Lab 5 - Standing wave.pdf

LAB 3: STANDING WAVE

EXPLORE STANDING WAVE IN STRING I. Learning Objectives 1. Explore transverse wave of a string. 2. Transverse wave generation is a function that depend to the drive frequency f. 3. Define the velocity of wave transmission.

II. Theory: Velocity of wave transmission relates with frequency f and wave-length by formula:

v -



 . f 

v is the velocity of wave or phase velocity. v depends on the strain (do cang) of string and some other parameter.

When 2 opposite of string connect fixed, the reflection of wave occurs on 2 opposite fixed points on the string. This makes standing wave appear at one frequency like standing oscilation. Distance between 2 wave nodes or anti-nodes (bung song) in series is half of wave –length. Only wave nodes generate fixed  points. With a standing wave with n anti-nodes in a string which’s length l, we have formula :

l -



n

 

2

 

(1)

With n = 1,2,3, …..

The frequency of anti-node in string is basic audio frequency Phase velocity v ( wave transmission velocity) is not change, (1) give us frequency of function generator.

 f n

v 

2s

n   (2)

In this experiment, a rubber string ho ld in vertical at 2 fixed points, it is drove to vibrate by a motor at a  beginning point of string. Frequency of driving is adjusted by a function generator.

III. Apparatus Orde

apparatu

Qt Qt

1

Rubber string

1

2

Motor

1

3

Function generator S12

1

4

Ruler

1

5

MF support

3

6

Steel bar 50 cm

3

7

Muti connector

1

8

MF connector

1

9

Green red couple wire, 100 cm

1

10

Digital Multimeter to measure frequency

1

IV. Experiment 4.1 Preparation:

Connect system like this image. - Fix motor STE to the bearer. Connect its wire line with a function generator. - Connect a rubber string with 75cm length with the oscilation bar of motor. Adjust the tight of the string by the position of bearer b. But it’s must not too tight - Connect function generator with the transformer’s o utput. - Use Digital Multi Meter, connect 2 probes of DMM with 2 pole of voltage output. Adjust DDM to measure frequency mode. - Set the voltage output of function generator U = 3Vpp, frequency x10Hz and in sine wave form.

4.2 Processing.

-

Adjust the string length l =75cm by moving the bearer. The string is tight a little.

-

Adjust function generator to have a standing wave with only 1 anti-node.

-

Increase frequency f step by step until find frequencies which have standing wave with number of anti-nodes n = 1,2,3,4,6. Adjust for the clearest standing waves.

-

Measure wave-length and fill to the t able.

-

Adjust the string length l = 80 cm by moving the bearer. Repeat this experiment with this length.

V.Report: Table1: String’s length l = 75 cm Order

Number of anti-nodes n

1

1

2

2

3

3

4

4

5

5

Frequency of function generator f(Hz)

Table2: String’s length l = 80 cm

-

Order

Number of anti-nodes n

1

1

2

2

3

3

4

4

5

5

Frequency of function generator f(Hz)

Give comments about the relative between frequency of function generator and number os antinode in the string. Compare with the formula (1)

-

Draw diagram of function frequency f n = a.n with n is the number of anti-node. Then calculate a  parameter.

-

With (2) we have a = v/2l. Then find the frequency of wave transmission in the string in each case.

-

Give comments about velocity of wave in each case.

VI. Questions 1. Explain the standing wave phenomena in the string 2. What are factors wave transmission velocity depends on?

EXPLORE STANDING WAVE IN SPRING I. Learning Objectives 1. Explore longitudinal wave in a spring. 2. Longitudinal wave generation is a function that depend to the drive frequency f. 3. Define the velocity of wave transmission in spring.

II. Theory: Explore the oscilation in a spring connect verticaly in bearer, 2 opposite pole connect to fixed points We have velocity of a oscilation relate with frequency f and wave-length by the formula: v



 . f 

(1)

v is call velocity of wave or phase velocity. v depends to the tight of spring and the structure of spring. When the spring connect to 2 fixed points, the reflection wave occurs in these points. Standing wave is generated in some frequency and look like a longtitidinal oscilation. Node and anti-node is the fixed  position in spring which are fixed compressed and slackened areas. Distnce between 2 node or anti-node in seri is a half wave-length. In standing wave with n anti-nodes in spring with length l, we have formula: l



n

 

2

 

(1)

With n = 1.2.3…

The frequency of anti-node in string is basic audio frequency Phase velocity v (velocity of wave transmission) is not changed, so (1) give us the frequency of function generator:  f n

v 

2s

n 

(2)

In this experiment, a spring connect vertically in bearer, and is driven to oscillate by a function generator which is connected to a pole of spring. We can adjust the driven frequency in function generator

III. Apparatus STT

Apparatus

SL

1

Large bearer

1

2

Small bearer

1

3

Steel bar 50cm

1

4

Steel bar 25cm

1

5

Connector

1

6

Ruler

1

7

Spring 4.5 N/m

1

8

Function generator

1

9

DMM

1

IV. Experiment 4.1. Preparation

Connect a system like this image - Connect 1 pole of spring to a higher bearer. Connect other pole to the oscilation generator. Connect oscilation generator to function generator. Keep spring not too tight. - Set up Function Generator to sine wave and frequency 0Hz. - Connect 2 probes of DMM to the output of function generator. Change to measure frequency mode.

4.2 Processing

- Turn the function generator on. - Increase frequency until you have standing wave in spring. A standing wave is a simplest oscilation with only 1 anti-node. Read and fill this frequency f 1 to table 3. Note: Adjust frequency to has clearest node and anti-node.

- Increase frequency of generator until you have 1 node and 2 anti-nodes in spring. This standing wave has frequency f 2. Read this value and fill to the table 3 - Increase frequency of generator until you have 2 nodes in the middle of spring. This standing wave has frequency f 3. Read this value and fill to the table 3 - Increase frequency of generator until you have maximum nodes in the middle of spring. Read this value and fill to the table 3 - Use ruler to measure the length of spring. Write value to table.

V.Report: - The length of spring: …………………. cm Table 3 Order

Frequency

1

f 1=…..

fn/f1

n

-

2

f 2=…..

3

f 3=…..

4

f 4=…..

Comment about the relation between frequency of generator and number of anti-node in spring. Copare with formula (1).

-

Draw diagram of function frequency f n = a.n with n is the number of anti-node. Then calculate a  parameter.

-

With (2) we have a = v/2l. Then find the frequency of wave transmission in the spring.

.

VI. Questions 5.1. Explain the standing wave phenomena in spring 5.2. Why are there errors of experiment ?