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- 1. Today: Energy, Standing Waves, Resonance, Sound Waves <ul><li>Exam questions will be similar to quiz questions </li></ul><ul><li>Essential that you practice the quizzes! </li></ul><ul><li>Covering material including this week </li></ul><ul><li>Quiz #3 Tuesday before class (covered on exam). </li></ul><ul><li>Exercises will be due before class Tuesday. </li></ul>Exam #1 is one week from Thursday In this room, BRING A PENCIL!!! http://www.physicscurriculum.com/Photos/Sound1.JPG
- 2. Homework problem…conservation of energy #1 #2 20 mph Initial speed for both Same initial height Q: Which hits ground with more speed? (neglecting air resistance) <ul><li>First, let’s discuss in groups! </li></ul><ul><li>Ball #1 </li></ul><ul><li>Ball #2 </li></ul><ul><li>Both are the same </li></ul>
- 3. Some good student answers “Some!”—many good ones not here, sorry Lisa: "The way I understand conservation of energy is that it can not be created or destroyed, it can be transformed into one form or another, but the amount of energy does not change. So, I would say that both balls have the same amount of speed when they hit the ground regardless of being thrown upward or downward because the amount of energy does not change regardless of the directions the balls are thrown. " Ritchy : "... and will hit the ground at the same velocity. Of course if the second ball is made from enriched uranium.... " John : "...After passing this point, ball # 2 will fall with the same speed as # 1 did and will follow the same trajectory, and therefore will hit the ground with the same speed ball # 1 did. " Adrian: “…it would regain the speed it had traveling upwards because it would not have transfered that energy elsewhere." Brian : "The law of the Conservation of Energy states that energy can be transformed but never created or destroyed. Because both balls are being thrown at the same speed in the same gravitational zone both balls have the same amount of energy and therefore will hit the ground at the same speed... Reuben: So while they will hit the ground at different times they will be at the same speed when they hit. " Audrey : "..The same amount of energy put in will be the same till it hits the ground because nothing is getting in its way. This is a trick question. " Aubrey: "Think of how ball #2 would look on a graph. It's velocity would slightly decrease until it reached the top of its path, and then increase on its way down until it hit the ground. Its velocity would be mirrored, then, the same on the way up as the way down...."
- 4. Homework problem…conservation of energy #1 #2 20 mph Initial speed for both Same initial height Q: Which hits ground with more speed? (neglecting air resistance) You could analyze with F = ma, Equations of motion, etc. But much easier using conservation of energy!
- 5. Homework problem…one viewpoint #1 #2 20 mph Initial speed for both Same initial height Q: Which hits ground with more speed? (neglecting air resistance) Which one has higher initial total energy (KE + PE)? Can the ball lose total energy while in the air (without air resistance)? KE = ½ m v 2 PE = m g h So which one would have more energy when hitting ground?
- 6. Homework problem…another viewpoint #1 #2 20 mph Initial speed for both Q: Which hits ground with more speed? (neglecting air resistance) If energy is conserved, then what will be the speed of ball #2 when it returns to the point it started? ? mph Potential energy is the same… Given that information, which ball would hit faster? Check student answers on WebCT (tomorrow night?) Answer is: same speed Think about energy flow and conservation of energy…this plays a part in waves too. #2
- 7. Clicker question--wavelength Let’s discuss this one in groups
- 8. Frequency and speed are the fundamental properties of a wave <ul><li>The frequency of the wave is determined by the frequency of the driving oscillation. (and possibly motion of the source…Doppler) </li></ul><ul><li>The speed of the wave is determined by the physics of the material. </li></ul><ul><li>The wavelength (e.g. distance between crests) is determined by the frequency and speed. </li></ul>(Wave speed = wavelength x frequency) Wavelength = Wave speed frequency
- 9. Reminder about amplitude and wavelength
- 10. Standing waves are the result of interference <ul><li>Interference of waves is addition of waves </li></ul><ul><ul><li>Waves have “+” and “-” regions for adding </li></ul></ul><ul><ul><li>Wave interference is a really important physics concept </li></ul></ul><ul><li>Today, we’ll look at interference as the cause for standing waves. </li></ul>What will happen when these waves meet? Falstad ripple tank applet
- 11. Standing waves are the result of interference <ul><li>Interference of waves is addition of waves </li></ul><ul><ul><li>Waves have “+” and “-” regions for adding </li></ul></ul><ul><li>Standing waves result from interference of a wave with its own reflection… only for special conditions </li></ul>http://www.falstad.com/ripple/
- 12. I wish we could look at wave interference with a real demo! Wave table!
- 13. Standing waves…stored energy <ul><li>Energy is “stored” in the wave…no net transport </li></ul><ul><ul><li>But results from the movement of energy BOTH ways! </li></ul></ul>Antinode, Highest energy Node , Lowest Energy Energy flow? Standing wave youtube demo http://www.youtube.com/watch?v=yCZ1zFPvrIc
- 14. Clicker Question—Standing Waves <ul><li>The picture to the right is a schematic of a standing wave on a stretched rope. </li></ul><ul><li>Which point labels an antinode? </li></ul>A B
- 15. Clicker Question—Standing Waves <ul><li>The picture to the right is a schematic of a standing wave on a stretched rope. </li></ul><ul><li>Which point labels an antinode? </li></ul><ul><li>“ A” is an antinode…antinodes are places with the highest amplitude …and the highest energy (“B” is a “node”) </li></ul>A B
- 16. Standing waves…only some “modes” will work <ul><li>Modes must satisfy “boundary conditions” </li></ul><ul><li>In this case, the ends must be antinodes for constructive interference. </li></ul>Notice the special frequencies Can only control the frequency, not wavelength! These special frequencies are resonant frequencies of the wave table (missing the citation for this wavetable video)
- 17. Resonance <ul><li>Resonance occurs when an wave is driven at the correct frequency for a standing wave </li></ul><ul><li>Disastrous resonance demos </li></ul><ul><li>Resonance a key to musical tones (more later) This gets us to sound waves </li></ul>The classic: http://www.youtube.com/watch?v=17tqXgvCN0E&feature=related| Also Tacoma MIT Resonance Demo http://www.youtube.com/watch?v=aZNnwQ8HJHU
- 18. Clicker Question—Sound waves <ul><li>If we could see a pure tone sound wave in the air, which of the following would we see? </li></ul><ul><li>Transverse displacements of molecules as in a wave on a string </li></ul><ul><li>Alternating regions of high density and low density </li></ul><ul><li>Twisting motion of air as in the wave table </li></ul>
- 19. Clicker Question—Sound waves <ul><li>If we could see a pure tone sound wave in the air, which of the following would we see? </li></ul><ul><li>Transverse displacements of molecules as in a wave on a string </li></ul><ul><li>Alternating regions of high density and low density </li></ul><ul><li>Twisting motion of air as in the wave table </li></ul><ul><li>Sound waves are longitudinal compression / rarefaction waves </li></ul>
- 20. Reminder of difference between transverse and longitudinal waves Transverse Wave Longitudinal wave Imagine this is a speaker (sorry, I am missing the citations for these animated gifs)
- 21. Sound in air is a Compression / Rarefaction Wave <ul><li>Slinky </li></ul><ul><li>Flame tube I’ll describe what the flame tube is. How should a standing wave of pressure nodes / antinodes affect the flame? </li></ul>
- 22. Note: we ran out of time here and did not get to discuss the following slides in today’s lecture (Feb. 3, 2009)
- 23. Last week’s puzzler: Wind and Doppler Effect <ul><li>Another perspective, may cause “aha!”: </li></ul><ul><ul><li>What if both the whistle and the person were moving in the same direction? Is that any different than a wind blowing? </li></ul></ul>The compression / rarefaction waves are what you hear… Remember it’s the frequency that determines the pitch
- 24. Last week’s puzzler: Wind and Doppler Effect <ul><li>Another perspective, may cause “aha!”: </li></ul><ul><ul><li>What if both the whistle and the person were moving in the same direction? Is that any different than a wind blowing?.... CLICKER Q! </li></ul></ul>
- 25. 1. Yes 2. No Does the wind affect the pitch of a factory whistle you hear on a windy day?
- 26. Author’s very good analogy, why wind does not affect pitch of sound <ul><li>If the first guy is only putting down items once per second… </li></ul><ul><li>How could a faster belt increase the number of items per second the second guy can pick up? </li></ul>
- 27. Ripple tank applet for Doppler Effect http://www.falstad.com/mathphysics.html ripple Nerf Doppler Demo Possibly this applet if it works http://physics-animations.com/Physics/English/waves.htm

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