Sound Spectrum -Lesson Plan

Pontifícia Universidade Católica de São Paulo

Junior Scientific Initiation in PUC/SP and the development of experimental activities in Physics

using the Classmate PC

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Lesson Plan

Author: Prof. Alessandro Washington Daniel (E.E. José Chaluppe)

11th

grade students from E.E. José Chaluppe

Bruna Alves Freires Teixeira

Oscar Hugo Lunguinho Falchetto

Jonny Antunes Machado

Supervision Prof. Marisa Almeida Cavalcante (PUC/SP) e Prof.

Cristiane Rodrigues Caetano Tavolaro (PUC/SP)

July 2009




Introduction

The purposes of Physics teaching in High School indicate as objectives to take the students

to understand the concepts, procedures and physical strategies that allow them to develop

subsequent studies and to acquire general scientific formation, applying their knowledge to

several situations, using them in the interpretation of Science, in technological and in daily

activities.

It is important to recognize that the pupils have the intention to learn, but perhaps not

what the school currently intends to teach them. That is, the education project many times has

little to see with the learning project.

Thus, what Physics must search in high school is to assure that the inquiry ability rescues

the inquiry spirit, the desire to know the world we inhabit. Not only in a pragmatic way, as

immediate application, but expanding the understanding of the world, in order to consider new

questions and, perhaps, to find solutions.

It is in that perspective that we propose this activity in that specific contents related to

Acoustic Physics will be approached, so that to understand a little more "how things work."

Through this Kit it will be possible to establish assemblies, that will allow us to study in

detail the resonance phenomena in resonant tubes, The sound wave generators and the resonant

spectra analyzers are obtained from shareware versions and free from softwares. Several

measures can be made from the determination of the speed of the sound to detailed studies of

different resonant spectra in multiple experimental conditions such as open tube, closed tube in

one of the extremities, in both extremities and different lengths. All activity was articulated in a

way to make possible to develop competences and abilities as:

To understand that tables, graphs and mathematical expressions can be different forms of

representation of a same relationship, with potentialities and own limitations, to be able to

choose and to make use of the most appropriate language in each situation, besides translating

the meanings of those several languages amongst themselves.

To elaborate analytical reports, presenting and discussing data and results, be of

experiments or of critical evaluations of situations, making use, whenever necessary, of the

appropriate physical language.




Objectives

This work has as objective presenting some experimental resources developed to

understand topics of Waves and Acoustics and specially determine the speed of sound. Besides

the innovative methodology, we can highlight the versatility of the high technology equipment

and low cost. On the other hand, those resources allow a simple assembly and easy handling

Content

The contents approached in this activity make possible to treat the following structuring

themes:

Sound waves, image and communication treated in the 11th grade of High School.

Standards and Structuring Themes

This activity can be done in the 11th grade of High School

Structuring Theme 4: Sound, Image and Information (11th grade)

To place yourself in the contemporary world it is necessary to understand the current

communication means and information that have in their base the production of images and

sounds, their reception processes, their codes and registration forms and the re-establishment of

their signals in the receiving devices. To study those mechanisms means to propitiate

competences to understand, to interpret and to deal in an appropriate way with technological

apparatuses, like television, Cd and DVDs players, the computer, the movies or even photography.

Activity

RESONANT TUBES

The system of resonant tubes allows us to take measures of speed of the sound in the air,

measures of wavelengths through formation of observable stationary waves with cork powder




inside of the tube or through the harmonic components that integrate the resonant spectrum of

the resonance tube.

SOUND WAVES IN TUBES

The sound is a longitudinal mechanical wave, in other words, it needs a medium to spread

and its propagation has the same direction that the disturbance that caused it. The sound wave

spreads through air creating compression and rarefaction areas in the medium. The operation

principle of most of the wind instruments is the production of stationary sound waves inside the

tubes (known as tube of Kundt). Only waves with certain frequencies are reproduced that are

called natural frequencies of vibration, similar to the frequencies that can exist in a vibrating cord.

The possible stationary waves that are formed inside of a tube of length L, for instance, with one

closed extremity can be studied from the procedure proposed in this experiment.

Calculating the speed of sound

Number of classes needed for the activity: 4 classes

Materials used and its operation

Figure 1: General view of the assembling.

Classmate PC

Cork powder

Speaker

microphone

tube




First Class

- To explain the objective of the experiment, its relationship with the daily life

- To present the material used to accomplish the experiment;

- To explain the operation of each one of the materials.

a) Classmate PC, its function is to receive signals through the sound board and to send it to

the software.

Figure 2: Classmate PC that will be used in the data collection.




Figura 3: Tube that will be used.

b) Tube of Kundt, it is used to put the cork powder and reception of the sound for analysis.

c) Cork powder is used for visualization of the resonance in the resonant tube.

Figure 4: Cork powder




d) speakers, they are used for sound emission.

Figure 5: connected to the Classmate PC.

a) microphone, it is used to capture the sound.

Figure 6: Microphone to capture the sound produced in the tube.

Second class

Speaker




ASSEMBLY OF THE EXPERIMENT

- To set up the experiment;

- To do demonstrations;

- To hypothesize.

1. To turn on the Classmate PC and to access the software Gram v6 *

Figure 7: Classmate PC screen showing Gram V6.

1) Connect the microphone to the Classmate PC sound board

Figure 8: Connecting the microphone to the Classmate PC.

3) Get a 50 cm Kundt tube.




Figure 9: Kundt Tube.

Third class

ACCOMPLISHING THE EXPERIMENT

- Assembly and experimentation;

- Analysis to elaborate the calculation;

- Calculating the speed of the sound.

1) We connected the microphone to the Classmate PC with software Gram-v6 opened

Figure 10: Connecting the microphone to the Classmate PC and capturing the sound in the tube.

2) We leave the microphone close to the tube.




Figure 11: Microphone close to the tube.

3) According to the illustration hit hard the extremity of the tube, producing the sound.

Figure 12: Hitting the extremity of the tube.

4) Through the Software Gram-v6 *, we analyze the frequency spectrum.




L.4≡λ

λ

vf ≡

4

λ≡L

Figure 13: Analyzing the frequency spectrum.

To have access to the software go to: http://www.elektrosmog.de/Software/gram6.exe or

http://xviiisnefnovastecnologias.blogspot.com/2009/08/software-de-analise-

sonora-gram-v6.html

5) The stationary wave of smaller frequency that is formed, is also called fundamental wave,

corresponds to the largest possible wavelength in this tube. The illustration shows the air

movement inside the tube. It is noticed that the displacement of the air molecules that are

close to the closed extremity of the tube is zero (knot) and that the maximum

displacement happens in the open extremity. The Java* simulation that produced the

illustration integrates the work methodology adopted in the study of the resonant tube.

The wavelength in this case is related to the length L of the tube by

or

and the oscillation frequency can be calculated by




L

vf

.4≡

L

vf

.4≡

Therefore:

* For more information on Java on longitudinal waves access: http://www.walter-fendt.de/ph11br/stlwaves_br.htm

Closed tube in one extremity

Figure 14: it shows the maximum displacement of the air particles in the open side and representation of the

corresponding opening. On the closed side, a knot of displacement of particles http://www.walter-

fendt.de/ph11br/stlwaves_br.htm.

6) We calculate the speed of sound using the following formula:

Where:

- f : frequency

- v : velocity

- L : tube length

Fourth Class

Calculation and analysis

Visualization of the resonance with cork powder




scmv

v

v

35000

200.175

50.4175

=

=

=

L

vf

.4≡

Calculations

The experiment was accomplished with a frequency registered by the software of 175 Hz in

the first possibility (knot), where the measure of the tube was of 50 cm of length and 3cm of

diameter.

Using the formula

Data:

F = 175 Hz

V = We will find out

L = 50 cm

Therefore:

Students report:

The speed of sound is calculated in m/s, then we transformed 35000 cm/s in 350 m/s. the speed

of the sound propagates with a speed of 340 m/s at 15°C. That was what tried to prove. But the

objective is to get to a value that is as close as possible.

Visualization of the resonance with cork powder

For this visualization we will consider an open tube in the two ends and through the available

simulation at http://www.walter-fendt.de/ph11br/stlwaves_br.htm fastens the length of the tube

to 50 cm and verify the frequency to obtain the 1st harmonic:




Fig.15: frequency observed for the fundamental frequency of the tube equal to 344 Hz.

Now position the speaker in front of the tube and using the signal generator software connect the

sound port of the classmate PC to the speaker.

Put the cork powder inside the tube and spread along all its length.

Fasten in the generator the frequency in about 344 Hz and vary this value (start for instance with

320 Hz and increase gradually) and observe the cork powder. There will be a value for which the

powder will vibrate (only in the ends of the tube). This value for which the vibration is its

maximum correspond the resonance frequency of the tube, open in the two ends.




Figure16: Image of the signal generator screen: to download, the address is

http://xviiisnefnovastecnologias.blogspot.com/search/label/Sine%20Wave%20Gene

rator

When that happens we have:

Like this, we can also obtain the value of speed of propagation of the sound where:

F. frequency obtained for the resonance condition

L. length of the tube

Figure 17: Image in that the resonance is observed for the open tube in the two ends.




To think!!

1) If we increase the size of the tube will you expect to obtain a frequency of resonance larger

or smaller than the obtained value? *

2) The value obtained for the speed of sound can be corrected depending on room

temperature? *

*Access the link and check!!!!

http://www.cepa.if.usp.br/e-fisica/apoio/textos/a10.pdf

Links

• http://picintel-profalessandro.blogspot.com : Blog of the project where you will

find more details concerning the experiment.

• http://picjrintelpucsp.blogspot.com/: Blog of the program of the Junior Scientific

Initiation of PUC/SP in partnership with Intel

• http://xviiisnefnovastecnologias.blogspot.com/search/label/velocidade%20do%20s

om : Link to access to information on the acoustics kit.

• http://www.cepa.if.usp.br/e-fisica/apoio/textos/a10.pdf: Link to the article about the

determination of the speed of sound published in Physics in the School

• Sound spectrum analyzer: Gram V6. Author: Philip Van Baren

www.monumental.com/rshorne/gram.html or

http://xviiisnefnovastecnologias.blogspot.com/2009/08/software-de-analise-

sonora-gram-v6.html

• Java simulation. Longitudinal waves. Author: Walter Fendt

www.walter-fendt.de/ph11br/stlwaves_br.htm

• Signal generator

http://xviiisnefnovastecnologias.blogspot.com/search/label/Sine%20Wave%20Gen

erator




Reference

• (PCN) - Parâmetros Curriculares Nacionais Ensino Médio – Parte III – Ciências da Natureza,

Matemática e suas tecnologias, Apresentação pag. 203 à 218 e Conhecimentos em Física

pag. 229 à 237.

CAVALCANTE, M. A. e TAVOLARO, C. R. C. Medindo a Velocidade do Som. A Física na

Escola (suplemento da RBEF) v.4 n.1, maio de 2003.

• http://www.cepa.if.usp.br/e-fisica/apoio/textos/a10.pdf

• BARBETA, V. B. e MARZZULLI, C. R. Experimento Didático para Determinação da

Velocidade do Som no Ar, Assistido por Computador. RBEF vol. 22 no 4, dezembro de

2000.

OLIVEIRA, L. M.; VEIT, E. A. e SCHNEIDER, C. Site: Novas Tecnologias no Ensino de

Física http://www.if.ufrgs.br/cref/ntef/index.html

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Sound Spectrum -Lesson Plan