs to be matched to the fork.

Microphone and Oscilloscope (3C55.70)
Show the output of a microphone on the oscilloscope. Observe patterns of voices, speech, tuning forks, and musical instruments.

3D - Instruments

3D20 - Resonance in Strings

Sonometer (3D20.10)
The ends of a stretched steel wire are hooked to an audio amplifier and a small horseshoe magnet is placed over the wire, so that transverse vibrations of the wire are transformed into currents along the wire. The currents are amplified and fed into an oscilloscope to display the waveform. The wire is finger plucked, and both tension and length are adjustable. Harmonics can be either ignored or intensified by changing placement of the magnet, and can also be damped out selectively with a small brush.

3D22 - Stringed Instruments

Guitar
An acoustic guitar.

Piano
A small upright piano is available in or from room A110 by arrangement.

Piano Key Action
Cutaway of a piano key and hammer mechanism to show complicated nature of the system used to properly strike piano strings in order to excite a note and avoid damping.

3D30 - Resonance Cavities

Note: The next two demos are most commonly used together.

Vertical Resonance Tube (256/512 Hz) (3D30.10)
A glass cylinder is filled with water to one of two preset levels and the tuning fork with a frequency equal to the resonant frequency for that level is held over the opening. It is noted that the sound is much louder than when the tube is filled to any other level.

Open and Closed Resonance Tube (256/512 Hz) (3D30.20)
A metal tube is cut to length to resonate at 256 Hz when closed and 512 Hz when open.

Resonance Tube with Piston (3D30.15)
A long glass tube with a moveable piston has a speaker at one end. Using a sound wave of known frequency, move the piston while listening for changes in sound intensity. Different points of maximum intensity will be found at regular spacing, which can be marked with stick-on dots on the side of the tube. The distance between the dots and the known frequency can be used to calculate the speed of sound in air.

Helmholtz Resonators (3D30.40)
Spherical cavities can be made to resonate loudly by a tuning fork of the corresponding frequency.

Kundt's Tube (3D30.60)
Air column resonance in a horizontal glass tube is shown by adding cork dust to the tube and driving the air column with a speaker at one end of the tube. Accumulation of cork dust shows nodes (displayed on overhead projector). Tube length may be varied with a sliding stop at the far end.

Rijke Tube (3D30.70)
A 6 cm diameter by 62 cm long glass tube has a piece of wire mesh across the tube 1/4 up from the bottom. The tube is held over a burner until the wire mesh glows red hot, then removed and held vertically. A loud tone is produced as a result of a standing sound wave in the tube. Turn the tube horizontal and the tone stops, then starts again when the tube is held upright.

3D32 - Air Column Instruments

Slide Whistle (3D32.15)
Toy whistle has a slide arrangement to vary column length and thus pitch.

Open and Closed End Pipes (3D32.25)
A variety of organ pipes with different lengths and removeable end pieces to show the effects of pipe length and the difference between open and closed end resonators.

Recorder
Used to discuss the effect of hole openings in effectively shortening the resonance length.

Ocarina
A toy musical instrument (resonant cavity with finger holes).

3D40 - Resonance in Plates, Bars, Solids

Xylophone Bars (3D40.10)
Individual rectangular bars mounted on sounding boards.

Xylophones
Wood or metal xylophones covering an octave or two.

Rectangular Bar Oscillations (3D40.11)
A long metal bar with a rectangular cross section. A high pitch longitudinal oscillation is excited by hammering the end. Two lower transverse frequencies are excited by striking one side or the other of the bar, with the wider side having the lower frequency.

Singing Rods (3D40.21)
An aluminum rod (approximately l.3 cm diameter by two meters long) is held at the center with one hand. The other hand strokes the rod between a rosined thumb and forefinger to produce loud, high frequency, longitudinal oscillations. The support point may be changed to produce harmonics of the fundamental tone, and two other rods of shorter lengths produce higher frequencies. Note: This demo requires some practice.

Chladni Plates (3D40.31)
Square or circular plates are driven by a speaker and oscillator. Sand sprinkled on the surface will collect along the nodal lines.

Drumhead (3D40.40)
A rubber sheet stretched over a circular frame is driven by a speaker from below and develops standing waves at certain frequencies. Grid lines on the sheet emphasize the displacement patterns (fundamental and 1st and 2nd overtones, which are not in harmonic multiples). Off-center placement of the speaker produces other patterns. Sheet tension can be adjusted to alter the fundamental frequency and overtones. Motion can be frozen using a strobe light.

Wine Glass Resonance (3D40.50)
Dip your finger in water and run it around the rim of a wine glass.

Water Spouting Bowl (3D40.51)
A 15" diameter decorative bowl with handles is partially filled with water. Wet your hands and then rub the handles to create resonance. The standing wave will cause the water to jump up several inches or more.

3D46 - Tuning Forks

Tuning Forks (3D46.15)
Various tuning forks for show and tell.

3E - Sound Reproduction

3E20 - Loudspeakers

Simple Speaker (3E20.10)
A simple speaker made from a coil taped to cardboard box lid. A board with several permanent magnets is brought nearby and the box lid becomes a decent speaker.

Cutaway Speaker (3E20.15)
A speaker that has been sliced to allow a side view of the cone motion when the speaker is speaking.