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  1. Your Comments I thought we didn't have to do the lecture thoughts before. Why do we have to do them now?What exactly is the topic breakdown for the final? How many questions from each topicPicked up my guitar for the first time in a while and messed around with physics.This is very clear and easy! I love waves!I was confused on the diameters of the string question.Best homework ever. As a guitar player, I thoroughly enjoyed it. Can this lecture have guitars? Please, let's have guitars.I really didnt understand the guitar problem, please go over it in class..Can we go over the Guitar problems? WOO-HOO 7 MORE DAYS OF CLASS LEFT!!!Test scores: 78,78,100. Awwwww yeah.my mom used to work at fermilab, if I told you I grew up literally surrounded by physicist and I STILL am not good at physics, would you give me an A for the recognized lost cause I am?Why do guitar players always get so much attention? Why can't oboe players get some love every once in a while?I've been awake for over 20 hours running on 3 hours on sleep. All of this seems difficult to me.For anyone running the marathon on Saturday (and everyone else as well), come out and support Make-A-Wish Foundation on Friday at Chi Omega's Carbo Load Pasta Dinner! $5 presale $7 at the door!

  2. (80.25%) (73.45%) (74.22%)

  3. 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.

  4. Show wave movie from last class http://www.youtube.com/watch?v=5_sfnQDr1-o

  5. Physics 211Lecture 24 Today’s Concepts: A) Superposition B) Standing Waves

  6. The Wave Equation

  7. CheckPoint y v Case A x y Case B x v Suppose a pulse in Case A described by the function y(x,t) = P(x-vt). Which of the following functions described the pulse in Case B? A) y(x,t)=P(x +vt) B) y(x,t)= -P(x +vt) C) y(x,t) = -P(x -vt)

  8. y v Case A x y Case B x v A) y(x,t)=P(x +vt) B) y(x,t)= -P(x +vt) C) y(x,t) = -P(x -vt) A) This is the equation when the wave is traveling in the negative x direction. B) because its going left it must be x +vt and because it is starts out below the x axis it must be negative C) The initial amplitude is negatice, so it is -P, and the velocity is negative, so it is -vt.

  9. Superposition Q: What happens when two waves “collide?” A: They ADD together! Movie (super_pulse) Movie (super_pulse2) “what happens when two waves that aren't the same amplitude collide?”

  10. Superposition A(1t) C(t)= A(t)+ B(t) The wave equation we derived last time is linear. (It has no terms where the variables x,tare squared.) For linear equations, if we have two separate solutions, A and B, then A + B is also a solution! B(2t) DESTRUCTIVEINTERFERENCE CONSTRUCTIVEINTERFERENCE

  11. Beats Can we predict this pattern mathematically? Of course! Just add two cosines and remember the identity: where and Demo cos(Lt) cos(Ht) how do we determine that the frequency is in rad/s or just /s or hertz

  12. Standing Waves What happens when two waves having the same frequency but moving in the opposite direction meet? Wave 1 Wave 1 Wave 1 Wave 2 Wave 2 Wave 2 zero (Nodes) Movie (super) Superposition Mechanics Lecture 24, Slide 12

  13. How it Works Stationary wave Changingamplitude How to make it: Demo

  14. Standing Waves (N = 1)

  15. Why is it that the guitar string must vibrate with fundamental frequency? What would happen if the frequency were just a little off? Does this have to do with harmonics on the strings? (N = 1)

  16. Standing Waves How do wind instruments work? Do they use air as a medium for standing waves? http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html

  17. CheckPoint Suppose the strings on your guitar are 24” long as shown. The frets are the places along the neck where you can put your finger to make the wavelength shorter, and appear as horizontal white lines on the picture. When no frets are being pushed the frequency of the highest string is 4 times higher than the frequency of the lowest string. Is it possible to play the lowest string with your finger on any of the frets shown and hear the same frequency as the highest string? A) Yes B) No 24 20 frets 16 12 8 4

  18. Clicker Question If you want to increase the frequency of a 24” string by a factor of 4 while keeping the tension the same, how long should the string be? A) 4” B) 6” C) 8” D) 12” 24 20 frets 16 12 8 4

  19. Clicker Question 6 Is there a fret that you can push on this guitar to make the string 6” long? A) Yes B) No 24 20 frets 16 12 8 4

  20. Clicker Question The highest string vibrates with a frequency that is 4 times that of the lowest string. Compare the speed of a wave on the high string and the low string: A) vhigh = vlow*2 B) vhigh = vlow*4 C) vhigh = vlow*16 vhigh vlow

  21. Clicker Question The speed of a wave on the high string is 4 times the speed on the lowest string. If the tensions are the same, how does the mass per unit length of the strings compare: A) mlow =mhigh*2 B) mlow = mhigh*4 C) mlow = mhigh*16 Recall vhigh vlow

  22. Clicker Question Two cylinders have the same length and are made from the same material. If the mass of the bigger one is 16 times the mass of the smaller one, how do their diameters compare? L A) dlow =dhigh*2 B) dlow = dhigh*4 C) dlow = dhigh*16 dsmall dbig

  23. CheckPoint dhigh dlow The 6 strings on a guitar all have about the same length and are stretched with about the same tension. The highest string vibrates with a frequency that is 4 times that of the lowest string. If the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare? A) dlow =dhigh*2 B) dlow = dhigh*4 C) dlow = dhigh*16 Mechanics Lecture 24, Slide 23

  24. dhigh dlow The highest string vibrates with a frequency that is 4 times that of the lowest string. If the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare? A) dlow =dhigh*2 B) dlow = dhigh*4 C) dlow = dhigh*16 B) My guitar uses standard Ernie Ball slinkies. The low E uses a .36 and the high E uses a .10. I love how guitar helps me do physics. Really, now, the frequency is inversely proportional to the square root of the mass, which means the mass density has to be be 16 times greater for the low string, which means the radius has to be 4 times as large.

  25. .012” .050” dhigh dlow We just found that the frequency of a string scales with its diameter if the tension is the same. This is really what you find if you examine a guitar:

  26. Different Example – 12 String Guitar The lighter string in these pairs is one octave higher (2x frequency). .028 .052 .022 .042 .014 .030 Their diameters are about half of the adjacent strings.

  27. Homework Problem v = L/t m= m/L Can we go over how changing the length affects things. Specifically the slinky problem on the homework last night.

  28. Homework Problem =4A/P =4Af Average speed = distance / time

  29. Homework Problem

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