Superposition of Waves
Principle of Superposition
- When two or more waves of the same type meet at a point, the resultant displacement is the algebraic sum of the individual displacements
Interference and Coherence
- Interference is the formation of points of cancellation and reinforcement where two coherent waves pass each other.
- Coherence occurs when waves have a constant phase difference.
- Conditions for Two-Source Interference:
- They must meet at a point
- They must be of the same type
- They must have the same plane of polarization
- Demonstrating Two-Source Interference:
- In water:
- Ripple generators in a tank
- In light:
- Double slit interference
- In microwaves:
- Two microwave emitters
- In water:
Formation of Stationary Waves
- A stationary waves is formed when two progressive waves, of the same frequency, amplitude, and speed, travelling in opposite directions are superposed.
- A node is a region of destructive superposition where waves always meet out of phase by π, therefore, displacement = 0.
- An antinode is a region of constructive superposition where waves meet in phase, therefore, the particle vibrates with maximum amplitude.
- Neighboring nodes and antinodes are separated by 1/2 λ
- Between two adjacent nodes, particles move in phase and they are out of phase with the next two nodes by π.
Stationary Waves at Different Times
Stationary Wave Experiments
- Stretched String
- A string either attached to a wall or a weight
- Stationary waves will be produced by the direct and reflected waves in the string.
- A microwave emitter is placed a distance away form a metal plate that reflects the emitted wave.
- By moving a detector along the path of the wave, the nodes and antinodes could be detected.
- Air Columns
- A tuning fork held at the mouth of an open tube projects a sound wave into the column of air in the tube.
- The length can be changed by varying the water level.
- At certain tube lengths, the air column resonates.
- This is due to the formation of stationary waves by the incident and reflected sound waves at the water surface.
- Nodes are always formed at the surface of the water.
Stationary and Progressive Waves
- Diffraction is the spreading of waves as they pass through a narrow slit or near an obstancle.
- For diffraction to occur, the size of the gap should be equal to the wavelength of the wave.
- a = split separation
- D = distance from slit to screen
- x = fringe width
- d = distance between successive slits = reciprocal of the number of lines per meter
- θ = angle from horizontal equilibrium
- n = order number
- λ = wavelength
- Comparing to Double-slit to Diffraction Grating:
- Maxima are sharper compared to fringes.
- Maxima are very bright; more slits, more light through.