9P.2.3.1 Waves & Sound
Analyze the frequency, period and amplitude of an oscillatory system.
For example: An ideal pendulum, a vibrating string, or a vibrating spring-and-mass system.
Describe how vibration of physical objects sets up transverse and/or longitudinal waves in gases, liquids and solid materials.
Explain how interference, resonance, refraction and reflection affect sound waves.
Describe the Doppler effect changes that occur in an observed sound as a result of the motion of a source of the sound relative to a receiver.
Overview
MN Standard in Lay Terms
A sound wave is the disturbance in a medium (such as air, water, or any other gas, liquid or solid matter) due to the movement of energy traveling through a medium as it propagates away from the source of the sound. The source of the disturbance is a vibrating object, such as an explosion or ringing bell. The vibration disturbs the particles in the surrounding medium; those particles disturb those next to them, and so on. The pattern of the disturbance creates outward movement in a wave pattern, like waves of seawater on the ocean. The wave carries the sound energy through the medium, usually in all directions and becomes less intense as it moves farther from the source. Sound waves can propagate as transverse waves (particle displacement is perpendicular to the direction of wave propagation) or as compression waves (particle displacement is parallel to the direction of wave propagation).
Big Idea
Forces can change the motion of an object in a repeatable and predictable pattern that can be represented or modeled both visually and mathematically as having wave like properties. Forces that act on objects in this way are known as restoring forces because the force is central seeking, that is always trying to bring an object back to its equilibrium or central position. When forces act in this way they set up vibrations in objects and cause them to oscillate about this central position. When the motion and displacement of the matter involved in the interaction is displaced regularly with time, its period, frequency and amplitude of motion may be measured and expressed as sine or cosine functions hence the idea of the wave model. When this energy propagates outward through a medium such as a solid, liquid or a gas it is a sound wave. Sound waves share the properties of other waves in that they may interfere with each other, cause standing waves and resonance in pipes (the basis for many instruments), reflect and be experienced as echoes and refract.
MN Standard Benchmarks
9P.2.3.1.1 Analyze the frequency, period and amplitude of an oscillatory system. For example: An ideal pendulum, a vibrating string, or a vibrating spring-and-mass system.
9P.2.3.1.2 Describe how vibration of physical objects sets up transverse and/or longitudinal waves in gases, liquids and solid materials.
9P.2.3.1.3 Explain how interference, resonance, refraction and reflection affect sound waves.
9P.2.3.1.4 Describe the Doppler effect changes that occur in an observed sound as a result of the motion of a source of the sound relative to a receiver.
The Essentials
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This means that you are free to copy and reuse any of my drawings (noncommercially) as long as you tell people where they're from.
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Our understanding of wave properties, together with appropriate instrumentation, allows us to use waves, particularly electromagnetic and sound waves, to investigate nature on all scales, far beyond our direct sense perception.
(Waves as carriers of energy and information)
Waves carry energy and information, without net motion of matter, from a source to a detector. Waves combine with other waves of the same type to produce complex patterns containing information that can be decoded by detecting and analyzing them.
Light and sound are major ways that we gain information and interpret the world around us. Our understanding of their wave properties, and of wave behavior in general, inform our models of how they interact with matter and how we can detect and interpret information carried in these signals. Light and other electromagnetic waves are extremely useful as probes of
phenomena on scales from the very large to the very small, far beyond the range of our direct sense perception. Instrumentation to produce, detect and interpret waves is a key tool in probing otherwise invisible systems and in communication and information technologies.
2) AAAS Benchmarks of Science Literacy and Atlas
from Benchmarks Online - Project 2061 - AAAS (Physical Setting) Benchmarks online
Motion (4F):
4F/H5ab - The observed wavelength of a wave depends upon the relative motion of the source and the observer. If either is moving toward the other, the observed wavelength is shorter; if either is moving away, the wavelength is longer.
4F/H6ab - Waves can superpose on one another, bend around corners, reflect off surfaces, be absorbed by materials they enter, and change direction when entering a new material. All these effects vary with wavelength.
4F/H6c - The energy of waves (like any form of energy) can be changed into other forms of energy.
Common Core Standards
Math standards
(8.1.1.5) Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved.
For example: (4.2×104)×(8.25×103) =3.465×108 , but if these numbers represent physical measurements, the answer should be expressed as 3.5×108 because the first factor, 4.2×104 , only has two significant digits.
(9.2.1.4) Obtain information and draw conclusions from graphs of functions and other relations.
Students can plot data of applied force and extension for a spring to determine the spring constant k.
(9.2.2.1) Represent and solve problems in various contexts using linear and quadratic functions.
(9.2.2.3) Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.
(9.3.1.3) Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems.
For example: 60 miles/hour = 60 miles/hour × 5280 feet/mile × 1 hour/3600 seconds = 88 feet/second.
(9.3.1.5) Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements.
For example: Suppose the sides of a rectangle are measured to the nearest tenth of a centimeter at 2.6 cm and 9.8 cm. Because of measurement errors, the width could be as small as 2.55 cm or as large as 2.65 cm, with similar errors for the height. These errors affect calculations. For instance, the actual area of the rectangle could be smaller than 25 cm2 or larger than 26 cm2, even though 2.6 × 9.8 = 25.48.
(9.4.1.3) Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.
(9.4.2.3) Design simple experiments and explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.
2010 Minnesota Academic Standards - English Language Arts K-12
Curriculum and Assessment Alignment Form
Grades 11-12 Literacy in Science and Technical Subjects
Minnesota Academic Standards: Language Arts
Anchor Standard | Benchmark |
1. Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text. | 1. Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. |
2. Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas. | 2. Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. |
3. Analyze how and why individuals, events, and ideas develop and interact over the course of a text. | 3. Follow precisely a complex multistep procedure when carrying out experiments, designing solutions, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. |
4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone. | 4. Determine the meaning of symbols, equations, graphical representations, tabular representations, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11-12 texts and topics. |
5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole. | 5. Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas. |
6. Assess how point of view or purpose shapes the content and style of a text. | 6. Analyze the author's purpose in describing phenomena, providing an explanation, describing a procedure, or discussing/reporting an experiment in a text, identifying important issues and questions that remain unresolved. |
7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words. | 7. Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. |
8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence. | 8. Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information. |
9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take. | 9. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. |
10. Read and comprehend complex literary and informational texts independently and proficiently. | 10. By the end of grade 12, read and comprehend science/technical texts in the grades 11-12 text complexity band independently and proficiently. |
Misconceptions
The following misconceptions are taken from :
Heller, P, & Stewart, G. (2010). College Ready Physics Standards: A Look to the Future. retrieved on 01/01/2011 from this source.
Several researched based sources for these misconceptions are found in that work.
1. Mechanical Waves
a. Waves transport matter; matter moves along with water waves as the waves move through a body of water.
b. Waves do not have energy.
c. A wave's amplitude affects its speed. Big waves travel faster than small waves in the same medium.
d. All waves are transverse waves - sound, surface water waves, and light.
e. Sounds can travel through empty space (a vacuum).
2. Sound and Pitch
a. Sounds can travel through empty space (a vacuum); sounds cannot travel through liquids and solids.
b. Pitch is related to intensity; pitch is the same as loudness; hitting an object harder changes the pitch of the sound produced.
c. he pitch of a tuning fork will change as it "slows down", (i.e. "runs" out of energy)
3. Doppler Effect. The pitch of whistles or sirens on moving vehicles is changed by the driver as the vehicle passes.
4. Reflection, Refraction, Diffraction, and Interference
a. When waves interact with a solid surface, the waves are destroyed
b. Refraction does not change the frequency or wavelength of the wave.
c. Waves bend around corners, but they don't bend around solid barriers or openings in barriers.
d. Double-slit interference shows wave crest and troughs.
5. When two pulses, traveling in opposite directions along a spring or rope, meet, they bounce off each other and go back in the opposite direction.
Vignette
As students are seated in the room Mr. Hertz passes out Popsicle or craft sticks and asks the students to explore the possible ways that they could make a sound with the stick. Students have many ideas but are coached in the direction of lying the sticks down flat near the edge of their desks so that part of the stick hangs over. While holding the stick to the table with one hand, the stick is plucked with the other thumb. Students notice that they hear a pitch from the vibrating stick. The students are then asked to pluck harder (amplitude) and see if they notice a difference. Then they are asked to change the length of stick overhanging the desk and pluck again. What, if anything, happened to the tone? What if they simply pluck harder? The students should note that plucking harder makes the tone louder whereas changing the length of the stick changes the pitch or frequency. Can they calibrate their sticks to play a simple song? Students are lead through a discussion about restoring force, amplitude, frequency, and period.
The students are then led to the lab to the investigate the properties of a vibrating mass/spring system, a system which vibrates slow enough to analyze carefully and methodically. Students are given 2 different springs, masses, a meter stick, a stopwatch or photogate. They investigate amplitude, mass, and spring constant as related to the period plotting each to make conclusions about the relationships. The lab is followed up with a demonstration of longitudinal waves on a slinky and view a vibrating speaker with a strobe light to discuss the propagation of sound waves. The students investigate sound waves using the computer with the PHET simulation Sound.
The next day the students investigate the vibrations created by different tuning forks with microphones and computer software measuring the describing the significance of the amplitude, frequency and period. Students can also analyze their voices or instruments using a microphone and free software such as Visual Analyzer as demonstrated in this video.
Resources
Suggested Labs and Activities
Vernier Investigations:
Vernier technology is a source of data collection that allows students to accurately predict and analysis data. The links below are the complete labs as posted by Vernier Software and Technology.
Simple Harmonic Motion (9P.2.3.1.1) - Measure the position and velocity as a function of time for an oscillating mass and spring system. Compare the observed motion of a mass and spring system to a mathematical model of simple harmonic motion. Determine the amplitude, period, and phase constant of the observed simple harmonic motion.
Mathematics of Music (9P.2.3.1.1) - Determine the frequencies of the notes of a musical scale. Examine the differences and ratio between these notes. Determine the mathematical patterns used in musical scales.
Sound Waves and Beats (9P.2.1.1.3) - Measure the frequency and period of sound waves from tuning forks. Measure the amplitude of sound waves from tuning forks. Observe beats between the sounds of two tuning forks.
Speed of Sound (9P.2.3.1.2) - Measure how long it takes sound to travel down and back in a long tube. Determine the speed of sound. Compare the speed of sound in air to the accepted value.
Tones, Vowels and Telephones (9P.2.3.1.1) - Use a Microphone to analyze the frequency components of a tuning fork and your voice. Record overtones produced with a tuning fork. Examine how a touch-tone phone works.
Speed of a Slinky Wave (9P.2.3.1.2) - Study transverse and longitudinal disturbances moving along a stretched Slinky lying on a low friction floor.
Superposition of Slinky Waves (9P.2.3.1.3) - Explore what happens when two wave pulses travel towards each other through a stretched Slinky.
Wave Pulse Propagation (9P.2.3.1.3) - Explore the shape of a transverse wave pulse and how it moves along a spring lying on a smooth floor.
Doppler Effect: Surface Water Waves (9P.2.3.1.4) - Verify the Doppler Equation for surface waves in water by using two high speed movies.
Doppler Effect: Sound Waves (9P.2.3.1.4) - Verify that the Doppler Equation can be used to predict the ratio of the apparent car horn frequencies before and after the car passes.
Pasco "Explorations in Physics"
Activity 20 - Sound Wave Properties (9P.2.3.1.1)
PDF (916 KB) Determine the frequency and wavetength of sound waves.
Activity 21 - Superposition and Interference in Sound (9P.2.3.1.3)
PDF (568 KB) Investigate the relationship of the beat frequency and the difference in frequency of two sound waves.
Pasco "Physics with the Xplorer GLX"
Activity 27 - Sound Wave Properties (9P.2.3.1.1)
PDF (352 KB) Determine the frequency and wavelength of sound waves.
Activity 28 - Interference-Beat Frequency (9P.2.3.1.3)
PDF (256 KB) Investigate the relationship of the beat frequency and the difference in frequency of two sound waves.
Student Practicum Problems:
Practicums For Physics Teachers (Ryan, Henry and Barber, Jon, 2008)
Two high school teachers developed practicums for students to solve problems using an understanding of physics concepts and critical thinking skills. This link does not get you to the activity, only an order form for the book. This is the only way of purchasing these practicums.
Interference Trombone - Calculate the frequency of the sound played into an interference producing slide trombone apparatus.
Instructional suggestions/options
Modeling Physics Resources in Waves and Sound at Arizona State University
Physics Quests from Delores Gende (9P.2.3.1.1, 9P.2.3.1.3)
A WebQuest, according to Bernie Dodge, the originator of the WebQuest concept from San Diego State University, "is an inquiry-oriented activity in which most or all of the information used by learners is drawn from the Web. WebQuests are designed to use learners' time well, to focus on using information rather than on looking for it, and to support learners' thinking at the levels of analysis, synthesis, and evaluation."
Additional resources
The Physics Classroom: Resource for both teachers and students. Website is sectioned into Read/Watch/Interact, Practice/Review, and Teacher Tools.
123Physics: Regents Review Questions, Physics Lessons, Videos, and Physics Clipart
Falstad.com: - java applets on waves and sound, and links to other simulations.
ComPADRE is filling a stewardship role within the National Science Digital Library for the educational resources used by broad communities in physics and astronomy. This partnership of the American Association of Physics Teachers (AAPT), the American Astronomical Society (AAS), the American Institute of Physics/Society of Physics Students (AIP/SPS), and the American Physical Society (APS) helps teachers and learners find, and use, high quality resources through collections and services tailored to their specific needs.
The Physics Front provides high quality resources for the teaching of physics and physical sciences courses. You may search or browse the Physics Front in order to find materials appropriate for your physics classes. Additionally, registering will allow you to share your experiences using materials. The Physics Front is a free service provided by the American Association of Physics Teachers in partnership with the NSF/NSDL.
Physics Win or Physics Fail?
Use your knowledge of physics to put these videos to the test!
Inspired by Rhett Allain's physics explanations at Dot Physics, Dan Meyer's blog series "What Can You Do With This?", and Dan's TEDx plea for a math curriculum makeover, I have been collecting video clips that are prime for my physics students to analyze.
Videos are categorized by topic to help teachers locate videos for the concepts at hand. Several videos are listed under multiple topics. The videos are presented without any further questions other than "Physics win or physics fail?" (real or fake?)
If you are looking around for some good labs to use or to tweek, check this site out. Items have been put here for physics teachers, by physics teachers, and range from first-year high school physics to AP material. The emphasis is on labs, but explanatory material is also available. The University sources on the bottom will direct you to even more great material. The collection of materials is growing all of the time.
Vocabulary/Glossary
- Restoring Force: The force that causes simple harmonic motion. The restoring force is always directed toward an object's equilibrium position.
- Oscillation: A back-and-forth movement about an equilibrium position. Springs, pendulums, and other oscillators experience harmonic motion.
- Simple Harmonic Motion: An object that moves about a stable equilibrium point and experiences a restoring force that is directly proportional to the oscillator's displacement.
- Period: The time it takes a system to pass through one cycle of its repetitive motion. The period, T, is the inverse of the motion's frequency, f = 1/T.
- Frequency: The number of cycles executed by a system in one second. Frequency is the inverse of period, f = 1/T. Frequency is measured in hertz, Hz.
- Hertz: The units of frequency, defined as inverse-seconds (1 Hz = 1 s-1). "Hertz" can be used interchangeably with "cycles per second."
- Amplitude: In reference to oscillation, amplitude is the maximum displacement of the oscillator from its equilibrium position. Amplitude tells how far an oscillator is swinging back and forth. In periodic motion, amplitude is the maximum displacement in each cycle of a system in periodic motion. The precise definition of amplitude depends on the particular situation: in the case of a stretched string it would be measured in meters, whereas for sound waves it would be measured in units of pressure.
- Wavelength: The distance between successive wave crests, or troughs. Wavelength is measured in meters and is related to frequency and wave speed by
= v/f. - Transverse Wave: Waves in which the medium moves in the direction perpendicular to the propagation of the wave. Waves on a stretched string, water waves, and electromagnetic waves are all examples of transverse waves.
- Longitudinal Wave: Waves that oscillate in the same direction as the propagation of the wave. Sound is carried by longitudinal waves, since the air molecules move back and forth in the same direction the sound travels.
- Sine Wave: Any oscillation, such as a sound wave or alternating current, whose waveform is that of a sine curve.
- Medium: The substance that is displaced as a wave propagates through it. Air is the medium for sound waves, the string is the medium of transverse waves on a string, and water is the medium for ocean waves. Note that even if the waves in a given medium travel great distances, the medium itself remains more or less in the same place.
- Wave Speed: The speed at which a wave crest or trough propagates. Note that this is not the speed at which the actual medium (like the stretched string or the air particles) moves.
- Compression: An area of high air pressure that acts as the wave crest for sound waves. The spacing between successive compressions is the wavelength of sound, and the number of successive areas of compression that arrive at the ear per second is the frequency, or pitch, of the sound.
- Rarefaction: An area of low air pressure that acts as the wave trough for sound waves. The spacing between successive rarefactions is the wavelength of sound, and the number of successive areas of rarefaction that arrive at the ear per second is the frequency, or pitch, of the sound.
- Doppler Effect: Waves produced by a source that is moving with respect to the observer will have a higher frequency and smaller wavelength if the source is moving towards the observer, and a lower frequency and longer wavelength if the source is moving away from the observer. The speed of the waves is independent of the motion of the source.
- Bow Wave Shock Wave: Progressive disturbance propagated through a fluid such as water or air as the result of displacement by the foremost point of an object moving through it at a speed greater than the speed of a wave moving across the water.
- Superposition Principle: The principle by which the displacements from different waves traveling in the same medium add together. Superposition is the basis for interference and is the algebraic sum of the amplitudes at given times.
- Wave Interference: The wave amplitude that occurs when waves of the same or different frequencies come together. If the energy is additive it is usually described as constructive interference, if subtractive then it is described as destructive interference.
- Reflection (Fixed and Free End): The phenomenon of light bouncing off a surface, such as a mirror.
- Standing Wave: A wave that interferes with its own reflection so as to produce oscillations which stand still, rather than traveling down the length of the medium. Standing waves on a string with both ends tied down make up the harmonic series.
- Natural Frequency: The frequency at which a system vibrates when set in free vibration.
- Forced Vibration: The setting up of vibrations in an object by a vibrating force.
- Resonance: The tendency of a system to oscillate with larger amplitude at some frequencies than at others.
- Beats: When two waves of slightly different frequencies interfere with one another, they produce a "beating" interference pattern that alternates between constructive (in-phase) and destructive (out-of-phase). In the case of sound waves, this sort of interference makes a "wa-wa-wa" sound, and the frequency of the beats is equal to the difference in the frequencies of the two interfering waves.
- Harmonics: The series of standing waves supported by a string with both ends tied down. The first member of the series, called the fundamental, has two nodes at the ends and one anti-node in the middle. The higher harmonics are generated by placing an integral number of nodes at even intervals over the length of the string. The harmonic series is very important in music.
- Timbre: The combination of qualities of a sound that distinguishes it from other sounds of the same pitch and volume.
Audacity is a free, easy-to-use and multilingual audio editor and recorder for Windows, Mac OS X, GNU/Linux and other operating systems. You can use Audacity to:
Record live audio.
Convert tapes and records into digital recordings or CDs.
Edit Ogg Vorbis, MP3, WAV or AIFF sound files.
Cut, copy, splice or mix sounds together.
Change the speed or pitch of a recording.
And more! See the complete list of features.
Here is an example video showing how to use Audacity to generate and analyze beats frequency.
Using Audacity to Analyze Beats
Visual Analyzer is a great free software program to let you analyze sound real time using only a microphone and the sound card in your computer.
"Many people do not have the money to buy an expensive Oscilloscope or a Spectrum Analyzer. A lot of musicians, for example, need a spectrum analyzer with an octave band analysis tool embedded. So, a good soundcard could be all the hardware they need. Together with their PC, that is, a lot of hardware already available at no cost. A recent soundcard with a sampling frequency of 96 or even 192 Khz will allows to manage signals with frequencies up to 96Khz ( well beyond the audio frequencies) transforming VA in a powerful set of instruments for general electronics and other applications. VA is useful anywhere you need a true oscilloscope, spectrum analyzer, frequency meter, voltmeter, function generator etc.
The idea of using the soundcard of a PC is not a new one (there are many of programs like VA) but I tried to write a program specifically made for the analysis of audio circuits for the electronics hobbyist. I think VA is probably less "extravagant" than other (i.e. less windows and frills) but full of substance and even a lot of original ideas.
Ripple Tank Simulator in 2D and 3D (9P.2.3.1.3 9P.2.3.1.4)
Doppler Effect Simulator (9P.2.3.1.4)
University of Colorado PhET Simulations (9P.2.3.1.3 9P.2.3.1.3 9P.2.3.1.3 9P.2.3.1.3
Each of the following visually appealing and engaging simulations allow students to experience and experiment with various configurations of Electricity and Magnetism as a powerful supplement to real world experimentation. Students may interact with and vary the physical parameters of the simulations. Many of the simulations allow students to visualize and engage with phenomena that may or may not be able to be done in the high school lab setting but add to the learning experience. All of these simulations have accompanying lesson plans, student documents, and teacher resources developed by teachers for you to use in your classroom.
Masses on Springs ( 9P.2.3.1.1)
A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring.
Pendulum Lab ( 9P.2.3.1.1)
Play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. It's easy to measure the period using the photogate timer. You can vary friction and the strength of gravity. Use the pendulum to find the value of g on planet X. Notice the anharmonic behavior at large amplitude.
Waves on a String ( 9P.2.3.1.1)
Watch a string vibrate in slow motion. Wiggle the end of the string and make waves, or adjust the frequency and amplitude of an oscillator. Adjust the damping and tension. The end can be fixed, loose, or open.
Wave Interference (9P.2.3.1.3)
Make waves with a dripping faucet, audio speaker, or laser! Add a second source or a pair of slits to create an interference pattern.
Sound (9P.2.3.1.3)
This simulation lets you see sound waves. Adjust the frequency or volume and you can see and hear how the wave changes. Move the listener around and hear what she hears.
Fourier: Making Waves (9P.2.3.1.3)
Learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves.
Videos to learn how to implement the National Standards using Inquiry Techniques from the Annenburg Foundation
To be viewed together here.
1. Introduction
Classroom footage and new footage of scientists in the field explain and illustrate the concept of inquiry.
Web Based Instructional Videos:
The following Videos are from the Annenburg Foundation's Mechanical Universe Collection Video on Demand found here.
16. Harmonic Motion ( 9P.2.3.1.1)
The music and mathematics of periodic motion.
17. Resonance ( 9P.2.3.1.3)
Why a swaying bridge collapses with a high wind, and why a wine glass shatters with a higher octave.
18. Waves ( 9P.2.3.1.1)
With an analysis of simple harmonic motion and a stroke of genius, Newton extended mechanics to the propagation of sound.
Hippocampus
HippoCampus is a project of the Monterey Institute for Technology and Education (MITE). The goal of HippoCampus is to provide high-quality, multimedia content on general education subjects to high school and college students free of charge. This site could be used in conjuction with your course to help teach the standards at various levels.
(9P.2.3.1.1) Simple Harmonic Motion, Period and Frequency
(9P.2.3.1.2) Types of Waves
(9P.2.3.1.3) Sound
(9P.2.3.1.4) Doppler Effect
Assessment
Assessment of Students
Peer Instruction: A User's Manual, (Mazur, Eric, Harvard University, Prentice Hall, 1997) - conceptual questions for using Student Response Systems.
Oscillations
CT7: Period of Oscillation of swing (9P.2.3.1.1)
CT8: Period of Oscillation of swing (9P.2.3.1.1)
CT9: Sound Beat patterns (9P.2.3.1.3)
CT13: Longitudinal waves in a slinky (9P.2.3.1.2)
CT14: Speed of wave in string (9P.2.3.1.2)
CT17: Interference of two waves on a string (9P.2.3.1.3)
Sound
CT1: Doppler effect and speed of sound (9P.2.3.1.4)
CT2: Doppler effect and frequency of sound wave (9P.2.3.1.4)
CT3: Doppler effect and speed of sound (9P.2.3.1.4)
(9P.2.3.1.1) 1. What is the primary difference between the sound produced by a middle-C played with a piano and with a tuning fork?
a. The tuning fork only vibrates at the fundamental frequency
b. The tuning fork and the piano both sound exactly the same
c. The tuning fork is entirely metal and thus louder.
d. The Piano is more expensive and therefore better sounding
e. A tuning fork cannot be produced that plays middle-C
Answer A
(9P.2.3.1.2) 2. Longitudinal waves can propagate through which of the following
a. gases only
b. liquids only
c. solids only
d. solids and gases only
e. solids and liquids only
f. liquids, solids, and gases
Answer F
(9P.2.3.1.4) 3. A train whistle emits a sound with a frequency of 500 Hz when standing in the station. If the same whistle is blown when it is moving toward the station at 40 mph what will be the approximate frequency someone standing at the station will hear?
a. 380 Hz.
b. 480 Hz.
c. 500 Hz.
d. 520 Hz.
e. 1000 Hz.
Answer D
(9P.2.3.1.4) 4. Compared with the sound you hear from the siren of a stationary fire engine, the sound you hear when it approaches you has an increased
a) speed.
b) frequency.
c) Both of these.
d) Neither of these.
Answer B
(9P.2.3.1.1) 5. You swing to and fro on a playground swing. If you stand rather than sit, the time for a to-and-fro swing is
a) lengthened.
b) shortened.
c) unchanged.
Answer B
(9P.2.3.1.1) 6. The property of a sound wave that is closely related to its loudness is
a. amplitude.
b. speed.
c. frequency.
d. wavelength.
e. color
Answer A
(9P.2.3.1.3) 7. Transverse waves can propagate through which of the following
a. gases only
b. liquids only
c. solids only
d. solids and gases only
e. solids and liquids only
f. liquids, solids, and gases
Answer C
(9P.2.3.1.1) 8. A pendulum has a period of 1 seconds. What happens to the period if the pendulum's length is doubled?
a. The new period is unchanged because the period does not depend on the length.
b. The new period is 0.7 seconds
c. The new period is 1.4 seconds
d. The new period is 2.0 seconds
Answer C
(9P.2.3.1.1) 9. The speed of a wave on a string is determined to be 50 m/sec. What happens to the speed of the wave when the frequency is doubled? Assume the tension remains the same.
a. The speed is unchanged because the wave speed does not depend on the frequency.
b. The speed of the wave is now 25 m/sec.
c. The speed of the wave is now 100 m/sec.
d. The speed of the wave is now 200 m/sec.
Answer A
(9P.2.3.1.1) 10. The speed of a wave on a string is determined to be 50 m/sec with a wavelength of 2 m. What happens to the wavelength when the frequency is doubled? Assume the tension remains the same.
a. The wavelength is unchanged because the wavelength does not depend on the frequency.
b. The wavelength of the wave is now 0.5 m.
c. The wavelength of the wave is now 1.0 m.
d. The wavelength of the wave is now 4.0 m.
Answer C
(9P.2.3.1.1) 11. The fundamental frequency of a vibrating string is determined to be 500 Hz when the tension is 100 N. What happens to the frequency when the tension is changed to 90 N? Assume the length of the string remains the same.
a. The frequency is unchanged because the frequency does not depend on the tension.
b. The frequency is now 475 Hz.
c. The frequency is now 545 Hz.
d. The frequency is now 725 Hz.
Answer B
(9P.2.3.1.1) 12. For an object suspended vertically from a spring, the time for one complete oscillation will depend on
a. the value for the spring constant k.
b. the distance the object was originally pulled down.
c. the mass of the object.
d. Both answers a and b.
e. Both answer a and c.
Answer E
(9P.2.3.1.2) 13. The speed of sound of helium is greater than for air at room temperature because
a. Helium is an inert gas and does not react with other elements very easily
b. there is not very much helium in the atmosphere
c. a helium molecule is lighter than either an oxygen or nitrogen molecule
d. oxygen reacts with other elements better than helium and therefore transmits sound waves faster.
Answer C
(9P.2.3.1.4) 14. As a train starts from rest and then accelerates down the track, coming toward me faster and faster, the speed of the sound waves coming toward me will
a. be some constant speed faster than the normal speed of sound in air.
b. depend on the speed of the train relative to the person.
c. be slower than the normal speed of sound in air.
d. be equal to the normal speed of sound in air.
Answer D
(9P.2.3.1.3) 15. Two harmonic waves are described by
y1 = 3 sin (4x - 700t) m
y2 = 3 sin (4x - 700t - 2) m
What is the amplitude of the resultant wave?
a. 8.0 m
b. 4.3 m
c. 6.0 m
d. 3.2 m
e. 3.0 m
Answer D
(9P.2.3.1.3) 16. Two harmonic waves are described by
y1 = 4 sin (8x - 300t) m
y2 = 4 sin (8x - 300t - 2)
What is the frequency of the resultant wave?
a. 300
b. 48
c. 8
d. 0.8
e. 150
Answer B
(9P.2.3.1.3) 17. A certain physical system has only 300 Hz and 900 Hz as resonant frequencies below 1000 Hz. What type of system could this be?
a. a string tied down at both ends
b. an air column open at one end and closed at the other
c. an air column open at both ends
d. an air column closed at both ends
e. There is no system that could possibly have that set of frequencies for its resonances.
Answer B
(9P.2.3.1.3) 18. A 200-Hz and a 209-Hz sound are emitted into the same volume of space. What is the beat frequency?
a. 409 Hz
b. 41.8 kHz
c. 9 Hz
d. 1.05 Hz
e. 205 Hz
Answer C
Assessment of Teachers
Modeling Instruction in High School Physics, Chemistry, Physical Science, and Biology
Materials and readings for teacher discussion and use for professional development
The Modeling Method of High School Physics Instruction has been under development at Arizona State University since 1990 under the leadership of David Hestenes, Professor of Physics. The program cultivates physics teachers as school experts on effective use of guided inquiry in science teaching, thereby providing schools and school districts with a valuable resource for broader reform. Program goals are fully aligned with National Science Education Standards. The Modeling Method corrects many weaknesses of the traditional lecture-demonstration method, including fragmentation of knowledge, student passivity, and persistence of naive beliefs about the physical world. Unlike the traditional approach, in which students wade through an endless stream of seemingly unrelated topics, the Modeling Method organizes the course around a small number of scientific models, thus making the course coherent. In 2000 the program was extended to physical science and in 2005 to chemistry, by demand of committed teachers. See this page.
Peer Instruction: A User's Manual, (Mazur, Eric, Harvard University, Prentice Hall, 1997) - conceptual questions for using Student Response Systems.
Oscillations
CT7: Period of Oscillation of swing (9P.2.3.1.1)
CT8: Period of Oscillation of swing (9P.2.3.1.1)
CT9: Sound Beat patterns (9P.2.3.1.3)
CT13: Longitudinal waves in a slinky (9P.2.3.1.2)
CT14: Speed of wave in string (9P.2.3.1.2)
CT17: Interference of two waves on a string (9P.2.3.1.3)
Sound
CT1: Doppler effect and speed of sound (9P.2.3.1.4)
CT2: Doppler effect and frequency of sound wave (9P.2.3.1.4)
CT3: Doppler effect and speed of sound (9P.2.3.1.4)
Differentiation
Strategies from Jarrett, D. (1999). The inclusive classroom: teaching mathematics and science to english-language learners. Northwest Regional Education Laboratory.
Thematic Instruction: Theme-based units can help ELL students connect prior knowledge to language and real-world applications.
Cooperative Learning: Students use language related to task, while conversing and tutoring one another.
Inquiry and Problem Solving: Inquiry and problem solving can be used prior to proficiency in English. Inquiry approaches in science can help student's language acquisition as well as their content knowledge.
Vocabulary Development: Students learn the meaning of words best during investigations and activities, instead of as a vocabulary list.
Modify Speech: Teachers can help ELL students by using an active voice, limiting new terms, using visual support, and paraphrasing or repeating difficult concepts. Slowing down speech, speaking clearly, and using a simple language structure will help ELL students with understanding.
Make ELL Students Feel Welcome: Encourage ELL students to express ideas, thought, and experiences. Focus on what student is say, not how they say it.
Book: Science Education for Gifted Students: A Gifted Child Today Reader (Johnsen, S. K. and Kendrick, J., 2005, Prufrock Press, Inc.)
A substantial resource for SpEd, ELL with specific suggestions for science classrooms. Teaching Today | How-To Articles | Supporting Special Education Students in Science
Parents/Admin
Administrators
Ideas adapted from (Daniels, H, Hyde, A, Zemelman, S, & Heinmann, Initials. (2005). Best practice: Today's standards for teaching and learning in America's schools. Portsmouth,NH:)
1. Students being challenged in thinking how sound is created, how it moves through different media, how it changes its motion in different surroundings, and how pitch (frequency) changes when a frame of reference changes.
2. Students testing their understanding of sound and its properties with investigations, or solving real life scenarios using the concepts and associated equations.
3. Students taking on responsibility for their own learning.
4. Students working in collaborative groups, analyzing, synthesizing, and defending conclusions.
5. Students sharing explanations for the results of investigation and their understanding of concepts.
6. Students continuously assessing and being assessed on their understanding of waves and sound as they change the conditions waves and sound undergo.
7. Students' concepts are being built on prior knowledge of motion, forces, waves, and sound.