Interference Of Waves

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

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

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

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

½ λ

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

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

Overtones Other natural frequencies of vibration Multiples of the fundamental

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

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

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

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?