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Major Concepts of Physics PHY102 – Lecture #4

Major Concepts of Physics PHY102 - 2006 Lecture #4 January 26th. Traveling Waves: Longitudinal versus Transverse Waves. 1. Major Concepts of Physics PHY102 – Lecture #4. 2005 Syracuse University. Update…Time is Flying. Tues., January 17 th : Lecture #1 Introduction to Course.

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Major Concepts of Physics PHY102 – Lecture #4

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  1. Major Concepts of Physics PHY102 - 2006Lecture #4 January 26th Traveling Waves: Longitudinal versus Transverse Waves 1 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  2. Update…Time is Flying Tues., January 17th: Lecture #1 Introduction to Course. Thurs., January 19th: Lecture #2 Waves and the Concepts Describing Them Tues., January 24th: Lecture #3 Interferences of Waves: Young’s Experiment Thurs., January 26th: Lecture #4 Traveling Waves; Longitudinal vs. Transverse Waves Tues., January 31st: Lecture #5 Diffraction: a close look Thurs., February 2nd, Lecture #6 Electromagnetic Waves Tues., February 7th; Lecture #7 Review Meeting, Part I Thurs., February 9th: Exam 1 2 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  3. Announcement: Quiz #1 Tuesday, January 31st, 8:00 AM This will include Lectures 1-4, and Workshop #1 3 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  4. Outline – Lecture Objectives #4 1)Review of the Thomas Young experiment (Demo). 2)       Transverse versus longitudinal waves; 3) How do we express a wave in mathematical form? 4) Introduction to Diffraction 4 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  5. First Example We have two waves. Suppose that the crest of the first wave overlaps the crest of the second wave. Then, the effect is that the net wave has increased amplitude at this point and time. This is constructive interference. d sin  = m, m= 0, 1, 2, 3, … d=the distance between slits 5 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  6. Second Example Suppose the crest of the first wave overlaps the valley of the second wave. Then, the net wave has its amplitude reduced. This isdestructive interference.  d sin  = (m+1/2), m= 0, 1, 2, 3, … 6 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  7. Demonstration of Interference Theinterference model. Two sinusoidal waves superpose on each other. When the waves are in-phase, we have constructive interference. When the waves are 180 degrees out-of-phase, we have destructive interference. 7 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  8. Interference Equations, 3 • For a bright fringe, produced by constructive interference, the path difference must be either zero or some integral multiple of of the wavelength • δ = d sin θbright = m λ • m = 0, ±1, ±2, … • m is called the order number • When m = 0, it is the zeroth order maximum • When m = ±1, it is called the first order maximum 8 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  9. Interference Equations, 4 • When destructive interference occurs, a dark fringe is observed • This needs a path difference of an odd half wavelength • δ = d sin θdark = (m + ½) λ • m = 0, ±1, ±2, … 9 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  10. Interference Equations, 5 • The positions of the fringes can be measured vertically from the zeroth order maximum • y = L tan θL sin θ • Assumptions • L>>d • d>>λ • tan θsin θ θ is small and therefore the approximation tan θsin θ can be used 10 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  11. Interference Equations, Final • For bright fringes (use sinθbright=m λ/d) • For dark fringes (use sinθdark=λ (m + ½)/d) 11 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  12. Lecture #4 Objectives 1)  Summary on Waves; Math form for simplest waves. 2) We will focus on the simplest of all wave: The traveling wave. 2) Examples…examples…(the best way to understand and learn) 12 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  13. Definitions 1. Traveling waves: waves that travel (move, propagate) Longitudinal wave: the vibration of the particles of the medium is in a direction along the wave motion Transverse wave: the vibration of the particles of the medium is in a direction perpendicular on the wave motion 13 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  14. Space Dependence Fix time t. Vary the location x along a straight line. We call x the propagation direction of the wave. For light, we say that x is the direction of the ray.  Then, the wave is periodic, for a traveling wave. The repeat-distance is the wavelength. Its symbol is λ. Mathematical form, fixed time t. The value of the size of the peak (relative to the zero-value) is called the amplitude. 14 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  15. Pure Wave Wavelength () disturbance  position 15 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  16. Pure Wave • Amplitude (A) disturbance position A 16 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  17. The wave form The precise form for the wave isWave value y = A sin (2πx/λ).Replacement of sine by cosine also expresses a wave. This replacement simply shifts the wave along the x direction by (1/4)λ. 17 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  18. Cosine moves the wave with /4 disturbance /2 cosine sine position A 18 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  19. About radians and degrees The angle inside the sine has units of radians. Reminder: One radian is that angle for which the arc length and radial length are equal. Check that this form is right: If we add the full wavelength λ to x, then the angle inside the sine simply increases by 2π. That is, by 360 degrees. Conclude: The wave-value is unchanged, as expected. 19 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  20. Time Dependence Now, fix the location x. Vary the time t. Then, the time dependence is also sinusoidal. The form for the t-dependence; Wave value = A sin (2πt/T). T is the period. It is the repeat-time. The frequency f of the wave is the number of full cycles per time. So, it is the inverse of T: f = 1/T. 20 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  21. The full form of the wave Now, let both x and t vary. The full form for the wave is:  Wave value = y = A sin [(2πx/λ) – (2πt/T)]= A sin [2π(x/λ – t/T)] This is the complete form for any traveling wave. It simply combines the previous two forms. 21 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  22. Introduction to Diffraction Observation: Suppose light passes through an opening that is large, compared to its wavelength λ. Then, we find: The shadow it casts is sharp. It appears that there is no spreading out of the light But: Suppose light passes through a tiny opening. We observe: The light spreads out like a fan. There is no sharp shadow. There is a bright area that fades into darkness. There are no sharp edges. 22 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  23. Introduction to Diffraction Second observation: If we look more carefully, we can see alternate dark and bright fringes at the edges. On close examination, even the sharpest shadow is blurred slightly at the edges. These phenomena define diffraction. 23 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  24. Cause of Diffraction Its cause is interference.Light rays intersect the opening at differing points (call them A, B, C, etc.) within the opening. Pick any point P on the screen.The path-length of the ray from opening to P depends on the location(A, B, C, …..) of the point it intersects the opening. 24 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  25. Example: Suppose the rays from A and B (both to P) have lengths that differ by a multiple of λ.Then, they interfere constructively, reinforcing each other. But suppose the rays from A and C differ by (1/2)λ. Then there is destructive interference. (cancellation). For some points P on the screen, constructive interference dominates. Then, we see a bright spot. For other points on the screen, destructive interference dominates. Then, wee see a dark spot.   25 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

  26. Homework Homework (next week) http://wps.prenhall.com/esm_giancoli_physicsppa_6 Go to Chapter 11; Go to Practice Questions 11, 18, 19, 20, 21, 22, 23 Click: submit answers for grading Send the results to your TA (by E-mail). 26 Major Concepts of Physics PHY102 – Lecture #4 2005Syracuse University

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