Principles of Superposition Flashcards
State the Principles of Superposition
When two or more waves of the same type meet at point in space, the resultant wave displacement at any point 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/2
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.
