Lesson Plan & Lecture Assignment Guide

College Board Standards: https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap-physics-1-2-course-and-exam-description.pdf

Lesson Plan Template

Your Name: Rama Balachandran Your Mentor Teacher: Dr. Gordon Ramsay

Grade Level:  11, 12 Subject Area: AP Physics 1

Lesson Title: Standing Waves Lesson Length: 90 min

ENVISIONING THE LESSON

Big Idea (of Unit) Driving Question & / or Lesson Essential Question:

Waves can transfer energy and momentum from one place to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena.

Guiding Question: How can standing waves be understood as one of the fundamental mechanism of production of all speech and music ?

Standards Addressed:

EK 6.3.1 : standing waves are the result of the addition of incident and reflected waves that are confined to a region and have nodes and antinodes. Examples should include waves on a fixed length of string and both open and closed pipes;

The possible wavelengths of a standing wave are determined by the size of the region to which it is confined. ( and boundary conditions) a. A standing wave with zero amplitude at both ends can only have certain wavelengths. Examples should include fundamental frequencies and harmonics.b. Other boundary conditions or other region sizes will result in different sets of possible wavelength.

Lesson Objectives:

6.D.3.3: The  student  is  able  to  plan  data  collection  strategies,  predict  the  outcome  based  on  the  relationship under  test,  perform  data  analysis,  evaluate  evidence  compared  to  the  prediction,  explain  any  discrepancy  and, if  necessary,  revise  the  relationship  among  variables responsible for  establishing  standing  waves  on  a  string  or in  a  column  of  air. [SP  3.2,  4.1,  5.1,  5.2,  5.3] 6.D.3.4:The  student  is  able  to  describe  representations  and  models  of  situations  in  which  standing  waves result  from  the  addition  of  incident  and  reflected  waves  confined  to  a  region. [SP  1.2]6.D.4.1:The  student  is  able  to  challenge  with  evidence  the  claim  that  the  wavelengths  of  standing  waves  are   determined  by  the  frequency  of  the  source  regardless  of  the  size  of  the  region.  [SP  1.5,  6.1] 6.D.4.2:The  student  is  able  to  calculate  wavelengths  and  frequencies  (if  given  wave  speed)  of  standing  waves based  on  boundary  conditions  and  length  of  region  within  which  the  wave  is  confined,  and  calculate numerical  values  of  wavelengths  and  frequencies.  Examples  should  include  musical  instruments.  [SP  2.2]

Relevant Conceptual Info. (Prior knowledge of students; misconceptions; conceptual connections):

Wave properties – transverse and longitudinal waves Measurable wave characteristics- frequency, wavelength, amplitude, speed and phase representation of a wave – mathematical and graphical Mechanism of standing waves in strings- harmonics

Common Misconceptions:

Standing waves are not different from traveling waves; Maintaining standing waves does not require energy; Changing the wavelength of the wave changes the speed of the wave in the medium in a nondispersive

medium like air . The speed of sound in air is unaffected by pressure or temperature; Standing waves of any frequency can be set up in a given medium with boundary conditions; Nodes are points of minimum pressure;

Conceptual Connections:

The Human voice system is a complex sophisticated musical instrument; Singers use resonances to shape the vocal tract effectively to amplify the sound and produce the desired

effect; Speech therapy uses the knowledge of articulation of basic sounds in relation to shaping the lips and the

position of the tongue in training ; Spectral analysis of sounds helps develop our understanding of speech patterns and voice production; Standing waves can be used to understand quantization of electron orbits and eigen modes in quantum

mechanics The basic equation defining production of sound can be derived from fundamental principles of mass and

energy conservation in fluids.

Assessment Strategies (including Pre-, Formative, and Summative Assessment activities):

Pre-

Pretest: ( To establish fundamental understanding of wave characteristics)Students work in pairs; Each one draws a wave on a given gird and the partner measures relevant characteristics to write down the mathematical equation that can represent the wave; students then verify each other’s answers;

Formative: compare and contrast worksheet, worksheet on spectral analysis, worksheet on standing waves in open and closed tubes

Summative: experimental investigation

ENABLING THE LESSON*

Phase One: Engage the Learner

These activities mentally engage students with an event or question. Engagement activities capture students' interest and help them to make connections with what they know and can do. The teacher provides an orientation to the unit and assesses students’ prior understanding of the concepts addressed in the unit.

Learning experiences:student activity 1: Students are given an array of random materials. ( rubber band, paper clip, balloon, paper, straw, )They will work in pairs and come up with a simple mechanism of producing sound and a technique of varying one quality of the sound produced. This must be reproducible multiple times and the outcome must be predictable;

Student Activity 2: Students are now given such a device- a singing tube and they work in small groups conducting their own explorations on the device. They will record their observations

Reference : The singing tube Vs Human Vocal Instrument Handout

Differentiation Strategies:

Depth of investigation;

What’s the teacher doing?

Teacher walks around providing guidance in case students struggle in carrying through the investigations. Some guiding questions are :

How is sound produced ?

Can you produce different sounds ?

What characteristic of the sound changes ?

What are the general mechanisms of producing sound ?

What type of waves are formed in the tube ?

In what ways is this mechanism similar to setting up waves in a string and what ways is this different ?

Are you able to produce harmonics ?

What are the students doing?

1. Students will be brainstorming ideas on producing sound and mechanism of changing the characteristics of sound;

2. Each group will demonstrate their creative ideas with other groups in front of the class

3. Students will work in small groups exploring a singing tube. They are handed a singing tube and no instructions other than safety tips. Students get to whirl the tube and note down interesting observations and questions on the board for class discussion.

Phase Two: Explore the Concept

Next, students encounter hands-on experiences in which they explore the concept further. They receive little explanation and few terms at this point, because they are to define the problem or phenomenon in their own words. The purpose at this stage of the model is for students to acquire a common set of experiences from which they can help one another make sense of the concept. Students must spend significant time during this stage of the model talking about their experiences, both to articulate their own understanding and to understand another's viewpoint.

Learning experiences:

Compare and contrast activity: singing tube and human vocal instrument

Reference: The singing tube Vs The Human Vocal Instrument (attached handout)

Differentiation Strategies:

What’s the teacher doing?

The teacher introduces the anatomy of the human vocal instrument to the class through a 1 minute introductory video- https://www.youtube.com/watch?v=JzyHKYQzPBk ; The teacher provides a template for students to do a comparison between the singing pipe and the human vocal system in terms of the structure , mechanisms of sound production and outcome.Structured template may be used

What are the student’s doing?

Students make a list of questions and observations on the board ;

Students use their introduction to the anatomy of the vocal instrument and as a group compare the two systems and record their understanding of the similarities and differences between the two;

Phase Three: Explain the Concept

Only after students have explored the concept does the curriculum and/or teacher provide the scientific explanation and

terms for what they are studying. The teacher may present the concepts via lecture, demonstration, reading, or

multimedia (video, computer-based). Students then use the terms to describe what they have experienced, and they begin to examine mentally how this explanation fits with what they already know.

Learning Experiences:

Teacher Interactive Lecture: Teacher introduces standing waves in pipes and guides the students into exploring harmonics of open and closed pipes; Reference: Open and Closed Pipes- worksheet

Student Activity 1: students research average length of male/female vocal tract and calculate the fundamental frequency of resonance of the tract and compare it to fundamental frequency of pitch;Teacher Lecture: Teacher introduces and explains how the shaping of the vocal tract with the position of the tongue and lips can shape the resonances of the vocal tract; Teacher explains how the vertical and horizontal position of tongue and the roundedness of the lips help shape the vocal tract to produce the different vowel sounds.

Student Activity 2: Students will work in pairs on this activity. They are given pictures of vocal tract shapes and they will work in pairs to match correctly the vocal tract shapes to the vowel sounds. Students work in pairs to observe each other as they sound out the vowels and discuss about the shaping of their mouths and the position of their tongue horizontally and vertically; They will use their observations to complete the activity;

Reference: Vocal Tract Shaping and Vowel Sounds – Handout

Differentiation Strategies:

Extension to vowel space;

What’s the teacher doing?

Teacher explains in detail the mechanism of sound production and resonances in pipes; Guides students in exploring the relationship between fundamental and harmonics in pipes;

Teacher explains vocal tract shaping and facilitates discussion and sharing of ideas from students about resonances in different musical instruments or in singing;

What are the students doing?

Students participate in this interactive session of taking their learning on standing waves in strings and applying it to pipes to derive the harmonics in open and closed pipes;

Students explore from their vowel sounding activity how the shaping of the vocal tract changes the vocal utterances and extend it to how music can be produced by using resonances of the vocal tract; Singers and Instrument players are invited to share their personal experiences of manipulating notes connecting it to resonances extending their learning;

Phase Four: Elaborate on the Concept

The next stage of the model serves to help students elaborate on their understanding of the concept. They are given opportunities to apply the concept in unique situations, or they are given related ideas to explore and explain using the information and experiences they have accumulated so far. Interaction between the students is essential during the elaboration stage. By discussing their ideas with others, students can construct a deeper understanding of the concepts.

Learning experience: Teacher introduces a spectrographic tool for simple spectral analysis and explains the concept of fourier analysis, time domain and frequency domain curves. She also introduces the terms formants and connects it to resonances of the vocal tract’ The teacher will guide the student’s exploration with the spectrographic tool in using it to complete simple spectral analysis.

Student Activity: Students evaluate their understanding by practicing on sample spectrograms and matching them with the waveforms; The handout on interpreting musical instrument power spectra allows students to work on their understanding and interpretation of power spectra and waveforms and also answer questions based on their understanding; The teacher provides feedback correcting misconceptions and guiding their correct reading of the graphs and waveforms;

Reference: Interpreting musical instrument power spectra -Handout

Differentiation Strategies:

Concept extension: Understanding and exploring the fft process in spectral analysis

What’s the teacher doing?

Teacher introduces fundamental concepts of spectral analysis

Teacher facilitates student collaborative sessions on argument driven learning

What are the students doing?

Students practice interpretation of spectral analysis data by using given waveforms and power spectra and use it to answer questions; They work in small groups collaboratively on argument driven approach – A student makes a claim based on his/her observation and another supports/refutes the claim citing valid reasoning ; They then discuss and arrive at a consensus- if the group cannot reach a consensus , they can seek help from the instructor or another group;

Phase Five: Evaluate students' Understanding of the Concept

The final stage of the model has a dual purpose. It is designed for the students to continue to elaborate on their understanding and to evaluate what they know now and what they have yet to figure out. Although the key word of the stage is evaluate, the word does not indicate finality in the learning process. Indeed, students will continue to construct their understanding of these broad concepts throughout their lives. Evaluation of student understanding should take place throughout all phases of the instructional model. The evaluate stage, however, is when the teacher determines the extent to which students have developed a meaningful understanding of the concept.

Student Summative Activity: Students will use their understanding of all concpets and integrate it into their own experimental design where students will obtain their own waveforms and conduct their own analysis using a spectrographic tool like audacity and present their findings to the class.

Teacher Guidance: Teacher uses an example activity from the research data on “ Acoustics of infant cries “ and details the analysis of the cry using the spectrographic tool. The teacher also guides them in the steps of using an audio file and obtaining the power spectrum and in the identification and interpretation of characteristics in the spectra. Teacher also guides them into writing their observations in the form of a report.

Differentiation Strategies:

Complexity of the investigation and depth of analysis

Scaffolding for students that need help

Using data available on the net or samples provided by teacher or recording their own data samples

What’s the teacher doing?

Teacher shares with students simple ideas for investigation;

Investigating the quality of the note played by different musical instruments;

Investigating the quality of the note sung by different singers

Investigating the recording of a baby cry at two different ages

Investigating the harmonic profile of a birdsong

Teacher offers guidance with spectral analysis and interpretation of spectra;

What are the students doing?

Students perform an experimental spectral analysis in small groups of sounds that they would like to investigate; They can either use recorded sound clips or produce their own sound files;

Spectrographic analysis tool – audacity or other

They perform the spectral analysis of the sound clips in their investigation and write a one page report on their observations and inferences;

Each group presents their investigation to one other group and receives feedback; Each group should at least listen to one other presentation and offer feedback;

Attachments:

1. The singing tube Vs The Human Vocal Instrument – A COMPARISON

Singing tube Vocal instrument

Structure : vibrating source energy source upstream duct downstream duct medium tube lengths

Mechanism : changing pitch loudness quality

Differences :

2. STANDING WAVES IN OPEN AND CLOSED PIPES- HANDOUTS

Pipe Open at one end :Length of pipe= l; v= speed of sound in air; speed = frequency x wavelength

Diagram Wavelength ( in terms of length)

Frequency Harmonic #

Pipe open at both ends:

L= length of the pipe; v= speed of sound in air

Diagram Wavelength ( in terms of length)

Frequency Harmonic #

3. Vocal Tract Shaping and Vowel Sounds – Handout

Given below are picture cards that show the shaping of the vocal tract and a corresponding linear plastic model of the vocal tract shape for different vowel sounds specified in the list below; Match the shapes of the vocal tract correctly to the vowel sounds. Work in pairs, so you can observe each other as you sound out the vowels; You may place your hand on your cheeks to notice the position of your tongue as you sound out the vowels;

AH as in FATHER

EE as in TREE

OH as in COLD

OO as in FOOD

EH as in FACE

Summarizing Thought: Think about what changes produce the change in frequencies resulting in different vowel sounds.

4.

5. Spectral Analysis of Baby Cry (P06_R5_1.0)