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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.

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

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  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

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