# Superposition and interference

### Superposition

• Principle of superposition: when two or more waves meet at a point, the resultant displacement is the sum of the displacements of the individual waves.
• A wave can be represented by a series of vectors.

### Phase

• Two waves are in phase when their peaks and troughs at exactly the same time
• They are out of phase when they occur at different times

### Constructive interference

• Occurs when two waves combine to give a larger wave
• This is at a maximum when two waves are in phase

### Destructive interference

• When two waves combine to give a smaller wave
• This is at a maximum when the path difference is a multiple of .5 of a wavelength
• They are 180o out of phase

• The headphones creates sound waves that cancel the external noise
• It is a destructive interference

### Beats

• If two waves of equal amplitude but slightly different frequency combine, the resulting sound wave will pulse like a beat
• When the waves are in phase, there is constructive interference, when they are out, there is destructive
• Beats per second = difference in frequencies (|f1-f2|)

### Interference – two point sources

• When waves from two point sources interact, superposition occur
• Antinodes occur where the waves add, constructive interference. They form antinodal lines
• Nodes occur when the waves subtract, usually equalling, destructive interference. They form nodal lines.

### Two speakers

• When two speaker produce sound antinodal lines occur where there is constructive interference (loud sound)
• Nodal lines occur where there is destructive interference (soft sound)