1. Interference Of Waves

2. Interference
When two or more waves act simultaneously on the same particle in a medium
Resultant displacement is equal to the sum of the individual displacements
Principle of Superposition – sum of two waves

5. Types of Interference
Constructive – 2 waves interfere to produce a resultant displacement greater than the displacement of one
Destructive – 2 waves interfere and produce a wave smaller than one wave

6. Phase
When the crests and troughs of two waves are aligned for constructive interference – In Phase
When crest of one wave repeatedly meet troughs of another wave and destructive interference occurs – Out of Phase

9. Standing Wave
Two interfering waves have the same amplitude and wavelength but opposite directions
Wave produced remains relatively stationary

11. Definitions
Node – points of standing wave that remain at rest – where destructive interference is occurring
Loop or Antinode – double crest or double trough – where constructive interference occurs

12. ½ λ

13. Natural Frequency
Only certain frequencies of waves produce standing wave patterns
Frequencies that produce standing wave patterns are called Natural Frequencies

14. First Harmonic Lowest frequency of standing wave
Also called fundamental freq.
One loop and two nodes
L = ½ 

15. Overtones Other natural frequencies of vibration
Multiples of the fundamental

16. First Overtone/ 2nd Harmonic
Two loops and three nodes
L = 

17. Second Overtone/ 3rd Harmonic
Three loops and five nodes
L = 3/2 

19. Frequency of given harmonic is a multiple of the fundamental frequency
Fn = n F1

20. Example
A piano string is 1.10m long and has a mass of 9.00g a) how much tension must the string be under if it is to vibrate at 131Hz? B) what are the frequencies of the first four harmonics?