vibrating cords _lesson plan

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

VIBRATING CORDS

Lesson Plan

Prof. Ethel Mazur Camargo Lopes Lima

11th grade students from E.E. José Chaluppe

Willian Silva Balbini Jonatas Fogaça Montenegro

Supervision Prof. Marisa Almeida Cavalcante (PUC/SP) e Prof. Cristiane R. C. Tavolaro

July 2009

(PUC/SP)

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

Objectives Take to High School students Physics experiments, aiming at the incentive and students' learning in the area of Physics.

To study the resonance of a vibrating cord fixed on the extremities.

Content Inserted in São Paulo State's new curriculum proposal 11th grade: Sound, image and communication • wave motion • Frequency; wavelength; amplitude of a wave; resonance.

Competences and abilities Representation and communication • Use and understand tables, graphs and graphic mathematical relationships to express physics knowledge.

• Express oneself correctly using the appropriate physics language and elements of its symbolic representation.

Investigation and understanding • To know and use physics concepts. Relate magnitudes, quantify and identify relevant parameters. Understand and use physics laws and theories.

• Build and investigate problems, identify the physics situation, use physics models, generalize from another situation, foresee, evaluate, and analyze prediction.

Socio-cultural and historical perception • To relate through written language experiments and questions relative to the identification of the relationship between magnetic field and electrical field; identify electromagnetic phenomena, establish relationships and identify regularities; use procedures and observation instruments, represent experimental results, elaborate hypotheses and interpret results in situations that involve electromagnetic phenomena.

Activity Number of classes necessary for the activity: 5 classes First class Theory development: wave; amplitude; frequency; propagation speed; wavelength.

Explain the objective of the experiment and its relationship with daily life.

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

A stretched cord with known density and tension is excited by the movement of one of its extremities, fixed to the nucleus of a speaker. The computer works as a frequency generator, controlling the signal applied to the speaker through its amplification system. It allows us to show the formation of stationary waves in the successive resonance frequencies and the quantitative relationship between frequency and the number of antinodes or nodes of the stationary wave formed in the cord. It also allows us to demonstrate the relationship between speed of the wave, density of the cord and traction.

Second class Assembly of the experiment.

Materials 1. Generation of signals software "Sine Wave Generator" (available on the internet) 2. Speaker 3. Speaker linked to Classmate PC 4. Wood base, with a graduated scale 5. Cord attached to a weight (connected to the speaker) 6. pulley 7. Classmate PC 3

1 7

5 6

2 4

Illustration 1: block diagram of the assembly.

Procedure for assembly of the equipment and details of its operation The audio signals with variable frequencies are obtained from the software "sine wave generator", available on the internet. Illustration 3 shows the screen that is observed on this software.

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

Illustration 2: Screen observed in the version for windows 98 of the software "sine wave generator" that allows to vary the frequency of vibration of the cord every 1 Hz.

A PVC pin was glued to the speaker (illustration 2) so that one can tie a string on its extremity. The speaker fits on a graduated wood rail.

Illustration 3: Inner speaker taken from one of the speakers. PVC pin attached to the speaker's membrane. The pin has a hole for us to tie the string.

In the audio exit of the Classmate PC we used computer speakers with an amplifier (with volume control) and the vibration is obtained from one of the inner speakers that was taken from one of the speaker's box.

The cord fixed on the PVC pin vibrates with the same frequency of the signal produced in the speaker. On the other extremity, a weight stretches out the cord that passes by a pulley. Fixing

PontifĂ­cia Universidade CatĂłlica de SĂŁo Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

a length for the cord, we can vary the vibration frequency to obtain different conditions of resonance on the cord. Illustration 4 displays one of the resonance patterns in which can distinguish antinodes and nodes.

Illustration 4: Stretched cord in resonance with the frequency imposed by the virtual generator: we can see the second harmonic with two antinodes and three nodes (we have a node in each fixed extremity, that is why three nodes in total).

Third Class Registration of the data obtained.

Experimental procedure 1. Put the speaker on the wooden base, so that the rope passes by the pulley, leaving the weight hanging on the other extremity (Illustration.1).

2. Fix and take notes of the distance of the extremity fixed on the speaker to the pulley, in other words, the length L of the cord.

3. Connect the speaker to the Classmate PC'S sound exit, set volume to maximum.

4. Open the generating signals software. Click on "mute" and leave the button "level" in 255. To vary the frequency, select the key 4 - 40 Hz and adjust the value with the + and - keys, until a stationary wave is visualized in the rope with an antinode. Take notes on the table below, the number of antinodes, the wavelength and the corresponding frequency.

5. Increase the frequency until two antinodes are obtained. Take notes on the table below, the frequency, the number of antinodes and the corresponding wavelength.

6. Obtain the other harmonic frequencies, increase the frequency gradually and write down its value for each resonance condition, forming antinodes and nodes. Take notes on table 1 below, the frequency, the number of antinodes and the corresponding wavelength.

7. Turn on the audio generator and vary the frequency until a stationary wave is formed on the rope. Count the number of antinodes of the formed wave. Continue to vary the frequency and, observe the resonances, build Table 1. To finish table 1, calculate the wavelength in each case.

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

8. Fix the corresponding frequency to the stationary wave with four antinodes.

9. Keeping the frequency constant, slide the speaker on the wooden base to reduce the length of the cord until three, two and one antinodes are successively obtained. Measure with a ruler directly on the cord and write the values down on table 2 below; the length of the cord and the wavelength in each case.

Fourth and fifth class Assembly of tables and graphs using the data obtained and analysis of the results.

Table 1 – Length of the cord L= 28,5 cm Frequency

Number

(Hz)

antinodes

of Wavelength (cm)

52

1

54,8

100

2

28,5

150

3

19

200

4

14,25

Illustration 5 shows the graph of the frequency over the wavelength and its corresponding function.

Illustration 5: Graph of the frequency of vibration of the cord over the wavelength.

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

Analysis of the result: The speed remains constant in the same condition, in other words, we are using the same cord and the same traction, what is varying is the length of the rope.

The wavelength and the length of the rope will have the same value, for 2 antinodes.

Observing table 1, we see that the length of the rope is fixed: L = 28,5 cm. In this case the wavelength will be equal to 28,5 cm as well.

N = nodes

V = antinodes

Illustration 6: In that vibration condition, the wavelength coincides with the length of the rope. Two antinodes correspond to a complete wave.

Therefore, we can obtain the speed of the wave in the cord doing: v=f.λ according to the table, for us to obtain 2 antinodes the value for frequency was 100 Hz, then v = 100 . 28,5 v = 2850 cm/s The value of the speed will always be the same, as we didn't change the rope or the traction. Therefore, for f = 52 Hz we will have v=f.λ v = 52 . 54,8 v = 2850 cm/s Illustration 7 shows the graph of the frequency over the number of antinodes that appear in the vibrant cord.

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

Illustration 7: Graph of the frequency of vibration of the cord over the number of antinodes.

Analyzing the graphs on illustrations 5 and 7 it is possible to notice that: 1. Finding the fundamental frequency of the cord (1 antinode), the others will all be whole multiples of the first.

2. The more the frequency increases, the smaller the wavelength, that is, they are inversely proportional.

3. The number of antinodes is proportional to the frequency.

Table 2 – Initial length of the cord L= 40 cm and f=140 Hz

1 antinode Length of the 9,5

2 antinodes

3 antinodes

4 antinodes

23,5

33,5

40

23,5

22,4

20

cord (cm) Wavelength (cm) 19

When observing the results of table 2 we see that if the frequency is fixed, the wavelength is practically constant, independent of the number of antinodes that appear in the cord.

EVALUATION

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

The evaluation of the work can be made through: • The analysis of the graphs obtained; • The composition and presentation of the reports; • Students' manifestations during the activities, in terms of posture towards their friends and their teacher, that is, the students' involvement in it.

Final considerations In this experiment we used the computer and low cost electronic components to find the resonance frequency. The appeal that the use of the computer exerts on adolescents favors the interest for the accomplishment of the experiment and a more significant learning of Physics concepts.

BIBLIOGRAPHY

Software “Sine Wave Generator" http://www.electronics-lab.com/downloads/pc/005/index.html accessed on 13/08/2009.

Project’s Blog: http://picintel-profethel.blogspot.com/ accessed on 13/08/2009.

Music and Speech Physics course’s Blog: http://fisica-cogeae-pucsp.blogspot.com/ accessed on 13/08/2009.

CAVALCANTE. M.A. TAVOLARO,R.C. Ondulatória e Acústica através de Experimentos Assistidos por computador, I X EPEF http://www.sbf1.sbfisica.org.br/eventos/epef/ix/atas/posteres/po5139.pdf LIBÂNEO, J. C., Didática. Coleção Magistério, Série formação do professor, Cortez Editora, São Paulo, 1994.

ALMEIDA, R de; FALCÃO, D; Brincando com a Ciência. Experimentos Interativos de Baixo Custo.

Museu de Astronomiae Ciências Afins, Rio de Janeiro: MAST, 1996.

CARVALHO, I. M. O Processo Didático. 6ª edição. Editora Fundação Getúlio Vargas, 1987.

CARVALHO, A. M. P; PEREZ, G. D. Formação de Professores de Ciências. Editora Cortez, São Paulo, 1993.

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

GREF, Grupo de Reelaboração do Ensino da Física, Física 2 e 3. Edusp, São Paulo, 2002.