1. L4 Transverse Waves revisited- Reflection, Interference, Standing Waves on String

3. Transverse wave propagation

4. Wave reflection at a fixed end: the restoring force in the boundary material causes an upward pulse to become a downward pulse upon reflection

7. Wave reflection at an open end: the upward pulse maintains its orientation upon reflection

10. PhET Simulation Wave on a String

11. Wave Interference/ Wave Superposition

16. Ct 4.5.2.sup The pulse on the left is moving right, the pulse on the right is moving left. What do you see at the "central moment" they pass through one another?

17. Ct 4.5.2.sup SIM www.physics.nyu.edu/~ts2/Animation/waves.html

18. Suppose the pulse reflected from a boundary and moving to the left seen earlier meets another pulse moving to the right…

20. Identical waves moving in opposite directions

21. Motion of point along the spring

22. Standing wave Applet http://webphysics.davidson.edu/A pplets/superposition/default.html (Example 2) http://webphysics.davidson.edu/A pplets/superposition/default.html

23. Standing wave representation

24. Standing Waves in a Stretched String

25. Conditions for standing waves

26. Recall that f=v/λ

28. Hence f n =n f 1 where f 1 = v/(2L) f 1 is called the fundamental frequency (the lowest possible frequency) All harmonics (n= 1,2,3,…) are possible excitations for a string held at both ends!

29. f 2 is called the 2nd harmonic, and is also sometimes referred to as the 1 st overtone (especially in reference to sound). f 3 is the 3d harmonic or the 2 nd overtone, etc.

34. Recall that v=f λ. Suppose we keep v and the length of the string constant. Can we establish a standing wave if we increase the vibrating frequency from f 1 to 1.2 f 1 ? A) yes B) no C) sometimes D) Not enough information given

35. Standing Waves on a String (rope) Demo