One Fine Wave Demonstration Device
by
Curtis Gabrielson
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
Bachelor of Science in Physics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 1993
Curtis Gabrielson, MCMXCIII.
The author hereby grants to MIT permission to reproduce and to
distribute copies
of this thesis document in whole or in part, and to grant others the
right to do so.
Signature redacted
A u th or .............................
..............................
Department of Physics
May 18, 1992
Signature redacted
%.
.
.......
J n King
J rofessor
Thesis Supervisor
Certified by............................
--.
Signature redacted
A ccepted by .............
....-..
Chairman, Departmental C
..
.....
....................
Aaron Bernstein
ittee on Unergraduate Theses
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One Fine Wave Demonstration Device
by
Curtis Gabrielson
Submitted to the Department of Physics
on May 18, 1992, in partial fulfillment of the
requirements for the degree of
Bachelor of Science in Physics
Abstract
With ideas from Professor John King, I designed and constructed an apparatus which
can, with the aid of an oscilloscope and an XY recorder, demonstrate various properties of waves and wave interaction. It is composed of an audio amplifier, two
oscillators, 4 speakers, a movable microphone, and several circuits producing the
required signals all mounted on a cart. The device can currently demostrate the
following wave related phenomena: speed, reflection and standing waves, phase, Lissajou figures, beats, amplitude and frequency modulation, diffraction, interference
of monochromatic waves from one and two sources, and interference of waves of low
coherence. In this report the apparatus and the demonstrations are detailed. The
component arrangement for each demostration is shown in schematic form, the switch
settings are given in tabular form, and the demostration is described. Representative
plots and pictures are given when possible. The apparatus is described in sufficient
detail to duplicate.
Thesis Supervisor: John King
Title: Professor
Contents
1
9
Introduction
11
2 Apparatus
3
2.1
M echanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
2.2
Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.3
Setting the Control Box
. . . . . . . . . . . . . . . . . . . . . . . . .
15
16
The Demonstrations
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
. . . . . . . . . . . . . . . . . . . . .
19
3.3
Beats and Lissajou Figures . . . . . . . . . . . . . . . . . . . . . . . .
21
3.4
Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3.5
Frequency Modulation
. . . . . . . . . . . . . . . . . . . . . . . . . .
27
3.6
Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.7
Interference: One Signal . . . . . . . . . . . . . . . . . . . . . . . . .
32
3.8
Interference: Two Signals . . . . . . . . . . . . . . . . . . . . . . . . .
36
3.9
Interference: Waves of Low Coherence
. . . . . . . . . . . . . . . . .
38
3.1
Speed
3.2
Reflection and Standing Waves
Conclusion and Recommendations
42
A The Demonstrations: A Summary
43
B Equipment
48
4
B.1 Tables of Components and Grand Schematic . . . . . . . . . . . . . .
3
48
B.2 Schematics for circuits constructed by myself . . . . . . . . . . . . . .
52
B.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
B.4 Things to be Done . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
4
List of Figures
2-1
The m achine. ................................
12
2-2
The control box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
3-1
Oscilloscope blip telling the time of travel. x=.5 ms/div . . . . . . . .
17
3-2
Speed Demonstration Table and Schematic . . . . . . . . . . . . . . .
18
3-3
Reflection Demonstration Table and Schematic . . . . . . . . . . . . .
20
3-4
A fine looking Lissajou figure.
90hz . . . . . . . . . .
22
3-5
Beats and Lissajou Figures Demonstration Table and Schematic . . .
23
3-6
Amplitude modulation: direct signal and signal from the microphone.
f.,
60hz,
fy
=
f, = 10khz, fm = 500hz . . . . . . . . . . . . . . . . . . . . . . . . .
25
3-7
AM Demonstration Table and Schematic . . . . . . . . . . . . . . . .
26
3-8
FM Demonstration Table and Schematic
. . . . . . . . . . . . . . . .
28
3-9
Diffraction pattern over 100 degrees . . . . . . . . . . . . . . . . . . .
30
3-10 Diffraction Demonstration Table and Schematic
. . . . . . . . . . . .
31
3-11 Interference pattern over small angle and same settings with right
speaker polarity reversed.. . . . . . . . . . . . . . . . . . . . . . . . .
34
3-12 Interference with Signal Split From One Source Demonstration Table
and Schem atic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3-13 Interference with Signals From Two Sources Demonstration Table and
Schem atic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
3-14 Highly filtered noise . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3-15 Low filtered noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3-16 Noise from two sources . . . . . . . . . . . . . . . . . . . . . . . . . .
40
5
3-17 Interference with Waves of Low Coherence Demonstration Table and
Schem atic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A-1 The first four demonstrations
41
. . . . . . . . . . . . . . . . . . . . . .
45
A-2 The next four . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
A-3 The last one . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
B-2 AM circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
B-3
52
B-1 Grand schematic
Circuit to provide signal to X of XY recorder . . . . . . . . . . . . . .
B-4 Noise generators with filters and amplifiers . . . . . . . . . . . . . . . .53
B-5 Microphone amplifier/filters with phase changing circuit and rectifier
6
54
A.1
.
List of Tables
Switch settings chart as it appears on the cart . . . . . . . . . . . .
44
B.1
Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
B.2
Switches and Potentiometers . . . . . . . . . . . . . . . . . . . . . . .
50
7
Acknowledgements
I want to thank Robert Plant, John Bonham, John Paul Jones, Jinny Page,
Jethro Tull, John Fogherty, Lynyrd Skynyrd, and especially Steve Miller and Tom
Petty for for thier supporting presence even in my times of greatest dispair. Thanks.
And as always, I will thank the beautiful goddess Athena for all her wonderful
underworldy powers. I know her better than I had ever wished to in my wildest
dreams.
8
Chapter 1
Introduction
Here I will forego discussing the importance of effective demonstrations in teaching
science, and also the relevance of understanding oscillations and wave properties when
learning physics. Instead I will give some reasons for using the type of device I have
developed. There are several methods with which to demonstrate wave properties.
Traditionally water waves have been used as a qualitative expose' of wave propagation
and interaction, and light waves have been used to achieve clear demonstrations of
the quantitative aspect. The apparatus I built is not necessarily summarily better
than light demonstrations but it has several key advantages.
The first is that the wavelengths dealt with are of a size which is tangible to the
students - on the order of 10 centimeters. Therefore the acting elements of the apparatus are visible and more easily visualizable. Second, some of the demonstrations are
witnessed audibly. This is a very effective way to demonstrate changes in frequency
or intensity such as is present in beats or constructive and destructive interference.
Third, the phase of a given wave is easily found by the detector - a microphone. When
plotted against a reference signal on the X-Y function of the oscilloscope, the phase
of the signal is apparent by means of the shape of a Lissajou figure. A dozen needles,
dials and digital displays can not form a more memorable impression than that of
a Lissajou figure. Lastly, and possibly not so important, the often unpleasant noise
made by the machine will keep students attentive if just out of irritation.
The apparatus, with the aid of a (single sweep) oscilloscope and an XY plotter can
9
currently demonstrate speed, reflection and standing waves, phase, Lissajou figures,
beats, amplitude and frequency modulation, diffraction, interference of nionochromatic waves from one and two sources, and interference of waves of low coherence, It
is possible also to demonstrate spectral analysis if the proper instrument is on hand.
With slight further development it would be possible to demonstrate (among other
concepts) refraction, two slit interference, and auto and cross correlation.
The apparatus is designed to require little understanding of electronics.
There
is a chart on the cart which gives switch settings required for each experiment and
relevant remarks. However, if the principle being demonstrated is not understood by
the demonstrator, problems are likely. It is wise for the demonstrator to wear ear
protection as he or she will often be leaning directly in front of the speakers to change
the controls. The audience will almost always be far enough away to be safe.
In the following report I will describe the apparatus, then give an explanation of
the demonstrations it is currently capable of performing.
10
Chapter 2
Apparatus
Figure 2-1 is a picture of the cart in all its splendor. In appendix two there is a table
listing each piece of equipment and its interfaces with the rest of the system. The
electronic components were purchased with the exception of the noise generators and
their filters, the microphone amplifier/filter, and the amplitude modulation circuit
which I built. Nearly all of the mechanical parts were constructed by myself.
2.1
Mechanics
As you can see the cart has three shelves, some speakers, and an arm. Most of the
electronics are mounted on the second shelf with the control box facing the rear and
the oscillators, their counters, and the power amplifier (PA) facing the front.
On
the bottom shelf is stored the box speaker and the reflection assembly as well as the
power supplies. Everything is tied down in some manner to prevent the parts from
being pilfered for other demonstrations or experimentation. The top is clear except
for the speakers and the arm assembly. Mounted underneath the arm at the pivot is
a protractor which is adjustable for use in any of the demonstrations.
The two speakers on the front corners of the top are positioned for the interference
demonstrations and the central raised one is for diffraction. The two side speakers
and the center pivot should always be in a line in order to make the interference
equations work correctly. Both the positions of the speakers and the microphone can
11
Figure 2-1: The machine
be varied creating the opportunity to show such dependencies in certain equations.
The microphone is mounted on a slider on top of the arm which is a piece of T
aluminum. It can be moved along the arm by means of a string and pulley system
connected at the rear to a potentiometer in order to plot its position on the XY
recorder. The microphone can also be moved up and down along a vertical rod using
a wing screw to facilitate demonstrations with speakers at different heights. Lastly,
the arm can be swung back and forth around its central pivot which is also connected
to a potentiometer. This enables a intensity vs lateral position plot in the interference
and diffraction demonstrations.
Right and left are defined from the student's stand point - looking at the cart
from the front. The sound can be shut off at any time by putting the speaker switch
(SPS) or the mode switch (MOS) on "OFF."
12
Figure 2-2: The control box
2.2
Electronics
Figure 2-2 is a picture of the control box. On it there are output plugs for an XY
recorder and an oscilloscope. Various other devices such as a spectrum analyzer or
an rms voltmeter could be connected to these outlets. (A voltmeter is required to
equalize the speaker's outputs in the interference demonstration.)
In addition, the
control box has many other switches and receptacles to which each part of the system
can be hooked. In fact, the only parts of the apparatus which are not on the box
and which need to be varied during a demonstration are the frequency and amplitude
control knobs on the oscillilators, the mono button on the PA, and the arm controls
on the side of the cart frame.
The oscillators are the heart of the apparatus. Each can make a signal from 1 hertz
to 100 kilohertz at a variable amplitude. Both generators are connected by their high
output plug, the right one also being connected to the external scope trigger through
the TTL output plug.
There is lead running into the left oscillator's "sweep in"
plug for use in demonstrating frequency modulation. Atop the oscillators are simple
13
frequency counters. The amplitude of the oscillators should be set to over half of
their full value for the counters to count correctly. It is good to leave the oscillators'
amplitude control set at about .6 of their maximum amplitude.
The power amplifier (PA) is used to power speakers in order to "hear" what the
signals sound like. The PA has two channels, one going to each speaker. The "tape"
input is used.
The two matching tweeters were chosen to create a high level of sound at a frequency of 8 kilohertz, the frequency used to demonstrate interference. However, their
lower limit is around 1 kilohertz and it is nice to do several of the demonstrations at
frequencies lower than that. Therefore a single broad range boxed speaker is present
to be used instead of the left speaker for those demonstrations. The phase of the left
PA output can be changed by a switch on the control box which simply changes the
polarity of the speaker leads (thus changing the polarity of the coil, etc). In addition,
the phase of the microphone can be linearly changed (not an entire 180 degrees) by
means of a potentiometer (PHP) and a phase changing circuit within the microphone
amplification circuit. (Therefore, you can change the phase of the microphone signal
only if it is being amplified.) This variable phase control makes it possible to correct
for standing waves in the room which make the interference maximums slightly out
of phase.
A working knowledge of an oscilloscope and an XY recorder is required to perform
these demonstrations. It is important to realize that the XY recorder can only be used
when the microphone amplifier/filter (MAS) is on. Otherwise, the pure microphone
signal can be viewed nicely, but only on a sensitive oscilloscope setting.
A simple
voltmeter is also good to have on the XY recorder's Y imput to moniter the signal
from the recitfier.
Circuits which I built are the following: amplitude modulation, noise generation
with variable
Q
filter and amplification, the microphone amplifier/filter, and the
voltage divider coupled to the arm to obtain a signal for the X plot of the XY recorder.
Each of these is described and drawn in appendix 2. With the exception of the X
voltage divider, these circuits are contained in the control box.
14
2.3
Setting the Control Box
As can be imagined these circuits and components must be connected in a variety of
ways to achieve the correct conglomeration of parts in order to perform the desired
demonstrations. It is a bit hairy, but not to worry: on the cart there is a small table
(which is reproduced in appendix 1). This table gives the switch settings for each
demonstration. If each switch is set to its specified setting, and the power is on, the
desire demonstration should burst forth from the machine. A bit of knowledge about
the innards of the box is helpful but not critical. It was built to be as intuitive and
idiot-proof as possible.
Each demonstration is done in one of 5 modes, selected by the mode switch (MOS).
(See appendix two for a full description of each component, switch, and potentiometer.) The speaker or combination of speakers is selected by the speaker switch (SPS).
The other very important switch is the Y sweep of the oscilloscope switch (YOS).
It selects and sends to the Y input of the oscilloscope either a signal being sent to
the speaker(s) or the microphone signal. This (in most cases) enables the students to
view the signal both before it is transfered into sound waves and after it has traveled
through the air and been converted into electromagnetic waves once more. Most of
the other switches are self explanatory (or seethe table in appendix 2).
15
Chapter 3
The Demonstrations
In this chapter, I will describe each demonstration, give its switch settings and
schematic, and display some of the results when possible.
These schematics are
not intended to be complete precise representations but rather to show arrangements
in general. To perform a demonstration, the switch setting table should be followed
closely. Appendix 1 gives, in a few pages, a table including the switch settings for
each of the demonstrations, as well as all of the schematics here. While the demonstrations are described in a logical order, any one or combination of them can be done
in any order.
General rules to promote good results include the following. If a given demonstration is not working, recheck all the switch settings against the table. Move as
little as possible when taking plots on the XY recorder. The reflections off you often
have a large effect. As a rule, the volume should be at the minimum level required to
get an effective demonstration in order to avoid saturation of op amps or saturation
of ears. In any given demonstration, vary as many of the parameters as possible.
This helps the students to see what dependences there are and exactly what is going
on. Another helpful device is to compare any given demonstration here to a similar
demonstration with light or water waves. The student will likely have seen those
before and the comparison will help solidify the concept.
16
-~
3.1
Speed
The box speaker is placed atop the cart and pointed in the general direction of the
microphone. With the right oscillator (OR) set at about 10 hertz in a square wave,
it produces a clicking sound. The start of each click triggers the scope and sends a.
signal to the microphone. The time it takes to get to the microphone is evidenced
on the oscilloscope by the length of the trace before the pulse is seen. The distance
from the speaker to the microphone can be measured and the speed calculated.
The trigger on the oscilloscope must be set at either positive and positive slope or
negative and negative slope in order to insure triggering on the sharp incline of the
square wave. It is easily found by turning the trigger level knob until a broad range
of trigger levels give the same picture on the CRT (see figure 3-1). A test is to move
the microphone or speaker and watch the blip move in proportion to the distance the
sound is traveling.
Figure 3-1: Oscilloscope blip telling the time of travel. x=.5 mis/div
17
DEMONSTRATION MOS
SPEE
SPS
St
MNS
YOS
MAS ARS TCS INS
out
mic
OFF
1 out
u n
0
-
OL
OR
10
square
OFF
-Y
ex
r out
r in
..........
--:---.
11
out
in
*
*
out
TTL
_
SYOS
XT
..
.s.i..
. ...
Figure 3-2: Speed Demonstration Table and Schematic
18
SCOP
tig
3.2
Reflection and Standing Waves
This is one of the weaker demonstrations simply because there is too much loss.
Good demonstrations of reflection take place in nearly closed chambers. In this case,
there are two reflecting boards facing each other with the box speaker inducing sound
waves between them. There is a little bench for the speaker to stand on. The reflector
for the far end of the arm has a slider similar to the microphone's. The arm is fastened
down with the obvious rubber band at the back and, if the XY recorder is to be used,
the ten turn potentiometer with the pulley should be connected to its plug (which
is fastened in a quick draw manner on the back left side of the cart). To select that
potentiometer, the switch ARS on the right side of the cart should be on "slide."
(There also is the knob used to center the XY recorder in a good position.)
OR
should be set at the desired frequency, around 8 kilohertz if the XY recorder is to be
used. If not, a lower frequency will probably work better. The microphone should be
set to the height of the speaker.
One way to achieve a standing wave is to find a maximum or a minimum by moving
the microphone, and then try to optimize it by moving the reflector. When you have,
try again to optimize it by moving the microphone. When you have found both points
of optimization, there is a reasonable approximation of a standing wave. Moving the
microphone forth and back on the arm will produce an interference pattern on the
oscilloscope and XY recorder. Near the speaker the minimum are not very low but
it can work fairly well toward the far end of the arm.
With the oscilloscope set to X-Y, the phase can be monitored and varied as is
described in the first section on interference. If the distance along the arm from one
max to another is measured, the wavelength can be found.
counter's frequency, the speed can be determined again.
19
Using c = Af and the
DB40NSTRATION -MOSI
SPS
I I
SB
CnON
MNS
I -out
I
YOS
mic
I -_
MAS
M JJC ._.J.INS
kboth>IsUde Ishort JOFF
OR
vmy
sine
_OL
t4tr
Co. E
Xy
Int-trig
...........
...........
1 out
r out
. ........
.
........
....
.......
.................
................
.................
....
...........:
..................
...............
.................
.................
.................
.......... .....
...
...
%
_RM
1 in
0
r
in
is
ng
.......................
........
..................
......
..............................
............
................
................
..........
.
out
.........
. . ... ....
........................
..................
I., .......
out
..........
4J
in
MAS
Ar i
TTL
0
YOS
..................
.....................
A, I
de"
...............................
........
Figure 3-3: Reflection Demonstration Table and Schematic
20
3.3
Beats and Lissajou Figures
As previously mentioned, this simple demonstration really shines. The phase telling
Lissajou figure is seen on the oscilloscope when set on X-Y mode, the right oscillator
being fed to the X and the left to the Y.
With the mono button (MNS) on the PA in, the speaker switch (SPS) set to SB,
and the box speaker placed on top of the cart, beats can be heard through a single
speaker if the frequencies of the oscillators are close. (Sometimes beat-like sounds can
be heard when the oscillators are in a ratio of frequencies.) In this set-up, the signal
is being combined in the PA and fed to the box speaker. The time plot of the beating
signal will be apparent with the YOS switch set to "mic." (Be sure the MAS switch
is on "off" to avoid the 8 khz filter). Set the YOS switch to "speaker signal" and the
left oscillator signal will be waiting there. Lissajou figures will then jump out when
the oscilloscope is set to the X-Y mode. This demonstration is conducive to playing
around with for long periods of time, even for senior professors.
Features of the Lissajou figures should be pointed out. Change the frequencies
and amplitudes of either oscillator to convince yourself and your students of what is
being shown. There will be a "circle" if both oscillators are at the same frequency,
and a steady figure any time the ratio of their frequencies form a rational number.
The ratio can be determined by dividing the number of peaks on the vertical by the
number on the horizontal (see figure 3-4). When there is a stationary figure with 11o
crossings, one frequency is a multiple of the other. These numbers can all be checked
by looking at the counters' digital readouts. Low frequency combinations will create
more stable figures; sometimes even stoppable.
Another option is to take off the PA mono button (MNS), turn SPS to "both"
and let the signals combine in the air. The results will be the same. A drawback is
that the tweeters are only good down to about a khz and some of the nicest sounding
beats occur around 100 hz.
21
Figure 3-4: A fine looking Lissajou figure.
22
f.,
= 60hz,
fy
= 90hz
YOS
<both>
MAS ARS TCS INS
OFF ~ -_OFF
F
out
l
OR
OL
vary
sine
vary
sine
SCOPE
T-Y then X-Y
int trig
ou ro
r out
*
DEMONSTRATION MOS SPS
MNS
BEATS AND
2 SB, then in, then
LISSAJOU FIGURES
BOTH
out
in for SB,
......-.
H
~d
out
1 in
r in
9
q
out for BOTH
-I ........
in
w
YOS
Figure 3-5: Beats and Lissajou Figures Demonstration Table and Schematic
23
3.4
Amplitude Modulation
Amplitude modulation looks very similar to beats on the scope.
The differences
between these two expressions:
y = Acoswit x Bcosw 2 t
y = (A
+
Bcos wit)cos W 2 t
should be made clear. The latter is a superposition of three frequencies and the first
is a superposition of only two.
In this demonstration, the oscillators are both fed into the circuit producing AM
and the modulated carrier is fed to the PA. The signal can be seen either by looking
at the AM circuit output directly or viewing the microphone output. (It may be an
incredible realization that the exact strange signal that is being fed to the speakers
is being translated by them into compressional waves in air and then translated back
into an electromagnetic signal by the microphone (see figure 3-6).) External triggering
should be used on the oscilloscope.
The frequencies given in the table work well to see and hear AM. Both the amplitudes and frequencies of the carrier (OL) and the modulator (OR) can be varied
to show the effect on the resulting signal. It may be especially interesting when the
modulator and carrier are very close in frequency. It is possible to set it up so that the
carrier frequency is beyond the range of human hearing and the microphone response.
In this case an AM signal will be seen on YOS "signal to speaker" but not on "mic."
Turn the modulator to square and triangle waves to see their effect. Point out that
the carrier need not be modulated by a periodic signal, in fact, if it is, it is useless as
an information carrier.
The other possibility here involves looking at the X to Y plot of the modulated
signal, X as modulator and Y as modulated carrier. A linear relation is seen between
the modulator and the modulated signals as is expected. This relation breaks down if
24
the amplitude is turned high enough due to the manner in which the signal is created.
Figure 3-6: Amplitude modulation: direct signal and signal from the microphone.
f, = 10khz, f, = 500hz
25
!'P"'_
DEMONSTRATION MOS
AM
3
SPS
SB
MNS
out
YOS
<both>
MAS ARS TCS INS ___OR
OL
SCOPE
OFF
~
~ OFF vary; maybe 500 vary; maybe 10k T-Y then X-Y
vary form, amp vary form, amp. _it trig
F :1
l
out
1 in
r
out
r
in
E$-,
III
1L
.....
.
..
............ .........
x
Figure 3-7: AM Demonstration Table and Schematic
26
3.5
Frequency Modulation
Frequency modulation is achieved in a simplistic manner. When a signal is fed
to the input jack on the oscillators, the frequency of the oscillator varies with the
amplitude of the input signal.
frequency modulation.
Naturally, if a sinusoid is input, we get sinusoidal
The square and sawtooth waves can be used to modulate
also. Very low frequency modulating signals are the most interesting to see and hear.
Again try the square and triangle waves. Viewing the Y to Y function on the
oscilloscope in this arrangement is possible but not very illuminating.
27
DEMONSTRATION MOS
FM
4
SPS
SB
MNS
out
YOS
<both>
MAS ARS TCS INS
OFF
~
ON
~
OR
OL
vary, ow)
vary wave form
vary
vary wave
S ........
1
out
...........
...
PA
.....
in
out
:o::+
4
-8
____
___
r out
r
n
INS
in
out
TT'L
0
____ ___ ____ ___(on)
Figure 3-8: FM Demonstration Table and Schenmatic
28
SCOPE
T-Y
form
int trg
3.6
Diffraction
The key to this demonstration is to place the microphone as close as possible to the
speaker. The diffraction speaker is used, naturally, and its proper position is directly
centered above the pivot bolt. It should be pointed in a direction approximately 45
degrees from the front edge of the table so that a 100 degree arm swing encompasses
both a microphone position of straight on and one of 90 degrees to the side. When
the arm is at the extreme position which has the microphone at 90 degrees, the
microphone should be about a half a centimeter from the edge of the speaker. Then
turn the arm so that the microphone is directly in front of the speaker. The volume
should be low enough so that the rectifying circuit for the Y function of the XY
recorder is not saturated.
(If the peak is flat, turn the volume down.) With the
microphone so close to the speaker, the effects of reflection and standing waves are
reduced greatly.
Before the demonstration, the equation for a diffraction intensity,
I=1 o(sina)2
\a/
where a = 1/20, should be discussed. In addition,
A/D
n=
should be shown and the values of A = 1.9 cm and D = 2.8 cm should be plugged
in to get a value of about 45 degrees for the first minimum.
A frequency of 17 kilohertz is used here for two reasons. With lower frequencies,
the diffraction pattern is greater than 90 degrees and cannot be seen. (In addition, it is
not clear what diffraction means when the source is smaller than the wave length.) At
17 kilohertz, the speaker produced a vague diffraction pattern which when calculated
gave an effective speaker diameter of 2.8 cm. The plate mounted on the front of the
speaker simply reinforces that dimension with the effect of making the pattern more
distinct. The other reason for this frequency is that the microphone amplifier/filter
29
has a secondary maximum here.
Reflection off the inner surface of the hole and off the microphone itself play a
role in making odd bumps on the graph. Still, it is remarkable and instructive how
close to zero amplitude it is possible to achieve at minimum with the microphone so
close to the speaker (figure 3-9).
Figure 3-9: Diffraction pattern over 100 degrees
30
DEMONSTRATION MOS
I
SPS
SD
MNS
out -
YOS
MAS ARS TCS ]N
mic--- ON s wing- s*hort FF
OR
17 k
sine
-OL
T-1
int tfig
.....
...
r ..
1 out
r out
.............
........
...
........
..........
............
771 ................
...........
.......................
1 in
r in
0
4
............
............
...........
...
.......
...............................
....
.....
..........
.............................
...........
....................
......
..............................
.......... t
...............................
out
9
ou
in
0
MAS
TTi
Yos
.
........ .
............
......
. ..
...
..................
.........
.....
....
%
...
%
XX
.....
.%*
......
..
..
...........
........
.................................
........
....
...
..
......
-.........
.1Figure 3-10: Diffraction Denionst ration Table and Schematic
31
3.7
Interference: One Signal
This is the classic "two monochromatic, in-phase sources" interference demonstration.
It works like a dream and the real gem is again the fact that the relative phase of the
signal at any point can be observed. At 8 kilohertz, the maximums are close enough
together to allow moving the arm by less than 20 degrees.
Therefore, small angle
approximations are fairly accurate and quantitative analysis can be done with the
XY recorder plot.
(The microphone amplifier/filter was designed specifically for this demonstration.
The amplification was necessary to get the XY plot and the filter was necessary to
make it smooth. Eight kilohertz was used simply because it gave the most distinct
maximums, and had least effect by the room reflection.)
First the two equations
sing = A/D
I = 4Icos2 1/20
should be shown and the calculations carried out. Be sure to point out the 1/20 in
the second one. Then, when performing the demonstration, the appropriate values
should be read using the protractor and XY recorder plot.
While the XY recorder should be made use of, interference at frequencies other
than 8 kilohertz is also instructive. At 8 kilohertz the maximums are so close that
it is sometimes difficult to tell which one is the center. Of course this can be easily
determined by viewing the X-Y function of the oscilloscope and looking for the oneto-one figure. But at lower frequencies, the fringes will be more widely spaced and
the center one will be obvious.
When the microphone is at center, the phase as seen on the oscilloscope in X-Y
mode should be nearly one-to-one. To make it exactly one to one, there are several
controls which have an effect.
The first is the frequency control on OR. A slight
32
change in frequency will give a big change in the phase of the signal at central max.
It may also shift the max to the left or right so be careful of that. If the X-Y figure
is still not flat one-to-one, adjust PHP. Be aware that PHP also has a small effect
on the amplitude of the signal. In addition it is good to know that the volume and
balance controls on the PA shift the phase of the central maximum. And don't forget
PHS flips the phase by 180 degrees.
To get a nice plot with maximums and minimums of approximately equal height
on the XY recorder it is necessary to make each of the speakers put out the same
level of sound.
The PA is not much good at this, especially on mono (MNS in).
(The "balance" knob varies the level of input to the PA, so it is worthless when on
mono.) The potentiometer RAP adjust the amplitude of the right output of the PA.
Equalization can be done the following way:
1. Set arm at the central maximum.
2. Turn volume down until there is less than 5 volts going to the Y of the
XY recorder.
3. Shift phase until it is exactly one-to-one.
4. Turn SPS to SL and note the voltage at the XY recorder.
5. Turn SPS to SR and adjust RAP until it matches SL's output.
Sometimes the room reflection interference pattern can make the maximums and
minimums slightly off even after the speaker outputs have been equalized. It is useful
to turn one speaker off and show the interference pattern in the room from one
source. This can be altered by rotating the cart a few inches. Another effect is the
maximums becoming slightly larger as the angle is increased. Due to the microphone
being closer to one or the other speaker, this effect can be used to compare with a
light demonstration in which a lens and collimator take care of this problem. The
effect is minimized by moving the microphone further out on the arm.
The previously discussed 1/20 should be clear when the arm is moved to the first
maximum; a reasonably straight one-to-negative one plot appears.
Likewise when
the arm is moved to the first maximum on the other side of the center, but when
advanced to the second maximums in either direction, astoundingly enough, the one-
33
to-one figure returns. The 180 degree phase switch (PHS) can be employed to show
that happens when the sources are 180 degrees out of phase. The central maximum
turns to a minimum as shown in figure 3-11.
Students should be given the opportunity to come within a few meters of the
machine and actually move their heads through the interference fringes. This is done
well at around one kilohertz. Different microphone distances can be tried also. In
theory, it should be possible to trace an intensity maximum straight outward from
the central theory. Room reflections make this difficult.
Figure 3-11: Interference pattern over small angle and same settings with right speaker
polarity reversed.
34
DEMONSTRATION MOS
SPS
MNS
YOS
in
MAS ARS TCS INS
ON swing short OFF
mic
ONE SIGNAL
OL
OR
8k
sine
-I
SCOPE
T-Y then X-Y
int trig
trn
1 out
r out
MNS
in
0
r
in
in
4
0X~
out
. ..
.
..
..
QI~
in
00
4J.
MAS
YOS
-""
04
.
.i.... ..
|| | ...
.||
S.r
Figure 3-12: Interference with Signal Split From One Source Demonstration Table
and Schematic
35
3.8
Interference: Two Signals
This demonstration is just to prove that it is not observable. The same procedure
is followed as in the one source demonstration, only mode 2 is used and different
frequencies are sent to each speaker. At greatly differing frequencies, a sweep of the
arm shows neither maximums nor minimums. However, if the frequencies are set
close together (at around 8 kilohertz to use the amplifier) beats are again heard and
the interference intensity pattern is varying so slowly with time as to show up on the
XY recorder.
Although nothing much quantitative can be done, it is very apparent from this
demonstration that there is always interference when tow waves meet. The only time
that we can observe it however, is when it is static or nearly static in time or space.
Otherwise, the intensities add and an even distribution is observed.
36
DEMONSTRATION MOS SPS
D N RENCE: 2 BOTH
TWO SIGNALS
MAS ARS TCS INS
ON swing short OFF
YOS
MNS
out
mic
OR_
8k
sine
OL
Si-COIE
vary
T-Y then X-Y
sine
int trig
0r
1 out
r out
MNS
1
in
out
r in
.C............
.3 -
out
in
9
6
9MAS
out
-I TTL
YOs
xy ;...........
..........
Figure 3-13: Interference with Signals From Two Sources Demonstration Table and
Schematic
37
3.9
Interference: Waves of Low Coherence
One of the deeper demonstrations, this one incorporates two noise generators and
sharp filters. The basic idea is that static spatial interference requires two sources
of nearly the same frequency and fixed phase difference. The noise generators create
signals of a very wide range of frequencies and the filters, when imposed, restrict that
frequency range. The equation AfAt ~ 27r and its Fourier equivalent AkAA
should be discussed.
27r
The parameter of Af is being squeezed in this case which
leads to a larger coherence time At or coherence length Ate. There is static spatial
interference when L, the length between points of a wave which are adding, is less
than the coherence length: L < Ate or L < AA.
At the "high
Q"
settings of COS these filters have a
Q
of around 40. Centered
at 8 kilohertz, this gives a Af of 160 hertz or a AA of 50 A. The first interference
maximum is L
-
OA, the second L
-
1A, etc., so it is clear that there should be many
fringes (and there are). At the "medium" setting the
AA = 5) and several fringes still occur. At the "low
Q is about 5 (Af - 1600 hertz,
Q" settings the filter is for all
practical purposes removed from the circuit and in theory the signal is pure noise.
However, the response of the entire system, PA through rectifier, is not flat and one
or two fringes still occur due to the peak in the response curve acting as a broad
filter. Some signal leakage or interaction between the noise generators and filters is
also probable. To completely rid the system of this effect would take some major
restructuring of the apparatus.
At any rate, settings 1 through 3 of COS give a noise signal of high, medium and
low coherence, respectively, from the right noise generator only. For the first part of
the demonstration, MNS should be in, splitting the right noise to both speakers. The
signal going to the speakers should be viewed (YOS on "signal to speaker") at each
coherence level before any movement of the arm is done. It is very apparent from the
sound alone that the signals from COS 1,2, and 3 are of different coherence lengths.
This also may be viewed form the microphone signal. With YOS on "mic," and TCS
on "long" to even out the sputtering noise signal, a slow sweep of the arm (to allow
38
for the longer time constant) should reveal the extent of static spatial interference in
each case (figures 3-14 and reflowQ).
Then, MNS should be taken off, and COS turned to 4 and 5 sending the left
noise to the left PS input and the right to the right. As is again apparent, 4 is of a
much higher coherence level than 5. Both of these settings will produce virtually no
interference due to the fact that each individual tiny noise pulse is out of phase with
whatever one it could be interfering with from the other generator. (It is important
to set the noise generators to give out the same amplitude of noise ahead of time.
See appendix 2.) Point out that the filtered noise coming form two different sources
sounds exactly like the filtered noise from one source and is filtered around exactly the
same frequency but, as the phase is not linked, interference can not be seen observed
(figure 3-16).
39
Figure 3-14: Highly filtered noise
Figure 3-15: Low filtered noise
Figure 3-16: Noise from two sources
40
DEMONSTRATION MOS SPS
INTERFERENCE: 5 BOTH
MNS
in, then
YOS
<both>
MAS
INS
ARS TCS
OR
ON swing long OFF
OL
SCOPE
~
T-Y
bigt
tg
out
LOW COHERENCE
.H
1
out
r out
A
1
in
MNS: in for
1, 2, 3.
Out for 4,5.
.COS
r in
COS
0
0
.
.~--.
MA4
MAS
YOS
yO
Figure 3-17: Interference with Waves of Low Coherence Denmonstration Table and
Schematic
41
Chapter 4
Conclusion and Recommendations
More than a dozen aspects of waves can be studied and demonstrated with this
apparatus.
The advantages of sound waves as a vehicle are fully exploited. While
there are some shortcomings, in general this device can be used by teachers of any
level with a minimum of time spent becoming familiar with it.
In addition, the
information in this article is sufficient for a similar device to be constructed.
With a bit more work, the apparatus could easily include spectral analysis and
demonstrations of refraction, hetrodyning, and correlation among others. Currently
it is a solid functional apparatus suitable to be used in small group or mass demonstrations as well as individual investigations.
42
Appendix A
The Demonstrations: A Summary
On the next page is the complete table as it appears on the cart. Switch settings and
remarks are given for each demonstration. Following it are the general schematics for
each of the demonstrations.
43
_ OFF
vary var
DEMONSTRATION;MOS
SPEED
I
SP5
MNS
YOS
SB
out
mic
TCS INS
~ OFF
MASARS
OFF
-
OR
OL
10
~
SCOPE
T-Y
ext trig
square
SB
REFLECTION
mic
out
<both> side
vary
short OFF
T-Y then X-Y Fasten down the arm in back, set up rectors, move microphone to proper height.
int trig
iCreate standing wave. Hook up rear pot on arm if XY recording.
Change PHS to see effect. Measure wave length and calculate Teed.
~
Sine
T-Y then X-Y Combine signals in PA
and then in air. StaBEATS
tionary figuresAND
Cu
2
USSAJOU FIGURESI
AM
SB, then
n, then
BOTH
out
SB
out
3
OFF
both>
~
sine
<both>
OFF
~
-
OFF vary- maybe 500
vary form, amp.
FM
co
DIFFRAC TION
4
SB
1
out
SD
<both>
out
mic
_
INTERFERENCE:
ONE SIGNAL
I
INTERFERENCE
2
BOTH
in
OFF
ON
_
mic
~
~
ON
varv(ow)
vary
vary wave form
swingI shot OFF
swing short
17 k
T-Y
-
OFF
out
mic
ON
swing short
OFF
vary
sine
5
BOTH
in, then
LOW COHERENCE
<both>
ON
swing long
OFF-
out
I -
I
---
are ratios of frequencies. Figures without crossings are even multiples.
int
Try all combinations. Don't forget to shut off INS when finished.
trig
T-Y then X-Y Raise micropone to level of SD. Place microphone very close to speaker.
int trig
Swing arm 100 degrees. Calculate expected position of minimum. Be sure volume is
low enough to give peak on XY recorder. Try to reduce minima by positioning the cart.
T-Y then X-Y Make central max in phase with PHP. Also change phase by pi with PHS
int trig
to shift maximums and mimmums. Notice phase change every 2 maximums.
Sweep through small angles. Calculate expected results.
s .e
BOTH
int trig
vary; maybel0k T-YthenX-Y OL is carrer, OR is modulator. Compare signal to speaker to signal from mic.
vary form, amp.
int trig
Make frequencies close. Don't put Carrier (OL) above hearing range.
vary wave fonn
TWO SIGNALS
INTERFERENCE:
sine
_sine
ON
REMARKSANDIDEAS
Adjust scope trigger level until blip is stationary. Check signal to speaker
(YOS) to see trigger pulse. Speed = distance speaker to microphone/ time on scope.
sine
T-Y then X- Y Try frequencies far away and very close together. Make is beat very slowly
and try to follow a maximum with the arm. Notice where maxes come in relation to phase.
int trig
T-Y
int trig
COS switch on 1,2 or 3 gives high, medium and low filtered noise from one noise
source. MNS should be in to see some interference. COS on 4 and 5 gives high
and low filtered noise from two sources. MNS should be out. Virtually no interference.
0
v$~ t
in
0
TTL
Yoe
K
ms
YOS
*
~~
.. ......
Reflection
Speed
I.t
1 =t
ut
r out
::::IMS in fex sp,
ut
1 n
r
f.. BOTS
I-
r n
-1 J:%
.... ...
-
-
0
1.
-t-
TTL
....-....
I
Beats and
Lissajou Figures
AM
Figure A-1: The first four demonstrations
45
eA
1 out
r
lin
r in
out
out
r out
x
X
out.
....
0
0
...
0 ...
.....
.
.
in
out
l
out
TTL
zus
7e
n
Diffraction
-on-
1
r
out
out
s
a
u
n
out
s
r
in
1 on
r
o
.
-.
out
in
+........
out
.
*
*E
e
L
out.n
i0
j
s
Yos
One Source Interference
:7:p
Ll
I.1
Xos
Two Source Interference
Figure A-2: The next four
46
lt
rout
Co in23
, 3
NOS
Out for 4,5.
1 in
r
in
NENNEliiOillii
Interference with Low
Coherence Sources
Figure A-3: The last one
47
Appendix B
Equipment
B.1
Tables of Components and Grand Schematic
Shown here are two tables containing of all the components, switches, and accessible potentiometers in the apparatus and their interfaces. Following is is the grand
schematic. Between it and the individual circuit diagrams, each piece of the apparatus is represented. For the most part, each of the circuit diagrams is represented by
one component in the grand schematic.
48
Description
+ and - 15 volts and ground
to 1 ampere
Global Specialties 2001. 0-100 khz,
.1-10v p-p, sin, sqr, or triangle .
Symbol
PS
Component(s)
power supply
OL
left oscillator
OR
right oscillator
same as OL
counters
Global Specialties Max 100. 1.5
600
CL,CR
right and left
PA
power amplifier
SL
tweeter left
SR
SD
ohm
Megohm input,
Interface(s)
control box,
and 120 volts ac
high output
input
output
5hz
high output
TTL
input
- 100Mhz
right and left input, MNS,
and right and left output
high and ground
tweeter right
Realistic SA150. 22 kohm (tape)
input 1.8 watts/channel (rms)
Realistic High Performance Cone
Tweeter. 4in. 8 ohms. Response 5-20 khz
same as SL
speaker (tweeter)
same as SL with diffracting plate.
high and low
Realistic Minimus 3.5. 8 ohm.
Archer pc-mnt. Condenser Element.
5 vdc. Response 20 hz - 15 khz
high and low
high and low
high and low
diffracting
SB
M
speaker (box)
microphone
MA
microphone amplifier,
filter, rectifier,
NGR,
noise generators with
NGL
filters
1 kohm output
see section B.2
MAS, and ground
and phase changer
AM
X
X
on
see section B.2
+ and - 15 volts,
output, COS, and ground
and amplifiers
amplitude modulation
circuit
circuit to give
input, output, dc
output, TCS, PHP,
see section B.2
see section B.2
carrier, modulator inputs,
and outputs and ground
+ 15 volts, ground, ARS,
XYP, high and low output
XY recorder
Table B.1: Components
49
Symbol
Switch or Pot
Description
MOS
mode
SPS
speaker
COS
coherence level
PHS
INS
YOS
180 deg phase change
left oscillator input
Y oscilloscope sweep
MAS
microphone amplifier
TCS
time constant
ARS
arm selector
MNS
mono
PHP
microphone phase
XYP
RAP
x centering
right amplitude
4P6T switch controlling PA inputs left and right and
oscilloscope output Y and Y, and off (seegrand schematic)
selects the arrangement for demonstration
2P6T switch selects left, both left and right,
right, diffraction, or box speakers or off
2P6T switch selects unfiltered, low filtered or high
filtered noise from one or both noise generators, or off
DPDT switch changes polarity of right output of PA
SPST switch turns off or on sweep input to OL
SPDT switch feeds Y oscilloscope sweep with
signal from microphone or signal to left PA input
SPDT switch selects between the microphone's weak unfiltered
signal and an amplified signal filtered around 8 kilohertz
SPDT switch selects long or short time constant
for Y on XY recorder
SPDT switch mounted on cart chasis selects between arm
angle and arm length plot for X on XY recorder
pushbutton switch on PA selects combining
the PA inputs or amplifying them separately.
potentiometer continuously varies the phase
of the microphone (located within mic amp circuit)
potentiometer centers X function of XY recorder
potentiometer varies the amplitude of the right PA
for speaker outpt equalization
Table B.2: Switches and Potentiometers
50
.....
....
09
4
33
5
2
SPS
L
4
5
-15
black
grnd
white
+15
red
PHS
:
R
2
1 out
r
RAP (5 ohm pot)
out
MOS
MNS
out
TTL
75 kohm,
1n
r
re
in3L
4
9.1
kohmi
e
4
LgR
5
2
3
5
hm
ired
r
: bottom wa
YOS
--
I e iI
rey
j
2.5
:3
4
in t. INS
out
red
.4
4:
,
o
2
o
top wafea-I
|
green
e
pup
PULP-Le
14
4:,
....
I
whi te
xy.....
Figure B-1: Grand schematic
51
4
B.2
Schematics for circuits constructed by myself
OL
car.
620 ohnms
15 kohm
OR
mod.
5 kohm
balanced
I
N5712
(both)
to left PA
Figure B-2: AM circuit
arm length pot (10 turn)
arm angle pot
t
I:
15 vdc
all pots
10 kohm
to x of XY recorder
Figure B-3: Circuit to provide signal to X of XY recorder
52
01
0,
002
shaded region
MM
...
k....
...
.....
...
....
22....M...
in shielded
box
~
.
"
...........
+M
-:-
..... ..r..
.....
t~~.
2....~
Y.....s..p...k.......h
q--r-------------.22
to
signal
M.
speaker
1N5712
.iMfjIMf
9. 1 kohm
-15 vdc
(
+15 vdc 750 kohm
360 kohm (slow)
/
to Y of XY recorder
jL
M
I kohm (fist)
f
40 ohm
all op amps: 741
Figure B-4: Noise generators with filters and amplifiers
53
MOsM"mamsmmmma
100 kohm
I Mohm
750 kohm
15 vdc
high Q
.0056
M470
.1Mr
Mohm
22 kohm
ohm
medium Q
510 ohm
10ohm
18
ohm
low Q
30 ohm
L
7/~> 4
Na/
.11M'1
5
100 kohm
3
1Mohm
750 kohm
15 vdc ().0056
0
1high
Mr
470ohm
. Mf
I Mohm
100
t
ohm
ohm
h510
I
low a
ohm
h30
*1
to right PA
.004 Mt
1kohm
,00 of mn
+
to left PA
100 mh
.00 4 Mt
5Skohm
100 mh
100 ohm
all transistors
2N3439 (npn)
all op amps 741
Figure B-5: Microphone amplifier/filters with phase changing circuit and rectifier
54
Discussion
B.3
Before I started building this creation, I knew very little about electronics.
Some
would say this is still the case. Many of the circuits were put in their final form simply
because they created the desired effects. In any event, the circuits can undoubtably
be improved by someone well acquainted with electronic construction.
Amplitude modulation was achieved with a couple of diodes, a couple of resistors
and a transformer (figure B-2). It is not important whether the transformer is step
up or down, only that it has an output in the center on one side. The modulator is
connected to the transformer and the carrier to the potentiometer center lead. This
circuit exploits the nonlinear characteristics of the diodes in the backward biased
direction to make a nearly symmetrically modulated signal.
The noise generators (figure B-4) utilize the noise created by back biasing a seniconductor. The transistor I used was a 2N3439 for no reason at all. The noise is
then amplified using the same transistor. To demonstrate coherence length, the noise
must be put through a very high
Q bandpass
filter. This was achieved simply and
elegantly with an LC filter. The L is a toroidal inductor of 100 millihenries. To center
the pass band at around 8 kilohertz required a capacitor of .004 /tF. It is valuable
to demonstrate two different coherence lengths so two different Q's are achieved by
varying the resistor in series with the filter. This then changes the output level so
the amplification must also be changed; thus the voltage divider after the exiting
capacitor. Amplification is then provided by a 741 op amp. The left one has a pot
in the feedback loop so its gain can be adjusted. This is necessary because different
transistors give different amounts of noise.
For the demonstration of two source low coherence interference, the output level
of each generator should be equal. To equalize them the following procedure may be
followed.
1. Place microphone in some firm position, set MNS out, COS to 4, SPS
to both, and unplug the left input to the PA.
2. Find the rms voltage at the Y input of the XY recorder. This is due
to the right noise generator.
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3. Unplug the right input to the PA and in its place plug in the lead from
the control box "left PA in." This feeds the left noise generator's output
to the same speaker.
4. Adjust the pot on the feedback loop of the left noise generator's amplifier so that the rms voltage at the XY recorder's Y input is the same
as it was with the right noise generator hooked up.
5. Then to be sure, plug each side into the the left PA input and the effect
should be the same. The amplitudes should also be the same when COS
is set to 5.
The microphone amplification circuit (figure B-5) is necessary to filter out all
unwanted frequencies in the interference denionstration.
It consists of two 741 op
amps with a phase changing circuit sandwiched between them. The primary filters
are on the feedback loops of the op amps. It is mounted in a box to protect the tiny
microphone signal from the other signals around. The signal is in fact shielded all
the way to the YOS switch.
The only other circuit is the one used to make the X signal for the XY recorder
(figure B-3). A 10 kohni potentiometer is hooked to the sweeping microphone arm
and to the central pivot. To make a linear circuit and to allow for adjustable range,
the center lead of this pot is connected to the center lead on another 10 kohm pot
making a classic bridge circuit. In addition, a 10 turn 10 kohm pot is mounted on
the arm with a pulley in a position to move the microphone along the arm for the
standing wave demonstration. This potentiometer can be put in the bridge circuit in
place of the pivot one by flipping switch ARS (on the side of the cart) to "slide."
When trouble shooting, an oscilloscope probe is invaluable. Replacing transistors
and op amps often solves the problem.
Cold solder joints are very possible also.
One reasons for resistors in odd places is that when the PA is on mono, the input
impedance is lowered and the two input signals are effectively shorted together.
B.4
Things to be Done
Here is a partial list of things that I can see should be done differently and additional
things that should be done.
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1.
The AM circuit should be more decoupled from the oscillators than it is at
present. The effects of modulation are sometimes seen on modes other than 3.
2.
The noise generator/filter/amplifiers should be completely silenced when COS
is on OFF. Furthermore, the noise should be made to be more pure to produce less
interference as is ideally expected.
3.
The PA and both oscillators really should be facing toward the rear of the cart
so the demonstrator does not have to lean around front to adjust them. The counters
need to be facing forward for students to see but that is all.
4.
If the "sweep in" of OR was used instead of OL, mode 4 would not be necessary.
The present set up is a result of poor foresight and the common predicaments involved
in using the prototype as the final product. To implement this change, many holes
and jacks would need to be rearranged on the control box.
5.
The MNS button could easily be reproduced on the control box to eliminate the
confusion of a switch on the PA.
6.
It should be made possible to link the phase of the two oscillators if only to
make more elegant Lissajou figures. This would require delving into the innards of
the oscillators.
7.
The whole apparatus could be polished up a bit. I basically ran out of time
when it came to aesthetics.
Other experiments which could be easily developed are two slit interference (I
actually had this working from two slits on a foam lined cardboard box), refraction
through a balloon filled with dense gas, and inputting music (specifically, hard rock
music) into the noise filter/amplifier circuit to see the resulting interference effects.
Demonstrations of spectral analysis, hetrodyning, and auto and cross correlation
would require significantly more electronics but are also possible.
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