genphylab manual 1 8

7/31/2019 GenPhyLab Manual 1 8

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Experiment No. SupplementManual

1 - 8 Ch. 15

Introductory Physics Office, Dept. of Physics, Korea Univ. (Last Update : 2012-05-09) PAGE 1/5

Understanding of Standing Wave Resonance Modes and

Wave Propagation Velocity on the Stretched String

1. Objective

Understanding the standing wave characteristics of a string fixed at both ends occurring from a sonometer device. Also calculating

the wave speed of the string by measuring the change of the strings frequency while changing the strings density and tension.

2. Theory

(1) The speed of waves on strings

Fig. 1 The wave passing through the string.

We can imagine the wave passing through the string as a part

of a circle as in the Fig. 1. If we assume that the line has a

uniform density , then for a length of the string we can

have the following relation for of the mass:

.

If we apply Newtons Law along the radial direction of , and

find the force of the same direction for Tension T, we can find:

sin

When is small, the speed of a wave passing a string is

. (Eq. 1)

(2) Standing waves

Fig. 2 Incident pulse and reflect pulse at the fixed end.

Wave transmission and reflection occur at the medium boundary

of the wave. When the medium (string) is fixed at its end, and

a pulse enters the string, then reflected wave at the fixed end

of the string changes its phase by as in the Fig 2.

When a sinwave enters a string fixed at both ends, two sin

waves traveling the opposite direction superpose each other

which creates constructive interference as follows:

sin

sin

sincos

(Eq. 2)

is not a function of , so it is not a traveling wave

expression, but it is a simple harmonic wave with an amplitude

of sin. Here, every point in the medium has the same

circular frequency , and the amplitude changes according to

the position of which follows sin .

(3) Standing waves in a string fixed at both ends

Fig. 3 The standing wave on the string fixed at both ends.

Since both ends of the string is fixed, a node must be made,

and the standing wave will occur when the below boundary

condition is satisfied. The relation between the length of the

string and the natural modes wave length will be as so:


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1 - 8 Ch. 15


Fig. 4 The standing waves on the string fixed at both ends with

different modes.

Generally, a wave satisfies the relation

, so the natural

modes frequency will be , and if we substitute

Eq. 1 in, we get

(Eq. 3).


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1 - 8 Ch. 15


3. Experimental Instruments

Items Amount Usage Arrange

Sonometer base with tension

lever1 set Makes stretched strings with different tension.

Place at the center of the

experiment table.

Wires 3 ea.Makes stretched strings with different linear mass

densities.

Place inside the basket of the

experiment table.

Bridges 2 ea. Makes stretched strings with different string length. Place on the sonometer.

Hanging mass 1 set Applies tension on a stretched string.Place inside the basket of the

experiment table.

Driver coil 1 ea.Generates waves on the stretched string with different

frequency.


experiment table.

Detector coil 1 ea.Measures the resonance frequency of standing waves

on the stretched strings.


experiment table.

BNC adaptor 1 eaConnects the detector coil to the voltage sensor

cable.


experiment table.

Voltage sensor cable 1 eaConnects the detector and the voltage sensor cable

to SW750.


experiment table.

Computer 1 set Acquires and analyzes data.Place at the center of the

experiment table.

Science Workshop750 interface

(SW750)

1 setSends generation signals to the driver coil and

receives frequency information from the detector coil.

Place at the center of the

experiment table.

SW750

-to-power adaptor &

connection cable

1 ea. Supplies power to SW750.Place inside the basket of the

experiment table.

USB cable 1 ea. Connects SW750 to a computer.Place inside the basket of the

experiment table.


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4. Experimental Procedures

(1) Setting the sonometer

1) Choose one of the strings and place the brass string retainer

in the slot on the tension lever. Never press the tension lever

with strong pressure. Loosen the string adjustment screw and

place the crimped lug that is attached to the other end of the

string. Tighten the string adjustment screw until the tension

lever hangs level.

2) Place bridges on the sonometer base in any distance to

determine the length of string.

3) Hanging the mass from the tension lever to apply thedesired tension, then adjust the string adjustment screw as

needed so that tension lever is level. The string tension is

determined as shown in the below figure. If you hang a mass

"M" from one of the level lever, the tension of string is equal

to Mg. g is gravitational constant ms . If you hang the

mass from slot two, the tension is equal to 2Mg.

4) Place the drive coil about cmfrom one of the bridges and

place the detector coil near the center of string. Connect the

two plugs on the drive coil to the "output" of SW750. Connect

the voltage sensor, BNC adaptor and drive coil output. Connect

the voltage sensor cable to channel A.

5) Start the Data Studio program. In the Experiment Setup

window, click-and-drag the analog sensor plug icon to channel

A. Select "Sound Sensor" from the list of sensors. To view the

data, click-and-drag a Scope display to the Sound Sensor icon.

Set the function generator to produce a sine wave. Slowly vary

the frequency of the function generator output. When you reach

a resonance frequency, you can see the motion of string and

hear the sound produced by the vibrating string.

Note : The driven frequency of the signal sensor may not be

the frequency at which the wire is vibrating. By overlaying the

driving frequency and vibrating frequency, you can see the

vibrating frequency is a multiple of the driving frequency.


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(2) Measurement of the resonance frequencies

1) Setup the sonometer with the wire1 ( kgm),

tension N, and m.

2) Slowly increase the frequency of the signal to the driver coil.

Listen for an increase in the volume of the sound from the

sonometer and/or an increase in the size of the detector signal

on the screen. Frequencies that result in maximum string

vibration are resonant frequencies. Determine the lowest

frequency at which the resonance occurs. This is resonance in

the first, or fundamental, mode. Measure this frequency and

record it.

3) Continue increasing the frequency to find the second and

third successive resonant frequencies. Record the resonance

frequency for each mode.

4) Change the string length m, by moving one of

bridges, and find the second successive resonant frequency.

Record the resonance frequency.

5) Change the string length , by moving one of



6) Change the tension to N, and the string length to

. Repeat the resonance frequency measurement

procedure from 2) ~ 5).


m. Repeat the resonance frequency measurement


8) Setup the sonometer with the wire2 kgm ,

tension N, and m. Find the second

successive resonant frequency. Record the resonance frequency.





bridges, and find the second successive resonant frequency.Record the resonance frequency.

11) Change the tension to N, and the string length

to m. Repeat resonance frequency measurement



m. Repeat resonance frequency measurement


13) Setup sonometer with the wire3 kgm,

tension N, and m. Repeat resonance

frequency measurement procedure from 9) ~ 10).


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Experiment No. SupplementPreliminary Report

1 - 8 Ch. 15


Understanding of the Standing Wave Resonance Mode and Speed on the

Stretched String

Student's

Mentioned

Items

Student ID Major Name Team Experiment Date

Lecturer Submission Place Submission Time

Lab D, E, F, 2nd Floor,

College of Engineering #2 Building

Students should write the Preliminary Reports in terms of the following sections and complete it by adding contents to the

attached papers. Contents of the Preliminary Reports should be written by hand, and not by a word processor. Attaching copied

figures and tables to the report is allowed. The Completed Preliminary Reports should be submitted to the Experiment Lecturer in the

laboratory at the beginning of the Experiment Class.

Section Note

1. Objective

2. Theory

General Physics Laboratory - Manuals and the following Chapters of Supplement can

be used as references when writing the Theory and Experiment sections.

Ch. 15 "Waves"

3. Experiment

4. Reference

Lecturer's

Mentioned

Items

Submission Place/Time Check Preliminary Report Points Evaluation Completion Sign

15


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Experiment No. SupplementResult Report

1 - 8 Ch. 15


Understanding of the Standing Wave Resonance Mode and Speed on the

Stretched String

Student'sMentioned

Items

Student ID Major Name Team Experiment Date

Lecturer Submission Place Submission Time

Introductory Physics Office

Report Box #

Students should write the Result Report in terms of the following sections and complete it by filling the Result and Discussions

and Solutions of Problems. Contents of the Result Reports should be written by hand, not by a word processor. Attaching copied

figures and tables to the report is allowed. The Completed Result Reports should be submitted to the place and at the time

specified by Experiment Lecturers

Section Note

1. Experimental ValuesDuring the Experiment Class, students should measure and calculate the experimental

values except for complicated tables or graphs in the Experimental Values section.

2. Results & Discussions

Students should complete the Result Reports by finishing the complicated tables or

graphs that were omitted in the Experiment Class and adding the Results and

Discussions section. Completed Result Reports should be submitted to the place and

at the time specified by Experiment Lecturers.

3. Solutions of ProblemsIf Problems in Result Reports are assigned, students should complete the Result

Reports by adding Solutions of the Problems.

4. Reference

Lecturer's

Mentioned

Items

Submission Place/Time Check Result Report Points Evaluation Completion Sign

40


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1 - 8 Ch. 15


1. Experimental Values

(1) Measurement of the resonance frequency of a stretched strings

Mass of the hanging mass ()

Linear

density

of the

string

kgm

Tension

N

Length of

the string

m

Number

of

anti-

nodes

Wave

length

m

Driven

frequency

Hz

Resonance

frequency

Hz

Speed of wave

Experimental

ms

Reference

ms

Wire 1

(0.022)


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1 - 8 Ch. 15


Linear

density

of the

string

kgm

Tension

N

Length

of the

string

m

Number

of

anti-

nodes

Wave

length

m

Driven

frequency

Hz

Resonance

frequency

Hz

Speed of wave

Experimental

ms

Reference

ms

Wire 2

(0.017)

Linear

density

of the

string

kgm

Tension

N

Length

of the

string

m

Number

of

anti-nodes

Wave

length

m

Driven

frequency

Hz

Resonance

frequency

Hz

Speed of wave

Experimental

ms

Reference

ms

Wire 3

(0.010)


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(2). Analysis plots

a). Resonance frequency vs Number of anti-nodes

kgm, and m

Tension N

Number of anti-nodes

Resonance frequency

Hz

Slope Hz

-intercept

-intercept Hz


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b). Resonance frequency vs the inverse of the string length.

kgm, and

Tension N

Length of a string m

Inverse of length

m

Resonance frequency

Hz

Slope Hzm

-intercept m

-intercept Hz

N and

Linear density of the

string kgm

Length of the string

m

Inverse of length

m

Resonance frequency

Hz

Slope Hzm

-intercept m

-intercept Hz


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c). Resonance frequency vs square root of tension on the string

kgm, and .


m

Tension N

Square root of Tension

N

Resonance frequency

Hz

Slope HzN

-intercept N

-intercept Hz

m and .


string kgm

Tension N

Square root of Tension

N

Resonance frequency

Hz

Slope HzN

-intercept N

-intercept Hz


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d). Resonance frequency vs inverse of square root of the linear density of the string

N, and .


m


string kgm

Inverse of square root

of linear density

mkg

Resonance frequency

Hz

Slope

Hzmkg

-intercept

mkg

-intercept Hz


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m and .

Tension N


string kgm

Inverse of square root

of linear density

mkg

Resonance frequency

Hz

Slope

Hzmkg

-intercept

mkg

-intercept Hz


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e). Experimental wave velocity vs reference wave velocity

Slope

-intercept ms

-intercept ms


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Introductory Physics Office Dept of Physics Korea Univ (Last Update : 2012 05 09) PAGE 10/10

2. Results and Discussions (This page should be used as the first page of Results and Discussions section. If the contents of Results

and Discussions exceed this page, additional contents should be written by attaching papers. Contents of Results and Discussions

should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.)

genphylab manual 1 8

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