Physics and Astronomy Demonstration Resources
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Physics and Astronomy Demonstration Resources |
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17. WAVES IN GENERAL
17a. Long Spring. Transverse waves are demonstrated using a long helical spring attached to the walls of the lecture hall. Pulses or wave trains may be sent the length of the spring; standing waves are impressive! 17b. Slinky Longitudinal waves may be demonstrated using a horizontally mounted slinky. When hung horizontally on strings, can show pulses, reflections, standing waves. 17c. Torsion waves Two torsional waves demonstrators are available. The small Leybold demonstrator may be used to show torsional waves. However, the end of the torsion bar is colored white and when observed end on appears as a transverse wave. The moment of inertia of the bars is variable by moving a small mass along each bar and hence the wave velocity can be varied. Observations of reflections at boundaries, standing waves, reflections at changes in material impedance and other similar wave phenomena are observed. The second torsional wave demonstrator is the Ealing-Shive machine. This large device is capable of showing a considerable array of wave phenomena including infinite wave trains, reflections at boundaries, impedance changes, impedance matching and so on. For further information you are referred to "Similarities in Wave Behavior" by John Shive available in the Demonstration office.
17d. The Columbia Wave Machine demonstrates transverse, longitudinal and fluid wave motions by using disks driven by a complex system of gears and levers. The device, constructed before the turn of the century, clearly shows the motions of the particles in these three forms of waves. For full effect do in the dark with UV illumination; very nice effect! 17e. Superimposed Waves Two people stand at either end of a long stretch of spring. Each sends a pulse down and the student audience is asked to observe the superposition of the two pulses as they travel through each other at the center of the spring marked by tape. Two positives or a positive and a negative pulse may be transmitted and the adding and subtracting of the waves is observed. It is usually necessary to repeat the experiment a number of times before all members of the audience see the effect.
17f. Superposition A projection device is available simulating the production of a standing wave by the superposition of two waves traveling in opposite directions. In use, the device is placed on the overhead projector and the handle turned. At any instant the device may be stopped and the superposition may be demonstrated by laying a straight edge across the device.
17g. CRTO Waves Two electronic oscillators are set up to be fed simultaneously into an oscilloscope and an audio amplifier/speaker system. Beats can be obtained for a wide range of frequencies on either oscillator and can be heard via the speaker amplifier combination. Accurate adjustment of the synchronization circuits of the oscilloscope is necessary to obtain a stationary pattern.
17h. Fourier Synthesis A repetitive wave may be synthesized using the Pasco Fourier Synthesizer. The device consists of fundamental oscillator and nine harmonics, each variable in phase and amplitude. Outputs are available to CRTO or to sound amplifier and speaker. The simplest to synthesize are the square wave and the saw tooth wave. The fundamental may also be switched to be a square or triangular wave for use with a Fourier analyzer. Due to the drift in phase as the unit heats up, it is advisable to preset the wave form long before the lecture and check just before use.
17i. Standing Wave A long nichrome wire is suspended between two stands and connected to a variac. At one end of the wire a large magnetron magnet is placed so that the poles are on either side of the wire. When the tension in the wire is correct, and a current is passed through the wire from the variac, the wire will start to vibrate due to the interaction of the current and the magnetic field. At approximately 60-90 on the variac, the wire will start to glow at the nodes, the antinodes not glowing due to cooling due to the rapid motion of the wire. The experiment is best observed in a darkened room.
17j. Standing Wave on a wire uses same idea as does 16-i except it uses white insulated wire for maximum visibility.
17k. Visible String Vibrations A string on a monochord is set
up so as to be illuminated by a stroboscope. Using the closed circuit
television system with a closeup lens, the slowed down vibrations of the string
may be observed by the whole class.
17l. Sand-filled Tube In place of the spring or ropes of 17-a
a sand tube may be used. The high density of this tube together with its rather
large damping coefficient makes it possible to cleanly observe pulsed waves.
17m. Doppler Shift(1) A small speaker is driven at about 1000
Hz. Long wires and a sturdy string enable the speaker to be whirled overhead.
Clear frequency shifts heard by the audience.
17n. Doppler Shift(2) Doppler shift may be demonstrated using
a single 2 or 4 KHz tuning fork. The tuning fork is sounded and rapidly swung
towards and away from the audience. The frequency shift may be observed in one
or two ways. If the tuning fork is swung towards and away from the audience
directly in front of the lecturer, the wave reflected from the lecturer is
relatively small and the direct observation of pitch change is relatively easy.
Alternatively, the tuning fork may be swung backwards and forwards in front of
the blackboards. The difference between the directly heard waves and the waves
reflected from the blackboard is such that beats in the order of two or three
hertz may be heard.
17o. Doppler Shift(3) A whistle is rotated rapidly using a
manual rotator. The warbling sound as the pitch varies as the tuning fork
approaches and recedes from the observer can be heard.
17p. Doppler Shift(4) At one end of the air track a pair of
ultrasonic transducers are placed and one of them is driven with an oscillator,
the other detects the reflected waves. The beam of ultrasound emitted from the
transducer is reflected from a wooden or metal sheet attached to a car on the
air track. The wave reflected from this reflector is received by a second
transducer. The signal from the transducer is amplified and beaten against the
output by the second oscillator tuned approximately 400 Hz lower than the first
oscillator. The different tone is further amplified and fed into a loud
speaker, representing the difference between the two oscillators. As reflector
is moved towards or away from the transducers, the pitch is heard to increase or
decrease. A tilted air track accelerates the reflector and a rapidly increasing
pitch is heard. The system, while complicated, has the advantage that
relatively small velocities produced large changes in pitch.
17q. Doppler Shift(5) Two tuning forks are mounted on the
perimeter of one of the bicycle wheels. When both forks are sounded and bicycle
wheel set rotating around a vertical axis, a beat pattern will be heard when the
forks are in such positions that one is approaching and one is receding. No
beat pattern will be heard when the wheel is rotating about the horizontal axis
that points toward the observer. The device may be used as a crude model for
Doppler Shift in a binary star system.
17r. Doppler Shift(6) A ripple tank is set up using the single
point oscillator on the wave generator. With the light source synchronized to
the frequency of oscillation, the source is slowly moved across the ripple tank.
The clumping of waves in front of the source and the spreading of waves behind
the source may be clearly seen. An excellent film loop also available for this
very experiment.
18a. The Helmholtz resonator consists of a variable cavity in
front of which is placed a tuning fork. The tuning fork is struck with a rubber
hammer and the volume of the cavity varied by moving the piston. At two places
along the displacement of the piston the amplitude of the sound will be heard to
increase dramatically.
18b. Resonance boxes are set up at either side of the lecture
hall. When one is struck hard and allowed to sound approximately five seconds
and then stopped, the second will be heard to continue oscillating. It is
usually best to perform the experiment with the resonance boxes pointing
vertically at the ceiling.
18c. Coupled Pendula Five pendula are arranged on a common
strand; two are of equal length and the others longer and shorter. When one of
the equal pendula is set in motion the second will start to oscillate shortly
afterwards. The other pendulums will not respond. If the system is left
oscillating for a considerable period of time, it will be found that all the
energy originally imparted to one of the equal pendulum will appear in the other
pendulum.
18d. Air Column Resonance; variable frequency. Open-open and
closed-open plastic tubes of same length give resonance when one-half and one-
quarter wavelengths, respectively, fit in the tube. Resonant frequencies are
600 and 300 Hz, respectively. Sound the speaker at resonant frequency then
demonstrate change in volume of sound as you remove and replace the column.
18e. Air Column Resonance; variable length. A glass tube is
arranged vertically with either a loud speaker or a tuning fork at the top end.
For one specific frequency the height of the water is varied by varying the
height of the external tank or by allowing the water to flow in from the faucet.
Resonances will be heard at various lengths of the air column. If one is using
a loud speaker, it is possible to set the air column length and vary the
frequency to hear the resonances. For a large class, it is advisable to place a
microphone in close proximity to the end of the air column to hear the
resonances.
18f. Organ pipes may be used to demonstrate resonant air
columns. A number of organ pipes are available. One set in the range C E G C
in the octave above middle C; the other set being variable. Very fussy
experiment; practice first.
18g. Wilberforce's pendulum may be demonstrated. This consists
of a large mass with slightly variable moment of inertia coupled to a long
spring. The frequency of a torsional oscillation of the mass and the simple
spring motion of the mass may be arranged to be nearly identical. When the
Wilberforce pendulum is set in motion by either rotating it a couple of times
around its axis or displacing it approximately 10 cm. from equilibrium, energy
will be transferred back and forth between the torsional and vertical modes of
oscillation.
18h. Mechanical resonance A vertical spring-mass system is
driven by a motor-oscillator. The response of the system as the driving
frequency is changed is observed. At resonance the system selfdestructs.
18i. Gas flame resonator A long tube about 10 feet long is
driven at resonance by an organ pipe or speaker placed close to a diaphragm on
one end of the tube. The tube has holes drilled along its length from which
emanates flaming natural gas. The height of the flame is indicative of the
motion of the gas in the tube. Up to 10 antinodes can be seen. Use small gas
flames, two or three cm. in height, when no sound is on. Use care that gas is
coming from all holes before igniting.
18j. Sympathetic vibrations A series of tuning forks are set
up along the length of a lecture bench, and a loud sound, preferably of a single
frequency, is made in the region of the tuning forks. A microphone, loud
speaker, and amplifier are used to show which tuning forks are sounding after
the event.
18k. Drum Vibrations The modes of vibration (both symmetric
and asymmetric) on a drum may be shown using a rubber diaphragm placed above a
large 12-inch loud speaker, which is driven from an oscillator and amplifier.
To facilitate observation of these vibrational modes, it is necessary to
illuminate the drum head with a stroboscope and to observe the waveform using
the closed circuit television system and close-up lens. A film strip is also
available for this.
19a. Gamut's bells are used to demonstrate the limit of
audibility of sound. They consist of short sections of steel bars that are
struck longitudinally and range in frequency approximately from 2 Khz to 25 Khz.
That the bells are oscillating and emitting sound even though the ear cannot
hear them may be shown by placing a microphone close to the bells and displaying
the resulting waveform on the oscilloscope.
19b. A guitar is used to produce resonances and overtones on
strings. Either two strings may be tuned to the same frequency or one string
fretted such that it has the same frequency as the other. When one is plucked
the other will be found to respond. It is also possible to excite the overtones
of the string by partially fretting the octave fret.
19c. The Fourier analyzer on the Tectronix 531 oscilloscope may
be used to show the spectral composition of any wave form. Simple wave forms
such as sine, triangle or square waves may be set up to be analyzed. As the
analyzer is a quite complex device, it is necessary that the experiment be
practiced a number of times before the lecture. Using the device it is possible
to see the harmonics of a 10 Khz. square wave out to approximately 300 Khz.
19d. A string on a monochord is plucked or bowed as the tension
is varied or the length is varied. The relationship between tension, length,
and density of the string and the resultant frequency may be derived.
19e. A variable length organ pipe is set up and driven by air
from the high pressure airline. The change in frequency is noted as the pipe is
opened and closed or lengthened and shortened.
19f. Glass discs, either square or round are arranged on a
vertical stand and shadow projected. Sand is sprinkled onto the discs and they
are bowed at various places around the edge. Due to the vibration of the disc
or plate the sand will form patterns along the nodes.
19g. Two 1,000 Hz tuning forks are simultaneously struck and
the lack of beat noted. Modeling clay is then attached to one of the tines of
one fork and the forks restruck. A distinctive beat tone will be heard.
19h. Two organ pipes are arranged on a common stand, one tuned
approximately five Hz higher. The frequency of either organ pipe may be varied
by varying the end correction of the pipe using one hand. In this manner the
number of beats may be made to change over a range from less than one beat per
second to a discordant twenty beats per second. It is found that at beat
frequency less than approximately one Hz the pipes tend to synchronize.
19i. The resonance boxes of 18-b are used to show beats, one
being off-tuned against the other by use of a piece of modeling clay.
19j. The trombone interferometer is used to show acoustical
interference when the path length differs. The system is driven using a horn
driver and amplifier combination from an electronic oscillator, the interference
pattern being observed by a flared horn placed at the other end of the
interferometer. As the length of one of the paths is varied, maxima and minima
will be heard. It is usually best to perform this experiment in the range of
two to three thousand Hz.
19k. Vacuum bell Two versions of this experiment are available.
In the first, a bell is placed under a bell jar and the system evacuated as the
bell rings. The sound will, of course, be heard to cease even though the bell
may be seen to still be ringing. The disadvantage of this system is that the
amplitude of the sound outside the bell jar is quite low. The second system is
the loud speaker in place of the bell. Here, loud sounds may be heard outside
the bell jar when it is not evacuated, and no noise when it is evacuated.
19l. Savarts toothed wheel is used to show that the pitch of
sound is related to the repetition rates of the sound impulses. The device has
nine tooth wheels attached to a common shaft whose rotation frequency is
variable. The first eight
sound the chromatic scale C through C'; the ninth wheel has imposed on it a
random pattern and produces noise.
19m. Two sirens are available for showing pitch frequency
relationship. The first consists of a flat metal disc with a series of holes
punctured on various diameters. A set of air jets is set up such that the air
from the jets blows through these holes. The disc is rotated using the large
electric
motor. The second device is a proper siren standard of pitch as used in the
last century for measuring frequencies. A disc with a series of holes punctured
in it is made to rotate by jet action of the air from the high pressure airline
as it is forced through the disc. The frequency of rotation of the disc is
varied by varying the air pressure and is measured by using a revolution counter
built into the device.
19n. A xylophone is available for demonstrating the general
principles of vibrating bars. The lack of simple relationship between length
and frequency may be shown.
19o. A rather poor violin is available for showing the
principles of bowing and using a microphone/amplifier/oscillator combination
also for showing resonances of the cavity and structure. The waveform produced
by the violin may be analyzed using the spectral analyzer. Twenty second loop
tapes are available for recording the sound produced by the violin. The
waveforms are then played back continuously into the spectral analyzer.
19p. A flute of somewhat disreputable character is available
for showing waveforms, spectral characteristics and general principles of the
wind instruments.
19q. Interference Two loud speakers are mounted on a common
bar that is rotatable around its center and both are driven from the same
oscillator. With the oscillator tuned to approximately 3 - 3.5 Kh, the loud
speakers are rotated forwards and backwards with respect to the audience
observer. Fluctuations in intensity due to the interference between the two
wave forms will be heard. It is possible to arrange for a reversing switch in
one of the loud speaker supply leads such that the phase of one speaker can be
reversed at any time.
19r. Speed of sound A loud speaker is attached to a sinusoidal
oscillator and driven at approximately 1000 Hz. Two microphones are attached to
the two inputs on the dual trace plug for the 531-A Oscilloscope. After making
sure that the two channels of the module are in the same phase mode, the two
microphones are placed next to each other approximately 50 cm from the loud
speakers. One microphone is then progressively moved further away from the loud
speaker, the shift in phase of one trace with respect to the other being noted.
When the two tracers are once again in phase, the distance travelled by the
moving microphone equals the wavelength of the sound. Knowing the frequency one
may calculate the velocity of sound.
19s. Lecture hall acoustics An outline cross-sectional model
of a lecture hall can be set up in the ripple tank. With the stroboscope turned
off, this device can be used to show the spreading of wave fronts from a speaker
or sound source. Water is dripped into the tank, one drop at a time, into the
area where the speaker would stand. The spreading of the wave fronts and
its reflection from the walls may be clearly seen.
19t. Ear tones Two oscillators are sent into a common
amplifier speaker combination. The oscillators are both tuned to 1000 Hz and
adjusted for deadbeat, the amplitudes being matched as closely as possible. As
one oscillator frequency is shifted from 1000 Hz upwards, a series of tones will
be heard. Firstly, the beat tone which increases in pitch; secondly, a tone
which is heard to decrease in pitch which is the beat between the second
harmonic of the 1000 Hz fixed oscillator and the moving tone. Other tones may
be heard which are beats between harmonics of the fixed tone and the moving
tone. All tones are artifacts of the ear. It is necessary to have the volume
quite high in order for all members of the audience to hear these tones, many of
which are due to non-linearity effects.
19u. Dispersion A long string is stretched the width of the
lecture hall and attached to stands at both ends. At one end a microphone is
placed in contact with the spring, the output being amplified by the public
address amplifier and fed into a large speaker. When the spring is plucked at
the far end from the microphone, a noise will be heard in the loud speaker
starting at a high pitch and progressively decreasing in frequency until the
thump of the transverse wave is received at the microphone. The effect is due
to dispersion of the pulse waveform in the spring medium.
19v. Free wave interference The velocity of sound may be
measured by observing standing waves set up between a loud speaker and a
reflector. The standing waves are detected using a microphone on a stand, the
signal being filtered to remove unwanted noise of the lecture halls. The output
of the filter is fed into an amplifier and then onto the oscilloscope. As the
microphone is moved, large fluctuations in amplitude will be seen. Knowing the
driving frequency of the oscillator driving the loud speaker and knowing the
distance between nodes of the standing wave pattern equals lambda/2, the
velocity of sound can be calculated.
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