Principles of Superposition Flashcards
State the Principles of Superposition
When two or more waves of the same type meet, the resultant wave displacement is given by the vector sum of the individual wave displacements at that point.
What are the conditions for formation of stationary waves?
Two progressive waves must have same speed, same frequency, same amplitude, and be travelling in opposite directions.
What are nodes?
These are positions on a stationary wave where resultant displacements is always 0.
What are antinodes?
These are positions on a stationary wave where resultant displacement is at maximum.
How are antinodes formed?
At the antinodes, the interfering waves always reinforce each other and thus give the resultant a maximum amplitude.
Resultant amplitude is sum of amplitudes of component waves and they add up to 2A.
Antinodes exist because the two constituent waves meet in phase at those positions. (0, 2pie, 4pie, …)
How are nodes formed?
At the nodes, the interfering waves always cancel each other completely.
Resultant displacement is always 0, thus amplitude is 0.
Nodes exist because the two constituent waves meet in phase at those positions. (pie, 3pie, …)
Characteristics of stationary wave
For a stationary wave, the energy is trapped within the stationary wave, both energy and wave form do not propagate.
Amplitude of particles depends on the position while for a progressive wave, the amplitude is same for all particles.
Stationary waves have points with maximum amplitude called antinodes and points at which displacement is always 0 called nodes.
In a stationary wave, the distance between 2 adjacent nodes = distance between 2 antinodes, AA= wavelength/2
In stationary wave, the distance between antinodes and nodes is NA=wavelength/4
Shape between 2 adjacent nodes NN is called inter-nodal loop and all points within the inter-nodal loop are always in phase and any 2 points in anti-nodal loop are in anti-phase.
Period on each point is the same in stationary waves except at the nodes where there is no vibration.
Fixed end and Free end characteristics
Free end will act as an antinode and fixed end will act as a node.
Explain how a stationary wave is formed in a tube and why are there piles of sand formed at certain spots.
The soundwave from the loudspeaker will be reflected at the closed end of the tube and this wave will travel through the tube in the opposite direction. 2 waves travelling in the opposite direction will form a stationary wave. The waves must be of the same nature and travelling through the same space, same amplitude, same frequency and same wavelength. The waves travelling in opposite direction will meet in antiphase at the sand due to their odd multiple of phase difference.
In terms of energy transfer, what is meant by the intensity of a progressive wave?
Intensity of a progressive wave means that there is a continous transfer of energy in the direction of propagation of the wave. The higher the energy the higher the intensity.
Some waves can be polarized, state the common features of these waves.
They are transverse waves, vibration is perpendicular to direction of propagation.
State the effect on the separation and intensity of the fringes when the width of each slit is increased but the slit separation remains constant.
Fringe separation increases, light will be less sharp and contrast will be less, the fringes observed on screen will be in same position.
State the effect on the separation and intensity of the fringes when light is incident at a small angle to the normal of the plane of the double slit.
Fringe separation will shift below and the fringe separation will be the same.
Define diffraction
Diffraction is the spreading of waves through an aperture.
When are 2 waves coherent?
2 waves are coherent if there is a constant phase difference between them.
