12 Superposition Flashcards
Principle of Superposition
When two or more waves of the same type, meet at a point in space, the resultant displacement of the waves at any point is the vector sum of the displacements due to each wave acting independently at that point
Stationary waves
Waves whose waveform does not advance and there is no translation of energy. The amplitude of the waves varies according to position from zero at the nodes to a maximum at the antinodes
Requirements for a stationary wave to form
- Two progressive waves of same frequency and same speed
- Travelling in opposite directions towards one another
- Having similar or identical amplitudes
- Unpolarised OR polarised along the same axis
Soft boundary
Reflected wave will not be inverted
Hard boundary
Reflected wave will be inverted
Characteristics of a stationary wave
- Waveform does not move/no net energy
- Certain points do not oscillate
- Distance between adjacent nodes = Distance between adjacent antinodes = λ/2
Node
Points that do not oscillate in a stationary wave
Antinodes
Points that have the largest amplitude
Relationship between pressure and displacement nodes in longitudinal stationary waves
Pressure nodes coincide with displacement antinodes
Pressure antinodes coincide with displacement nodes
Fundamental frequency of a stationary wave in a string
f = v/2L
Where L is the length of the string
Closed end of a pipe is the displacement [ ]
node
Open end of a pipe is the displacement [ ]
antinode
Fundamental frequency of a stationary wave in an open pipe
f = v/2L
Fundamental frequency of a stationary wave in a closed pipe
f = v/4L
End Correction
The pressure node in an open end is slightly outside the tube
