1 / 29

PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 16:

PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 16: Chapter 16 – Physics of wave motion Review of SHM Examples of wave motion What determines the wave velocity Properties of periodic waves. Some comments on Simple Harmonic Motion. k. m =1 kg.

stevie
Download Presentation

PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 16:

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 16: Chapter 16 – Physics of wave motion Review of SHM Examples of wave motion What determines the wave velocity Properties of periodic waves PHY 113 C Fall 2013 -- Lecture 16

  2. PHY 113 C Fall 2013 -- Lecture 16

  3. Some comments on Simple Harmonic Motion k m=1 kg Suppose that you know: (in standard units) x(t)=2 cos(2pt+3p) What is k ? k = m(2p)2 PHY 113 C Fall 2013 -- Lecture 16

  4. Some comments on Simple Harmonic Motion k m=1 kg Suppose that you know: (in standard units) x(t)=2 cos(2pt+3p) What is the frequency of oscillations ? w=2pf=2pf=1 Hz PHY 113 C Fall 2013 -- Lecture 16

  5. Some comments on Simple Harmonic Motion k m=1 kg Suppose that you know: (in standard units) x(t)=2 cos(2pt+3p) What is amplitude of the displacement ? xmax=2m PHY 113 C Fall 2013 -- Lecture 16

  6. Some comments on Simple Harmonic Motion k m=1 kg Suppose that you know: (in standard units) x(t)=2 cos(2pt+3p) What is the maximum velocity ? v(t)=-2(2p)cos(2pt+3p) vmax=4p PHY 113 C Fall 2013 -- Lecture 16

  7. Some comments on Simple Harmonic Motion k m=1 kg Suppose that you know: (in standard units) x(t)=2 cos(2pt+3p) What is the maximum acceleration ? a(t)=-2(2p)2cos(2pt+3p) amax=8p2 PHY 113 C Fall 2013 -- Lecture 16

  8. Some comments on Simple Harmonic Motion k m=1 kg Suppose that you know: (in standard units) x(t)=2 cos(2pt+3p) What is the displacement at t=0.3 s ? x(0.3)=2 cos(2p(0.3)+3p) =2(0.309)=0.618 m PHY 113 C Fall 2013 -- Lecture 16

  9. Some comments on driven Simple Harmonic Motion k F(t)=F0sin(Wt) PHY 113 C Fall 2013 -- Lecture 16

  10. Webassign question (Assignment 14) Damping is negligible for a 0.175-kg object hanging from a light, 6.30-N/m spring. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.430 m? PHY 113 C Fall 2013 -- Lecture 16

  11. The phenomenon of wave motion • The wave equation • Wave variable • What does the wave equation mean? • Examples • Mathematical solutions of wave equation and descriptions of waves position time PHY 113 C Fall 2013 -- Lecture 16

  12. Example: Water waves Source: http://www.eng.vt.edu/fluids/msc/gallery/gall.htm Needs more sophistocated analysis: PHY 113 C Fall 2013 -- Lecture 16

  13. Mechanical waves occur in continuous media. They are described by a value (y) which changes in both time (t) and position (x) and are characterized by a wave velocity c: y=f(x-ct) or y=f(x+ct) PHY 113 C Fall 2013 -- Lecture 16

  14. Waves on a string: Typical values for c: 3x108 m/s light waves ~1000 m/s wave on a string 343 m/s sound in air PHY 113 C Fall 2013 -- Lecture 16

  15. Transverse wave: PHY 113 C Fall 2013 -- Lecture 16

  16. Longitudinal wave: PHY 113 C Fall 2013 -- Lecture 16

  17. General traveling wave – t = 0 t > 0 PHY 113 C Fall 2013 -- Lecture 16

  18. iclicker question: t=0 t=1 s t=2s PHY 113 C Fall 2013 -- Lecture 16

  19. Dy qB Dx Basic physics behind wave motion -- example: transverse wave on a string with tension T and mass per unit length m y PHY 113 C Fall 2013 -- Lecture 16

  20. The wave equation: Solutions: y(x,t) = f (x ±ct) functionof any shape PHY 113 C Fall 2013 -- Lecture 16

  21. iclicker question Is it significant to write the wave equation with the special symbols? Yes No PHY 113 C Fall 2013 -- Lecture 16

  22. Examples of solutions to the wave equation: Moving “pulse”: Periodic wave: phase factor “wave vector” not spring constant!!! PHY 113 C Fall 2013 -- Lecture 16

  23. phase (radians) Periodic traveling waves: velocity (m/s) period (s); T = 1/f wave length (m) Amplitude PHY 113 C Fall 2013 -- Lecture 16

  24. Snapshot of periodic wave at t=t0 l f l = c Time plot of periodic wave at x=x0 1/f PHY 113 C Fall 2013 -- Lecture 16

  25. Combinations of waves (“superposition”) “Standing” wave: PHY 113 C Fall 2013 -- Lecture 16

  26. Summary of wave properties: PHY 113 C Fall 2013 -- Lecture 16

  27. Example from webassign: PHY 113 C Fall 2013 -- Lecture 16

  28. phase (radians) Periodic traveling waves: velocity (m/s) period (s); T = 1/f wave length (m) Amplitude PHY 113 C Fall 2013 -- Lecture 16

  29. Example from webassign: PHY 113 C Fall 2013 -- Lecture 16

More Related