Remember: “Practice HW #11” posted on WebAssign (0 points, covers Dead Week material)

1. Remember: “Practice HW #11” posted on WebAssign (0 points, covers Dead Week material) Solutions will be posted tomorrow afternoon • Last Time: SHM Position, Velocity, Acceleration; Pendulum Motion • Today: Intro to Wave Properties (useful for PHY 213), (Will not cover 13.9 – 13.11) Review of a few select topics

2. Final Exam Details 7 Multiple Choice Problems 7 x 10 = 70 points 1 Short Answer Problem 20 points 4 Free-Response Problems 25 + 25 + 30 + 30 = 110 points 200 points + Bonus Problem: 10 points Reminder : Thursday, December 16, 10:30 a.m. –12:30 p.m. (normal location)

3. Office Hours Next Week Will hold normal office hours : Tuesday: 2:00 p.m. –4:00 p.m. Wednesday: 1:00 p.m. –4:00 p.m.

4. What is a Wave ? Throw a rock into a still pond. Ripple pattern emerges … undisturbed level drop rock here Wave Moves in This Direction A water wave (or disturbance) “transmits” a disturbance from one location to another, but water is not carried with it. (i.e., a floating object moves up/down, but not horizontally)

5. Mechanical Waves Water waves are an example of “mechanical waves”. They are essentially the motion of a disturbance. Sound waves are another example of mechanical waves. Travel through the air as a result of variations in air pressure from one location to another. [No sound in the vacuum of outer space !!] Mechanical waves require : (1) A source of a disturbance (2) A medium that can be disturbed (3) Some physical connection or mechanism through which adjacent portions of the medium can influence each other.

6. Electromagnetic Waves (PHY 213) In contrast to mechanical waves, electromagnetic waves do not require a medium through which to propagate. As you will learn in PHY 213, EM waves can travel through vacuum (e.g., light travels from the Sun to the Earth via EM waves in the vacuum of outer space).

7. Types of Waves • Waves can be classified according to the different motions of the mediumthrough which the wave passes. • Type #1: Traveling/Transverse Waves • Motion of the medium is perpendicular to the direction of motion. Wave moving in this direction Water (the medium) is moving up and down

8. Another example of a transverse wave !! http://www.youtube.com/watch?v=fztuYEEJMvM&NR=1

9. One thing to note about traveling/transverse waves is that they can transmit disturbances very long distances, relative to the distance that the medium itself moves up/down. [Think about a tsunami !!] SE Asia Tsunami (2004)

10. Types of Waves • Waves can be classified according to the different motions of the medium through which the wave passes. • Type #2: Longitudinal Waves • Medium moves in the same (parallel) direction as the wave motion direction. Example: Slinky (demo) • Sound waves are longitudinal waves. As sound waves move through the air, gas atoms and molecules vibrate back/forth in same direction as sound is moving.

11. Transverse vs. Longitudinal Waves http://paws.kettering.edu/~drussell/Demos/waves/wavemotion

12. Properties of Traveling/Transverse Waves crest undisturbed position amplitude wavelength velocity trough Wavelength: Distance between two successive points that behave identically (e.g., crest-to-crest, or trough-to-trough, distance Amplitude: Maximum displacement of the wave from undisturbed position

13. Properties of Longitudinal Waves Wavelength is distance between centers of compression (or centers of rarefaction) Compression Rarefaction Compression

14. Speed, Frequency, & Wavelength Suppose a wave is moving in the x-direction. Wave speed defined to be : A wave advances a distance of one wavelength in a time equal to one period of the vibration : The frequency is jus t f = 1/T : v : m/s Applies to water waves, sound waves, EM waves, etc. f : Hz [1/s] λ : m

15. Example: 13.41 This wave is traveling in the positive x-direction and has a frequency of 18.0 Hz. Find its : (a) amplitude, (b) wavelength, (c) period, (d) speed

16. Example: 13.43 (modified) The FM radio station WCDA in Lexington/Versailles broadcasts at a frequency of 106.3 MHz. Radio waves are electromagnetic waves, which travel at the speed of light, 3.00 x 108 m/s. • Find: • The radio waves’ period • The radio waves’ wavelength

17. Review of Select Topics

18. Recall: Gauss’s Law for Gravitational Force m2 m1 F21 F12 attractive gravitational force The Third Law. Equal but opposite directions. Action/Reaction pair. 1 F21 = –F12 Magnitudes are equal, calculated with Newton’s Law of Universal Gravitation. 2 Gauss’s Law: The gravitational force exerted by a uniform sphere on a mass located outside the sphere is the same as if the entire mass of the sphere were concentrated at its center. 3

19. Using Gauss’s Law Suppose two spheres are positioned as shown. What is the magnitude of the gravitational force they exert on each other? m1 m2 2R R R

20. Recall: Force of Static Friction force of static friction external applied horizontal force y sled x ground As long as the sled is not moving: As we keep increasing F , fs also increases. Right when the sled is on the verge of slipping (about to start moving) : Once F > fs,max, the sled accelerates in the +x-direction The magnitude of fs is at a maximum: fs,max

21. Recall: Force of Static Friction • The magnitude of the force of static friction between any two surfaces can have values : μs : coefficient of static friction [dimensionless, has no units] n : magnitude of the normal force exerted by one surface on the other • When an object is on the verge of slipping (about to move) : This condition is called “impending motion”. • The inequality, fs < μsn , holds when the applied force F < μsn .

22. Example: 4.52 A block of mass M = 2.0 kg is held in equilibrium on an incline with angle θ = 30. If the coefficient of static friction between the block and incline is μs = 0.300, find : The minimum value of F The normal force exerted by the incline on the block

23. We’re Done !! It was a pleasure lecturing this course.