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

4. 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

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

7. 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

8. ½ λ

9. Natural Frequency
Standing waves can occur at more than one frequency for any given vibrating object – Natural Frequencies

11. First Harmonic Lowest frequency Also called fundamental freq.
One loop and two nodes
L = ½ 

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

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

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

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

17. 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?