1. Waves Lecture 4

2. Goals  Gain an understanding of basic wave classification  Learn about mathematically modeling waves  Gain an understanding of wave phenomena such as refraction

3. Matter as a Wave  Matter, which is the stuff making up you, actually behaves as a wave and a particle  It exhibits properties such as interference like a wave and collisions like a particle  Modeling matter waves is beyond the scope of this course and is covered in quantum mechanics

4. Mechanical Waves  Mechanical waves are very different than matter waves  In these waves, only energy is transported without actual matter transportation  It is due to neighbor atoms disturbing each other (examples include sound, Slinkys, and water waves)

5. Electromagnetic Waves  Electromagnetic phenomena, which include light, also exhibit wave like behavior, the require no medium to move through  They interfere, refract, etc and for most of the 19 th Century were believed to be purely waves  Similar to matter waves though, they do have a particle like nature that can be seen during collisions

6. More on Wave Classification  The previous waves can be categorized as transverse or longitudinal (or possibly a mixture of both as in ocean waves) Waves Transverse ElectromagneticMatterMechanical Longitudinal Mechanical

7. Transverse and Longitudinal Waves  Transverse Waves vibrate perpendicular to the direction of the energy flow  Longitudinal Waves vibrate parallel to the direction of energy flow

8. Waves and Energy  Given an energy source, such as a star, where energy propagates outward through wave phenomena, the following holds (when no energy is absorbed or reflected)

9. Lets try a Problem  Given a light bulb that produces an intensity of approximately 1 Watt/m 2 at distance of 2 meters from the bulb, what is the intensity 4 meters away from the bulb?

10. Waves on a String  The previous example required no medium for the wave to propagate  The next example is a mechanical wave propagating energy on a taunt string  The following equation is used

12. Period Waves  Periodic waves repeat a pattern  They have a period and velocity

13. Harmonic Waves  A Harmonic Wave is a type of periodic wave that is sinusoidal  The Simple Harmonic Motion we studied previously is modeled in terms of harmonic waves  The intensity of the wave is proportional to the energy and therefore proportional to the square of the amplitude

14. Traveling Harmonic Waves  Certain types of Harmonic Waves travel  This one travels is the positive x direction, a positive sign in front of kx would mean the wave travels in the negative x direction

15. Lets try Sketching a Traveling Wave

16. Superposition  Two waves can either add together constructively or destructively, this is constructive superposition

17. Reflection  Traveling waves can reflect off boundaries  If we neglect loss of energy their amplitude will remain unaltered

18. Refraction  Waves can also refract when moving from one media to another

19. Lets try an Example  Light initially moving in air of n = 1 at 70 degrees with respect to the horizontal moves into glass with n = 1.33. Find the new angle with respect to the horizontal

21. Additional Notes