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Physics 211 Lecture 23

This lecture focuses on harmonic waves, their types, properties, and the relationship between frequency, wavelength, and speed. We will also discuss the concept of wave functions and their behavior when moving in different directions.

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Physics 211 Lecture 23

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  1. Physics 211Lecture 23 Today’s Concept: Harmonic Waves

  2. Your comments None, this pre-lecture seemed pretty straightforward. Thank Goodness!Do we have to know this for finals?2 things, are there any left handed desks in Loomis 141, and why did the little girl on the merry-go-round on the test have a gun?Strange stuff. I just feel like there's a million different variables and I don't know how to use absolutely all of them. Can we talk about that? Please and thank you! (Who said you can't be polite even if I will never have a comment on the physics wall of fame?)Hey Prof Sorry I couldn't do the prelecture completely today. Have Calc 2 exam in the evening, and I am sitting at Grainger right now at 6am today, after pulling an all nighter here. So don't judge me for not doing the prelecture. So please go slow today. Haven't done the prelecture.Can we experiment waves with my guitar and some heavy riffs? After all these exams, all I want to do is grab my axe and jam a little. It makes sense, after all, music is all about physics.by reading this you are agreeing to give me an A in the class :)When an atom breaks down and converts to energy (nuclear reaction I believe) are the waves considered to be without mass?They say that the reason why only the Jedi and Sith can regularly wield lightsabers is due to their ability to predict the gyroscopic effects of the active lightsaber...so would a master physicist who understood gyroscopic motion be a Jedi Master or a Sith Lord??ILLINI CLUB SOFTBALL NATIONALS THIS WEEK!! GUNNA BRING HOME THE GOLD

  3. http://www.youtube.com/watch?v=72PAHqkBXq0 This is how I feel after physics tests

  4. Final Exams Combined exam: Wednesday May 9 at 1:30 pm.Conflict exam: Thursday May 10 at 8 am. You may take either one but must signup for the conflict in your gradebook. Please check if you have a major conflict with both exams !!

  5. Clicker Question Combined final: Wednesday May 9 at 1:30 pm.Conflict final: Thursday May 10 at 8 am.  A:I have checked my schedule already. I will take the combined final. B:I have checked my schedule already. I will take the conflict final. C: I have checked my schedule already. I can not take either of the above. I have already notified Paco at rdjain1@illinois.edu D:I have checked my schedule already. I can not take either of the above. I will notify Paco later today at rdjain1@illinois.edu E: I have not checked my schedule but I will do so today. I will notify Paco today if I have a problem.

  6. As you're deciding what to put on the board before class today, might I suggest this comic?: http://xkcd.com/895/ I feel like this is a good summary of Physics.

  7. A wave is a traveling disturbance that transports energy but not matter. Examples: Sound waves (air moves back & forth) Stadium waves (people move up & down) Water waves (water moves up & down) Light waves (what moves?) What is a Wave? “I think I speak for many people when I say that there will be quite a bit of disappointment if we do not do the "stadium wave" in lecture..”

  8. Types of Waves Transverse: The medium oscillates perpendicular to the direction the wave is moving. This is what we study in Physics 211. Movie (twave) Longitudinal: The medium oscillates in the same direction as the wave is moving. Movie (lwave)

  9. Wave Properties Amplitude: The maximum displacement Aof a point on the wave. Wavelengthl A Wavelength: The distance between identical points on the wave. Movie (tspeed) Period: The time Pit takes for an element of the medium to make one complete oscillation. String:

  10. y A x y B x WavesAandBshown above are propagating in the same medium. How do their frequencies compare?A) wA< wBB) wA=wBC) wA>wB A) Same medium, same speed. Since B has a shorter wavelength, it has a higher frequency.. B) Its the same medium so they have the same velocity.

  11. Clicker Question The speed of sound in air is a bit over 300 m/s, and the speed of light in air is about 300,000,000 m/s. Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. What is the ratio of the frequency of the light wave to that of the sound wave? A) About 1,000,000 B) About 0.000001 C) About 1000

  12. Suppose we have some function y = f (x): How to make a Function Move y f(x - a) is just the same shape moveda distance a to the right: x 0 x = a y Let a = vtThen f(x - vt) will describe the same shape moving to the right with speed v. v x 0 x = vt y x 0

  13. Consider a wave that is harmonic in x and has a wavelength of. Harmonic Wave y Now, if this is moving tothe right with speed vit will be described by: v x l y A x If the amplitude is maximum atx = 0 this has the functional form:

  14. Clicker Question y = f (x-vt) y y y If a function moving to the right with speed v is described by f (x-vt) then what describes the same function moving to the left with speed v? v x x x 0 0 y A)y = - f (x-vt) v B) y = f (x + vt) x 0 C) y = f (-x + vt)

  15. y y y y y y v x x x x x x 0 0 0 0 y v x 0 Suppose the function has its maximum at f (0). x – vt = 0 y = f (x-vt) v x = vt x – vt = 0 A) y = -f (x-vt) v x = vt x + vt = 0 v x =-vt B) y = f (x+vt) -x + vt = 0 v x = vt C) y = f (-x+vt) Moves to the right when the signs in front of the x and t terms are different Moves to the left when the signs in front of the x and t terms are the same

  16. CheckPoint y A x We have shown that the functional form y(x,t) = Acos(kx- wt) represents a wave moving in the +xdirection. Which of the following represents a wave moving in the –xdirection? A) y(x,t)=Acos(wt- kx) B) y(x,t)=Asin(kx- wt) C) y(x,t)=Acos(kx+ wt)

  17. Energy

  18. CheckPoint y A x y B x Waves A and B shown above are propagating in the same medium with the same amplitude. Which one carries the most energy per unit length? A) A B) B C) They carry the same energy per unit length

  19. CheckPoint y A x y B x Which one carries the most energy per unit length? A) A B) B C) Same A) The amplitude is the same for both but the frequency of wave A is bigger.. B) higher frequency is higher energy C) The height of the waves is the same, so the energy is also the same..

  20. Homework Problem

  21. Homework Problem

  22. Homework Problem

  23. Homework Problem Average speed = distance traveled / time taken Distance traveled by a piece of rope during one period is 4A

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