PASCO WA-9611, WA-9613 User Manual

Includes

Teacher's Notes

and

Typical

Experiment Results

Instruction Manual and
Experiment Guide for
the PASCO scientific
Model WA-9611, and 9613

SONOMETER

012-03489E

5/95

WA-9613

DRIVER

WA-9611

SONOMETER

WA-9613

DETECTOR

KEEP WEIGHTS AS NEAR TO FLOOR

AS POSSIBLE IN THE EVENT THE

SONOMETER WIRE SHOULD BREAK

CAUTION!

1.75 kg MAXIMUM
LOAD ON LEVER

100.5 Hz

© 1988 PASCO scientific $5.00

012-03489E Sonometer

T able of Contents

Section Page

Copyright, Warranty and Equipment Return......................................................ii

Introduction ......................................................................................................1

Equipment ........................................................................................................1

Setup and Operation..........................................................................................2

Using the Sonometer and the WA-9613 Driver/Detector Coils:

Sonometer w/WA-9613, Driver/Detector Coils ...........................................3

Sonometer and Driver/Detector w/PASCO Computer Interface ...................4

Power Amplifier w/Series 6500 Computer Interface .................................... 4

Power Amplifier w/CI-6550 or CI-6565 Computer Interface .......................4

Function Generator w/Series 6500 Computer Interface ................................ 5

Function Generator w/CI-6550 or CI-6565 Computer Interface ...................6

Replacing Sonometer Strings ............................................................................7

Theory of Waves on a Stretched String..............................................................8

Experiments:

Experiment 1: Resonance Modes of a Stretched String ........................ 11

Experiment 2: Velocity of Wave Propagation ......................................13

Suggested Research Topics ..............................................................................16

Teacher’s Guide...............................................................................................17

Technical Support ....................................................................Inside Back Cover

i

Sonometer 012-03489E

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-9611 Sonometer
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: Dave Griffith
Teacher’s guide written by: Eric Ayars

Address: PASCO scientific

10101 Foothills Blvd.
Roseville, CA 95747-7100

Phone: [phone]
FAX: [phone]
email: [e-mail]
web: www.pasco.com

ii

012-03489E Sonometer

Introduction

Introduction

The PASCO scientific Model WA-9611 Sonometer is an
enhanced version of the classic sonometer. You can per­form the standard, qualitative sonometer experiments,
varying the tension, length, and linear density of the string
and observing the effects on the pitch of the plucked string.
Also, you can perform quantitative experiments, verifying
the equations for wave motion on a string by adding the
WA-9613 Driver/Detector Coils, a function generator ca­pable of delivering 0.5 A of current, and an oscilloscope (or
a computer interface and power amplifier) where,

l = wavelength
L = length of string

Equipment

The WA-9611 Sonometer comes with the following
equipment (see Figure 1):

• Sonometer base with tensioning lever

• Two bridges

• 10 wires (guitar strings), 2 each of the following di­ameters (linear densities):

— 0.010" (0.39 gm/m)
— 0.014" (0.78 gm/m)
— 0.017" (1.12 gm/m)
— 0.020" (1.50 gm/m)
— 0.022" (1.84 gm/m)

Additional Equipment

To perform qualitative experiments, you will also need a
mass hanger and no more than 1.75 kg of mass to hang
from the tensioning lever.

Bridge

WA-9613

DRIVER

String

WA-9611

SONOMETER

WA-9613

DETECTOR

KEEP WEIGHTS AS NEAR TO FLOOR

AS POSSIBLE IN THE EVENT THE

SONOMETER WIRE SHOULD BREAK

n = number of antinodes
V = velocity of wave propagation
T = string tension
m = linear density of string
n = frequency of wave

The driver and detector coil can be placed anywhere along
the string. The driver coil drives string vibrations at any
frequency your function generator (or computer-compat­ible power amplifier) will produce. The detector coil allows
you to view the vibration of the string on your oscilloscope
or computer interface. With a dual trace oscilloscope or a
computer interface, you can examine phase differences be­tween the driving frequency and the string vibrations.

Recommended Equipment

If you wish to accurately measure the frequency and
wavelength of the string vibrations, you will also need:

• WA-9613 Driver/Detector coils

• CI-6550 or CI-6565 Computer Interface and a
Power Amplifier (CI-6552)

OR

• Series 6500 Computer Interface, CI-6508 Input
Adapter Box, and a function generator capable of
producing 0.5 A

OR

• dual trace oscilloscope and a function generator
capable of producing 0.5 A

Optional Equipment (for use with function
generator)

• banana plug patch cords and BNC-to-banana
adapter (for connecting the function generator to
the BNC connector on an oscilloscope)

Tensioning

lever

CAUTION!

1.75 kg MAXIMUM
LOAD ON LEVER

Sonometer base

Figure 1 The Sonometer and Suggested Accessories

1

Sonometer 012-03489E

Setup and Operation

To setup the sonometer (see Figure 2):

➀ Choose one of the ten strings and place the brass

string retainer into the slot on the tensioning lever.

➁ Loosen the string adjustment screw and place the

crimped lug that is attached to the other end of the
string over the screw head, as shown.

Crimped lug

Brass string retainer

➂ Tighten the string adjustment screw until the

tensioning lever hangs level.

➃ Place the bridges in any locations you wish, to deter-

mine the length of the string.

➄ Hang a mass (approximately 1 kg) from the tensioning

lever to produce the desired tension, then adjust the
string adjustment screw as needed so that the
tensioning lever is level. See Figure 3. (The lever must
be level to accurately determine the string tension
from the hanging mass.)

String tension is determined as shown in Figure 3. If
you hang a mass “M” from slot one of the lever, the
tension of the string is equal to Mg, where g is the
gravitational constant (9.8 m/s

2

). If you hang the mass
from slot two, the tension equals 2Mg; if you hang it
from slot three, the tension is 3 Mg, etc.

➅ You can now:

- Vary the tension of the string by hanging the mass
from different slots in the tensioning lever. (Always
adjust the string adjustment screw so the lever remains
level.)

String adjustment screw

Figure 2 Sonometer Setup

String tension (T)

Slot 1 2 3 4 5

Figure 3 Setting the Tension

Tensioning lever

Bridges

5Mg

4Mg

3Mg

2Mg

1Mg

Hanging

Mass

(mass = M)

(weight = Mg)

- Vary the length of the string by adjusting the distance
between the bridges.

- Vary the linear density of the string by changing
strings.

- Pluck the string to observe how each of these vari­ables effects the resonant frequency.

2

End plate

String

Adjustment

screw

Aluminum Cylinder

Figure 4 Reversing the End Plates

End plate

012-03489E Sonometer

➤NOTE: At some lab stations, you may want the
tensioning lever to hang over the left end of the
table instead of the right (see Figure 4). In this case,
you can switch the end plates so that, when per­forming the experiment, the metric scale will still
be right side up. To switch the endplates:

➀ Loosen the string adjustment screw and remove

the string.

➁ Unscrew the two screws that hold each end plate

onto the sonometer and remove the end plates.

➂ Slide the aluminum cylinder out of the slot.
➃ Slide the cylinder into the slot on the other end

of the sonometer, then switch the end plates.

Using the Sonometer and the WA-9613
Driver/Detector Coils:

Sonometer and Driver/Detector Coils with a function
generator and oscilloscope:

➀ Connect the Driver and Detector Coils to the function

generator and oscilloscope as shown in the diagram.
Connect the driver coil directly to the output of the
PASCO PI-9587B Digital Function Generator. Con­nect the detector coil directly to channel two of an os­cilloscope that has a BNC connector. You can use ba­nana plug patch cords and a BNC-to-banana plug
adapter to connect the output of the function generator
to channel one of an oscilloscope that has a BNC con­nector. (If you are using a single trace oscilloscope,
connect only the detector coil to the oscilloscope.)

➁ Position the driver coil approximately 5 cm from one

of the bridges.
Depending on the wave pattern you are trying to pro-

duce, you might want to place the driver at some other
position. It will drive the string best if it is placed at an
antinode of the wave pattern. However, if you place it
near one of the bridges, it will work reasonably well
for most frequencies.

➂ Position the detector midway between the bridges ini-

tially, though for some patterns you may want to repo­sition it to best pick up the signal. As with the driver
coil, it works best when positioned near an antinode of
the wave pattern.

➃ Set the gain on channel-one of the oscilloscope to 5

mV/cm. Adjust the oscilloscope so it triggers on the
signal from the function generator.

➄ Set the function generator to produce a sine wave. Set

the frequency to a value between 100 and 200 Hz. Ad­just the amplitude to about 5 V (approximately half of
maximum). Slowly vary the frequency of the function
generator output. When you reach a resonant fre­quency, you should see the motion of the string and
the sound produced by the vibrating string should be a
maximum. The wave pattern shown on the oscillo­scope should become a clean sine wave. If you can’t
see or hear the string, raise the amplitude of the func­tion generator output slightly and try again.

Driver coil Detector coil

WA-9613

DRIVER

FREQUEN

CY

HE
RTZ

PI-9587B
DIGITAL FUNCTION
GENERATOR ­AMPLIFIER

WAVEFO

RA
NGE

RM

EXTERN

AL

INPUTG

ND

AMPLITU

ADJU

ST

DE

M

MI

AX

N

Function generator

WA-9611

SONOMETER

OUTP

UT

TT
L

HI

Ω

G
ND

LO

Ω

WA-9613

DETECTOR

KEEP WEIGHTS AS NEAR TO FLOOR

AS POSSIBLE IN THE EVENT THE

SONOMETER WIRE SHOULD BREAK

200 Mhz OSCILLISCOPE

BK PRECISION

Channel 1 (trigger) Channel 2

Figure 5 Using the Driver and Detector Coils

CAUTION!

1.75 kg MAXIMUM
LOAD ON LEVER

INTENSITY

TRACE NOTATION

POS

AC

DC

CH 1

∞

400V

MODEL

MAX

2120

Oscilloscope

3

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 X­Y

T X­Y
LINE

CH1
CH2

CH 2
VOLTZ/DIV

V

COUPLE SOURCE

AC

mV

CH1

X-POS

λ - Y

SLOPE

+

CH2

-

ALT
EXT

POSNORM

TIME/DI
V

VAR SWEEP

AC

CAL

DC

CAL

CH4

CAL EXT

CH 2

∞

200V

POWER

400V

MAX

MAX

Sonometer 012-03489E

Table 1

Computer Interface Device to drive coil Software FFT?
Apple II AI-6501 Power Amplifier Power Amplifier (Apple II) no

Apple II AI-6501 function generator Data Monitor (Apple II) no
DOS - PC CI-6500 Power Amplifier Power Amplifier (MS-DOS) no
DOS - PC CI-6500 function generator Data Monitor (MS-DOS) yes
Macintosh CI-6550 Power Amplifier Science Workshop (Mac) yes
Macintosh CI-6550 function generator Science Workshop (Mac) yes
Windows - PC CI-6565 Power Amplifier Science Workshop (Windows) yes
Windows - PC CI-6565 function generator Science Workshop (Windows) yes
Windows - PC CI-6500 function generator Data Monitor (Windows) yes

Sonometer and Driver/Detector Coils with a PASCO
Computer Interface

There are several ways to use a PASCO Computer Inter­face with the sonometer. The method you use depends on
the kind of computer, the interface (e.g., CI-6500, CI­6550, etc.), the device to control the coil, and whether you
wish to do frequency analysis (Fast Fourier Transform or
FFT) of the standing waves. See Table 1.

Using the Power Amplifier with a Series 6500
Computer Interface:

➀ Connect the Power Amplifier DIN plug to channel C

of the interface. Connect the Sonometer Driver Coil to
the output of the Power Amplifier.

➤ CAUTION: Do not turn on the power amplifier
until you have set the output amplitude from within
the program.

➁ Connect the BNC plug on the Sonometer Detector

Coil 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 5.1.)

➂ Start the Power Amplifier program and set the output

to a 3-5 V sine wave; then turn on the power ampli­fier. Show channel A and channel C on the screen, so
you can see both the driving force and the resultant
motion of the wire.

➤ NOTE: The Power Amplifier program does not
have a frequency analysis feature (Fast Fourier
Transform or FFT).

Using the Power Amplifier with a CI-6550 or CI-6565
Computer Interface:

The Science Workshop program that comes with the CI-
6550 or CI-6565 interface allows you to do frequency
analysis (Fast Fourier Transform, or FFT) of the standing
waves. This can be used for an in-depth analysis of the
harmonics present in a standing wave, analysis of noise,
or observation of multiple simultaneous resonances.

➀ Connect the Power Amplifier DIN plug to channel C

of the interface. Connect the Sonometer Driver Coil to
the output of the Power Amplifier.

➤ CAUTION: Do not turn on the power amplifier
until you have set the output amplitude from within
the program.

CI-6502

POWER AMPLIFIER

FOR USE WITH PASCO SERIES 6500 INTERFACES

ON

CAUTION!

PASCO

SERIES

WHEN LIGHT IS ON
WAVEFORM IS DISTORTED.

6500

INTERFACE

DECREASE AMPLITUDE!

SYSTEM

Power Amplifier

KEEP WEIGHTS AS NEAR TO FLOOR

AS POSSIBLE IN THE EVENT THE

SONOMETER WIRE SHOULD BREAK

Interface

A ▲

ON

GAIN = 1,10,100

ISOLATED

WA-9613

DETECTOR

ANALOG CHANNELS

B ■ C ●

=

GAIN

1

ISOLATED

GAIN = 1

REF TO GND

CAUTION!

1.75 kg MAXIMUM
LOAD ON LEVER

ANALOG INPUT

PASCO

SERIES

6500

INTERFACE
SYSTEM

INPUT ADAPTOR

FOR USE WITH PASCO SERIES 6500 INTERFACES

(±10V MAX)

Model CI-6508

GAIN SELECT

X 100

X 10

X 1

NOTE: SWITCH

FUNTIONS ONLY WHEN

ADAPTOR IS

CONNECTED TO INPUT
MARKED ▲ ON THE
SIGNAL INTERFACE

SIGNAL OUTPUT

0 to ±10 V
1 A MAX

WA-9613

DRIVER

WA-9611

SONOMETER

CI-6510

SIGNAL INTERFACE

+

FOR USE WITH PASCO SERIES 6500 SENSORS

DIGITAL CHANNELS

1234

PASCO

SERIES

6500

INTERFACE
SYSTEM

Adapter Box

Figure 5.1 Using the Power Amplifier and Series 6500 Interface

4