Superposition and interference
- 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.
- When you add the waves, add the vectors
- 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
- Occurs when two waves combine to give a larger wave
- This is at a maximum when two waves are in phase
- 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
Noise cancelling headphones
- The headphones creates sound waves that cancel the external noise
- It is a destructive interference
- 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.
- 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)