1. Chapter 16 4 Superposition 4 and 4 Standing Waves

2. Section 16-1: Superposition of Waves When two or more waves combine, the resultant wave at any point, is the algebraic sum of the individual waves.

3. Superposition and the Wave Equation y 3 = c 1 y 1 + c 2 y 2 superposition

4. Interference of Harmonic Waves

5. Constructive interference

6. Destructive Interference

7. Beats

8. Phase difference due to a path difference Waves are in phase if the phase difference, δ= n(2π) This results in constructive interference

9. The waves are exactly out of phase when δ= (n+½)2π This results in destructive interference

10. Example 16-2 p 485

13. Intensity versus path difference for two sources that are in phase.

14. Two sources that are in phase, or have a constant phase difference are said to be coherent. The Double Slit Experiment: doubleslit

15. Section 16-2: Standing Waves String fixed at both ends The standing wave condition is when L = n(½λ) and f n = nν/2L =nf 1

16. A classic Steinway piano

17. String fixed at one end.

18. Wave functions for standing waves String fixed at both ends wavesuperposition

19. String fixed at one end

20. Standing sound waves on the surface of the sun

21. Some of the many modes of oscillation of a ringing handbell