1. Major Concepts of Physics PHY102 – Lecture #6 1 2016  Syracuse University Lecture #6 What are the quantitative aspects about waves? February 8th Spring 2016 Prof. Liviu Movileanu http://movileanulab.syr.edu/MajorConceptsPhysics2016.html lmovilea@syr.edu Room 211, Physics Bldg., 443-8078 Major Concepts of Physics PHY102

2. Major Concepts of Physics PHY102 – Lecture #6 2 2016  Syracuse University Hints on homework problems. Some examples  Review quantitative description of waves  Review quantitative description of interference  Young’s double-slit experiment Announcements Lecture objectives

3. Major Concepts of Physics PHY102 – Lecture #6 3 2016  Syracuse University Important relationships

4. Major Concepts of Physics PHY102 – Lecture #6 4 2016  Syracuse University A simple example of wave equation A transverse sinusoidal wave is represented by the following equation y = 0.2sin(20t – 0.1x) m Assuming that the units of the quantities in the equation are meters and seconds, find: a) the amplitude of the wave; b) the wavelength; c) the time period; d) the velocity of propagation (state the direction of propagation);

5. Major Concepts of Physics PHY102 – Lecture #6 5 2016  Syracuse UniversityAnswer a) The amplitude of the wave is: A = 0.2 m b) The wavelength: =2  /k=2  /(0.1)=20  m c) the time period:  =2  /T, then T=2  /  = 2  /20 =  /10 s d) the velocity of propagation (state the direction of propagation); v= /T=200 m/s

6. Major Concepts of Physics PHY102 – Lecture #6 6 2016  Syracuse University 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

7. Major Concepts of Physics PHY102 – Lecture #6 7 2016  Syracuse University Second Example Suppose the crest of the first wave overlaps the trough of the second wave. Then, the net wave has its amplitude reduced. This is destructive interference. d sin  = (m+1/2), m= 0, ±1, ± 2, ± 3, …

8. Major Concepts of Physics PHY102 – Lecture #6 8 2016  Syracuse University Demonstration of Interference The interference 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.

9. Major Concepts of Physics PHY102 – Lecture #6 9 2016  Syracuse University The Thomas Young double-slit experiment The pattern consists of a series of bright and dark parallel bands called fringes Constructive interference occurs where a bright fringe occurs Destructive interference results in a dark fringe

10. For a bright fringe, produced by constructive interference, the path difference must be either zero or an integral multiple of the wavelength δ = d sin θ bright = 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 Major Concepts of Physics PHY102 – Lecture #6 10 2016  Syracuse University Interference Equations

11. When destructive interference occurs, a dark fringe is observed This needs a path difference of an odd number of half wavelengths δ = d sin θ dark = (m + ½) λ –m = 0, ±1, ±2, … Major Concepts of Physics PHY102 – Lecture #6 11 2016  Syracuse University Interference Equations

12. 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 Major Concepts of Physics PHY102 – Lecture #6 12 2016  Syracuse University

13. For bright fringes (use sinθ  bright =m λ  /d) For dark fringes (use sinθ  dark =λ (m + ½)λ /d) Major Concepts of Physics PHY102 – Lecture #6 13 2016  Syracuse University Interference Equations, Final

14. 14

15. 15 Example 25.5 Major Concepts of Physics PHY102 – Lecture #62016  Syracuse University

16. 16 Another Example (see Problem 32- Textbook) Light incident on a pair of slits produces an interference pattern on a screen 2.50 m from the slits. If the slit separation is 0.0150 cm and the distance between adjacent bright fringes in the pattern is 0.760 cm, what is the wavelength of the light? [Hint: Is the small angle approximation justified?] 2016  Syracuse UniversityMajor Concepts of Physics PHY102 – Lecture #6

17. 17 2016  Syracuse University 1.Homework #2 is due on this week’s laboratory session. Homework #3 is due on week of Feb 22-26. 2. This week: Workshop #3, “Interference” 3. Do you want to be challenged? More MCAT preps #1? Work problems throughout the sections 25.1, 25.4 4. Next lecture (Lecture #7), Wednesday, Feb 10, Review Meeting for Exam #1Announcements