1. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Physics I 95.141 LECTURE 24 12/8/10

2. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Administrative Notes Physics I Final: –TUESDAY 12/14/10 –Olney 150 (HERE) –8:00 A.M. Review Session Sunday (5/13), 6:30 pm, OH218. Practice Exams Posted –Will try to post solutions in near future Practice problems posted –3+ Will Be on Exam –Everything from the semester is fair game

3. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Review of Lecture 23 Introduced concept of the pendulum, and determined restoring Force acting on pendulum for small displacements. Natural frequency, Period of pendulum given by Introduced damping force to harmonic motion Discussed Forced Oscillations Used A o to discuss concept of resonance

4. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Chapter 15: Waves A wave is a displacement that travels (almost always through a medium) with a velocity and carries energy. –It is the displacement that travels, not the medium!! –The wave travels over large distances, the displacement is small compared to these distances. –All forms of waves transport energy

5. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Characteristics of Waves A continuous or periodic wave has a source which is continuous and oscillating –Think of a hand oscillating a piece of rope up and down –Or a speaker playing a note This vibration is the source of the wave, and it is the displacement that propagates. If we freeze that wave in time (take a picture) x

6. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Characteristics of Waves We can freeze the wave in time, and plot displacement vs. position: Or we can look at a single point in space, and plot displacement vs. time. x t T T

7. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Characteristics of Waves Amplitude (A): Maximum displacement of medium from equilibrium. Wavelength(λ): Distance, in space, between successive crests (or troughs) of wave. Period (T): Time between successive crests or troughs at a fixed position Frequency (f=1/T): Number of crests passing through a fixed point in a second. Velocity (v= λf): Speed at which displacement or disturbance propagates in space.

8. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Types of waves Transverse Wave: A transverse wave is a wave where the direction of the displacement or disturbance is perpendicular to the direction of wave propagation. Examples: –Wave on a string, water waves (on ocean, or ripples in pond), light waves, the wave in a stadium Longitudinal Wave: A longitudinal wave is a wave where the direction of displacement is parallel to the direction of wave propagation Examples –Sound waves, shock waves

9. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Properties of Waves The speed of a wave depends on the properties of the medium the wave is travelling through –A vibration on a string travels with a velocity given by –Sound waves will travel with different speeds in water or in air –Light travels with different speeds through different materials, depending of the material’s index of refraction (n)

10. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Mathematical Representation of Waves Say we freeze a wave in time.

11. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Mathematical Representation of Waves Now we look at the wave 1s later. Wave has moved to the right by 0.5m!

12. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Mathematical Representation of Waves Now we look at the wave 1s later (t=2s). Wave has moved to the right by 1m!

13. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Mathematical Representation of Waves Now we look at the wave after 6s (t=6s). Wave has moved to the right by one wavelength!

14. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Mathematical Description of a Wave

15. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Mathematical Description of a Wave Equation for a forward travelling wave: Equation for a backward travelling wave:

16. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Wave Equation Equivalent to Newton’s 2 nd Law for Particles, equation of motion for waves. In 1-D:

17. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Superposition of Waves If you have multiple waves passing through the same area of space, the total displacement is simply the sum of the displacement from all of the waves.

18. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Superposition of Waves If you have multiple waves passing through the same area of space, the total displacement is simply the sum of the displacement from all of the waves.

19. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Superposition of Waves If you have multiple waves passing through the same area of space, the total displacement is simply the sum of the displacement from all of the waves.

20. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Superposition of Waves If you have multiple waves passing through the same area of space, the total displacement is simply the sum of the displacement from all of the waves.

21. Department of Physics and Applied Physics 95.141, F2010, Lecture 24 Superposition of Waves If you have multiple waves passing through the same area of space, the total displacement is simply the sum of the displacement from all of the waves.