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

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

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

½λ
Natural Frequency
Only certain frequencies of waves
produce standing wave patterns
 Frequencies that produce standing
wave patterns are called Natural
Frequencies

First Harmonic
Lowest frequency of standing wave
 Also called fundamental freq.
 One loop and two nodes
 L=½

Overtones
Other natural frequencies of vibration
 Multiples of the fundamental

First Overtone/
nd
2
Harmonic
Two loops and three nodes
 L=

Second Overtone/
rd
3
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?