PASCO WA-9612 User Manual
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Includes
Teacher's Notes
and
Typical
Experiment Results
Instruction Manual and
Experiment Guide for
the PASCO scientific
Model WA-9612
RESONANCE
TUBE
012-03541E
3/95
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SPEAKER INPUT
.1 W MAX
ON
ON
OFF
OFF
100.5 Hz
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13
WA-9612
RESONANCE TUBE
© 1988 PASCO scientific $7.50
012-03541E Resonance Tube
T able of Contents
Section Page
Copyright, Warranty and Equipment Return...................................................ii
Introduction .....................................................................................................1
Equipment and Setup.......................................................................................1
Using the Resonance Tube:
with the PASCO Series 6500 Computer Interface ..............................3
with the Power Amplifier: ................................................................... 3
with the Data Monitor Program:..........................................................3
Waves in a Tube Theory:.................................................................................4
Experiments:
Experiment 1: Resonant Frequencies of a Tube.................................. 7
Experiment 2: Standing Waves in a Tube ...........................................9
Experiment 3: Tube Length and Resonant Modes .............................13
Experiment 4: The Speed of Sound in a Tube....................................15
Suggested Demonstration ...............................................................................17
Suggested Research Topics ............................................................................18
Teacher’s Guide..............................................................................................19
Technical Support................................................................. Inside Back Cover
i
Resonance Tube 012-03541E
Copyright, Warranty and Equipment Return
Please—Feel free to duplicate this
manual subject to the copyright restrictions below.
Copyright Notice
The PASCO scientific Model WA-9612 Resonance
Tube manual is copyrighted and all rights reserved.
However, permission is granted to non-profit educational institutions for reproduction of any part of this
manual providing the reproductions are used only for
their laboratories and are not sold for profit. Reproduction under any other circumstances, without the
written consent of PASCO scientific, is prohibited.
Limited Warranty
PASCO scientific warrants this product to be free from
defects in materials and workmanship for a period of
one year from the date of shipment to the customer.
PASCO will repair or replace, at its option, any part of
the product which is deemed to be defective in material or workmanship. This warranty does not cover
damage to the product caused by abuse or improper
use. Determination of whether a product failure is the
result of a manufacturing defect or improper use by the
customer shall be made solely by PASCO scientific.
Responsibility for the return of equipment for warranty
repair belongs to the customer. Equipment must be
properly packed to prevent damage and shipped
postage or freight prepaid. (Damage caused by
improper packing of the equipment for return shipment
will not be covered by the warranty.) Shipping costs
for returning the equipment, after repair, will be paid
by PASCO scientific.
Equipment Return
Should the product have to be returned to PASCO
scientific for any reason, notify PASCO scientific by
letter, phone, or fax BEFORE returning the product.
Upon notification, the return authorization and
shipping instructions will be promptly issued.
ä
NOTE: NO EQUIPMENT WILL BE
ACCEPTED FOR RETURN WITHOUT AN
AUTHORIZATION FROM PASCO.
When returning equipment for repair, the units
must be packed properly. Carriers will not accept
responsibility for damage caused by improper
packing. To be certain the unit will not be
damaged in shipment, observe the following rules:
➀ The packing carton must be strong enough for the
item shipped.
➁ Make certain there are at least two inches of
packing material between any point on the
apparatus and the inside walls of the carton.
➂ Make certain that the packing material cannot shift
in the box or become compressed, allowing the
instrument come in contact with the packing
carton.
Credits
This manual authored by: Clarence Bakken
This manual edited by: Eric Ayars
Teacher's guide written by: Eric Ayars
Address: PASCO scientific
10101 Foothills Blvd.
Roseville, CA 95747-7100
Phone: (916) 786-3800
FAX: (916) 786-3292
email: techsupp@pasco.com
web: www.pasco.com
ii
012-03541E Resonance Tube
Introduction
The PASCO Model WA-9612 Resonance Tube lets
you investigate the propagation of sound waves in a
tube. You can observe standing wave patterns in a
closed or open tube, and locate nodes and antinodes
while varying the length of the tube. You can measure
the speed of sound in the tube either indirectly, by
measuring the frequency and wavelength of a resonance mode, or more directly, by using a triggered
oscilloscope to measure the transit times for sound
pulses along the tube. The tube also has two holes in it
that can be covered or uncovered to investigate the
physics of wind instruments.
Equipment and Setup
The WA-9612 Resonance Tube comes with
the following equipment (see Figure 1):
• 90 cm clear plastic tube with a built-in metric
scale
• Two tube mounting stands, one with a built-in
speaker and a mount for the microphone
• Miniature microphone with a battery powered
amplifier (battery included) and a coax connector
for direct attachment to an oscillosocope
Waves in the tube are produced by a speaker and
detected by a miniature microphone. The microphone
can be mounted beside the speaker to detect resonance
modes, or it can be mounted on a rod and moved
through the tube to examine wave characteristics
inside the tube.
➤ NOTE: To use the Resonance Tube, you
will need an oscilloscope to examine the signal
detected by the microphone, and a signal generator capable of driving the 32 Ω 0.1 W speaker.
• Moveable piston
• Microphone probe rod (86 cm brass rod, not
shown)
• Clamp-on hole covers
Clamp-on hole
covers
Miniature
microphone
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Microphone battery
and circuitry
Tube mounting
Coax
adapter
OFF
OFF
ON
ON
Moveable piston
Tube with built-in metric scale
Speaker
Microphone
mount
stands
SPEAKER INPUT
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Figure 1 Equipment Included with the WA-9612 Resonance Tube
1
.1 W MAX
WA-9612
RESONANCE TUBE
Resonance Tube 012-03541E
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You will also need:
• A function generator capable of driving the 32 Ω,
0.1 W speaker (such as the PASCO PI-9587B
Digital Function Generator.
• An oscilloscope (such as the PASCO SB-9591)
• Banana plug hook-up wires for connecting your
function generator to the speaker
To set up the Resonance Tube
(see Figure 2):
➀ Set up the equipment as shown in Figure 2. The mi-
crophone can be mounted in the microphone hole
below the speaker, or, as shown in the lower insert,
it can be taped to the end of the microphone probe
rod and inserted through the mounting hole so that
nodes and antinodes can be located within the tube.
You can also vary the effective tube length by inserting the moveable piston as shown in the upper
insert. The end of the piston rod that is outside the
tube should be supported to avoid putting excessive
strain on the piston.
➁ Set the frequency of the function generator to ap-
proximately 100 Hz, and the amplitude to zero,
then turn it on. Slowly raise the amplitude until you
hear a sound from the speaker.
➤ CAUTION: You can damage the speaker by
overdriving it. Raise the amplitude cautiously.
The sound from the speaker should be clearly
audible, but not loud. Note also that many
function generators become more efficient at
higher frequencies, so you may need to reduce
the amplitude as you raise the frequency.
➂ Turn on the oscilloscope and switch on the battery
powered amplifier. Set the sweep speed to approximately match the frequency of the signal generator
and set the gain until you can clearly see the signal
from the microphone. If you can’t see the microphone signal, even at maximum gain, adjust the frequency of the signal generator until the sound from
the speaker is a maximum. Then raise the amplitude of the signal generator until you can see the
signal clearly on the oscilloscope.
➃ You can now find resonant modes by adjusting the
frequency of the sound waves or the length of the
tube, and listening for a maximum sound and/or
watching for a maximum signal on the oscilloscope.
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SPEAKER INPUT
.1 W MAX
ON
ON
OFF
OFF
200 Mhz OSCILLISCOPE
BK PRECISION
MODEL 2120
INTENSITY
TRACE NOTATION
AC
DC
CH 1
POS
∞
FOCUS
TRIG LEVEL
-
MANUAL AUTO
NORM
CH1
EXT
EXT
CH2
VERTICAL MODE
CH 1 VOLTZ/DIV
CAL
V
mV
VAR VAR
PULL XS PULL XS
T X-Y
+
T X-Y
CH1
CH2
CH 2 VOLTZ/DIV
COUPLE SOURCE
AC
LINE
V
CH1
CH2
ALT
EXT
mV
X-POS
λ - Y
SLOPE
+
-
POSNORM
TIME/DIV
VAR SWEEP
AC
CAL
DC
CAL
CH4
∞
CH 2
CAL EXT
POWER
200V MAX
400V MAX400V MAX
Function generator
RANGE
HERTZ
PI-9587B
DIGITAL FUNCTION
GENERATOR - AMPLIFIER
ADJUST
WAVEFORM
AMPLITUDE
MIN
EXTERNAL
INPUT GND
OUTPUTFREQUENCY
TTL
HI Ω
GND
LO Ω
MAX
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WA-9612
RESONANCE TUBE
Oscilloscope
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SPEAKER INPUT
.1 W MAX
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ON
ON
OFF
OFF
Using the moveable piston to vary the
Using the microphone probe rod
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WA-9612
RESONANCE TUBE
tube length
Figure 2 Equipment Setup
2
012-03541E Resonance Tube
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➤ NOTE: In most textbooks, an open tube is
considered to be a tube that is open at both ends.
A closed tube is considered to be a tube that is
closed at one end and open at the other. In
keeping with this convention, the speaker and
microphone should be postioned several centimeters back from the end of the tube, so the microphone/speaker end of the tube is open.
If a resonance mode is excited in the tube, a pressure
antinode (a displacement node) will always exist at a
closed end of the tube. An open end of the tube
corresponds, more or less, to a pressure node (a
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SPEAKER INPUT
.1 W MAX
ON
ON
OFF
OFF
CI-6502
POWER AMPLIFIER
CAUTION!
WHEN LIGHT IS ON
WAVEFORM IS DISTORTED.
DECREASE AMPLITUDE!
SIGNAL OUTPUT
0 to ±10 V
1 A MAX
+
PASCO
SERIES
6500
INTERFACE
SYSTEM
FOR USE WITH PASCO SERIES 6500 INTERFACES
ON
Figure 3
CI-6510
FOR USE WITH PASCO SERIES 6500 SENSORS
DIGITAL CHANNELS
1234
PASCO
SERIES
6500
INTERFACE
SYSTEM
SIGNAL INTERFACE
ON
ANALOG CHANNELS
A ▲
GAIN = 1,10,100
ISOLATED
B ■ C ●
=
GAIN
1
ISOLATED
GAIN = 1
REF TO GND
Using the Power Amplifier:
Connect the Power Amplifier DIN plug to channel C
of the Interface. Connect the output of the Power
Amplifier to the resonance tube speaker, but DO NOT
TURN THE POWER AMPLIFIER ON UNTIL YOU
HAVE SET THE OUTPUT AMPLITUDE FROM
WITHIN THE PROGRAM.
Connect the BNC plug on the resonance tube microphone to the BNC jack on the CI-6508 Input Adapter
Box, and the DIN plug on the Adapter Box to channel
A of the Interface. Turn the amplification select switch
on the CI-6508 to 100x. (See Figure 3.)
ANALOG INPUT
PASCO
SERIES
6500
INTERFACE
SYSTEM
Model CI-6508
INPUT ADAPTOR
FOR USE WITH PASCO SERIES 6500 INTERFACES
(±10V MAX)
tube.
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Start the program. (Consult your
manual for details on the operation of the program if necessary.) Set the output
to a 1 V sine wave, then turn the CI-6502
GAIN SELECT
X 100
X 10
X 1
Power Amplifier on. Show channel A and
NOTE: SWITCH
FUNTIONS ONLY WHEN
ADAPTOR IS
CONNECTED TO INPUT
MARKED ▲ ON THE
SIGNAL INTERFACE
channel C on the screen, so you can see both
the speaker output and the waveform in the
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WA-9612
RESONANCE TUBE
displacement antinode). However, the pressure node
will, in general, not be located exactly at the end of the
tube. You can investigate the behavior of the sound
waves near the open end using the microphone.
Using the Resonance Tube with the
PASCO Series 6500 Computer Interface
There are two ways of using the PASCO Series-6500
Computer Interface with the resonance tube, depending on whether you intend to drive the resonance tube
with the CI-6502 Power Amplifier or with a separate
function generator.
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SPEAKER INPUT
.1 W MAX
ON
ON
OFF
OFF
HERTZ
PI-9587B
DIGITAL FUNCTION
GENERATOR - AMPLIFIER
RANGE
ADJUST
WAVEFORM
INPUT GND
AMPLITUDE
MIN
EXTERNAL
OUTPUTFREQUENCY
TTL
HI Ω
GND
LO Ω
MAX
PASCO
SERIES
6500
INTERFACE
SYSTEM
Figure 4
CI-6510
SIGNAL INTERFACE
FOR USE WITH PASCO SERIES 6500 SENSORS
DIGITAL CHANNELS
1234
ON
ANALOG CHANNELS
A ▲
GAIN = 1,10,100
ISOLATED
B ■ C ●
=
GAIN
1
ISOLATED
GAIN = 1
REF TO GND
Using a Function Generator:
Connect the BNC plug on the Resonance tube microphone to the BNC jack on the CI-6508 Input Adapter
Box, and the DIN plug on the Adapter Box to channel
A of the Series-6500. Turn the amplification select
switch on the CI-6508 to 100x.
If you have a CI-6503 Voltage Sensor, use it to link
the function generator and channel B of the CI-6500.
(This step is optional; it allows you to use the function
generator for triggering, with slightly improved
results.) See Figure 4.
Start the program. (Consult your manual for details on
the operation of this program if necessary.) In oscillo-
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scope mode, set triggering to automatic
on channel B. Show channels A and B
on the screen, and find the resonances you are
interested in. If you wish, turn on the fre-
GAIN SELECT
X 100
quency analysis option (FFT) and observe the
X 10
X 1
NOTE: SWITCH
FUNTIONS ONLY WHEN
ADAPTOR IS
CONNECTED TO INPUT
MARKED ▲ ON THE
SIGNAL INTERFACE
frequencies that are contributing to the stand-
ANALOG INPUT
(±10V MAX)
PASCO
SERIES
6500
INTERFACE
SYSTEM
Model CI-6508
INPUT ADAPTOR
FOR USE WITH PASCO SERIES 6500 INTERFACES
ing wave.
(*Available only for the Macintosh
MS-DOS version of the Data Monitor.)
3
®
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and for the
WA-9612
RESONANCE TUBE
Resonance Tube 012-03541E
Waves in a T ube Theory:
Sound Waves
When the diaphragm of a speaker vibrates, a sound
wave is produced that propagates through the air. The
sound wave consists of small motions of the air
molecules toward and away from the speaker. If you
were able to look at a small volume of air near the
speaker, you would find that the volume of air does
not move far, but rather it vibrates toward and away
from the speaker at the frequency of the speaker
vibrations. This motion is very much analogous to
waves propagating on a string. An important difference is that, if you watch a small portion of the string,
its vibrational motion is transverse to the direction of
propagation of the wave on the string. The motion of a
small volume of air in a sound wave is parallel to the
direction of propagation of the wave. Because of this,
the sound wave is called a longitudinal wave.
Another way of conceptualizing a sound wave is as a
series of compressions and rarefactions. When the
diaphragm of a speaker moves outward, the air near
the diaphragm is compressed, creating a small volume
of relatively high air pressure, a compression. This
small high pressure volume of air compresses the air
adjacent to it, which in turn compresses the air adjacent to it, so the high pressure propagates away from
the speaker. When the diaphragm of the speaker moves
inward, a low pressure volume of air, a rarefaction, is
created near the diaphragm. This rarefaction also
propagates away from the speaker.
In general, a sound wave propagates out in all directions from the source of the wave. However, the study
of sound waves can be simplified by restricting the
motion of propagation to one dimension, as is done
with the Resonance Tube.
Standing Waves in a Tube
Standing waves are created in a vibrating string when
a wave is reflected from an end of the string so that the
returning wave interferes with the original wave.
Standing waves also occur when a sound wave is
reflected from the end of a tube.
A standing wave on a string has nodes—points where
the string does not move—and antinodes—points
where the string vibrates up and down with a maximum amplitude. Analogously, a standing sound wave
has displacement nodes—points where the air does not
vibrate—and displacement antinodes—points where
the amplitude of the air vibration is a maximum.
Pressure nodes and antinodes also exist within the
waveform. In fact, pressure nodes occur at displacement antinodes and pressure antinodes occur at
displacement nodes. This can be understood by
thinking of a pressure antinode as being located
between two displacement antinodes that vibrate 180°
out of phase with each other. When the air of the two
displacement antinodes are moving toward each other,
the pressure of the pressure antinode is a maximum.
When they are moving apart, the pressure goes to a
minimum.
Reflection of the sound wave occurs at both open and
closed tube ends. If the end of the tube is closed, the
air has nowhere to go, so a displacement node (a
pressure antinode) must exist at a closed end. If the
end of the tube is open, the pressure stays very nearly
at room pressure, so a pressure node (a displacement
antinode) exists at an open end of the tube.
Resonance
As described above, a standing wave occurs when a
wave is reflected from the end of the tube and the
return wave interferes with the original wave. However, the sound wave will actually be reflected many
times back and forth between the ends of the tube, and
all these multiple reflections will interfere together. In
general, the multiply reflected waves will not all be in
phase, and the amplitude of the wave pattern will be
small. However, at certain frequencies of oscillation,
all the reflected waves are in phase, resulting in a very
high amplitude standing wave. These frequencies are
called resonant frequencies.
In Experiment 1, the relationship between the length of
the tube and the frequencies at which resonance occurs
is investigated. It is shown that the conditions for
resonance are more easily understood in terms of the
wavelength of the wave pattern, rather than in terms of
the frequency. The resonance states also depend on
whether the ends of the tube are open or closed. For
an open tube (a tube open at both ends), resonance
occurs when the wavelength of the wave (l) satisfies
the condition:
L = nl/2, n = 1, 2, 3, 4,….
where L = tube length.
These wavelengths allow a standing wave pattern such
that a pressure node (displacement antinode) of the
4
012-03541E Resonance Tube
wave pattern exists naturally at each end of the tube.
Another way to characterize the resonance states is to
say that an integral number of half wavelengths fits
between the ends of the tube.
For a closed tube (by convention, a closed tube is open
at one end and closed at the other), resonance occurs
when the wavelength of the wave (l) satisfies the
condition:
L = nl/4, n = 1, 3, 5, 7, 9,….
These wavelengths allow a standing wave pattern
such that a pressure node (displacement antinode)
OPEN TUBE
N
A A
Fundamental: Open tube
A
occurs naturally at the open end of the tube and a
pressure antinode (displacement node) occurs naturally
at the closed end of the tube. As for the open tube, each
successive value of n describes a state in which one
more half wavelength fits between the ends of the tube.
➤ NOTE: The first four resonance states for open
and closed tubes are diagramed below. The first
resonance state (n = 1) is called the fundamental.
Successive resonance states are called overtones. The
representation in each case is relative displacement.
N
N
AA
1st Overtone: Open tube
A
CLOSED TUBE
N
N
N
N
A
2nd Overtone: Open tube
Fundamental: Closed tube
N
A
2nd Overtone: Closed tube
A
Resonance States:Open and Closed Tubes
A
N
N
A
A
A
A
N
N
N
N
A
3rd Overtone: Open tube
A
A
1st Overtone: Closed tube
N
A
3rd Overtone: Closed tube
A
N
N
N
A
A
N
A
A
N
A
5
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