Define superposition .

Superposition occurs when two or more waves arrive at the same point and overlap, so that their displacements combine to give a resultant displacement.

The principle of superposition states that when two or more waves overlap at a point, the displacement at that point is equal to the .......... of the displacements of the individual waves.

The principle of superposition states that when two or more waves overlap at a point, the displacement at that point is equal to the sum of the displacements of the individual waves.

How should individual wave displacements be combined when applying the principle of superposition?

As vector quantities, since individual displacements may be positive or negative.

True or False? After two pulses meet and overlap, each pulse continues travelling on as normal, unaffected by the interaction.

True. Once the pulses have passed through each other, they carry on with their original shape and direction, as if the interaction had not occurred.

On a diagram showing the superposition of two water waves, what does a region of zero resultant displacement indicate about the individual waves there?

The individual wave displacements at that point are equal and opposite, so they cancel to give a flat (zero) resultant.

Define a stationary wave .

A stationary wave is produced by the superposition of two waves of the same frequency and amplitude travelling in opposite directions (usually a travelling wave and its reflection), forming a wave pattern whose peaks and troughs do not move.

Define a node and an antinode on a stationary wave.

A node is a point of zero amplitude (no vibration) An antinode is a point of maximum amplitude (maximum vibration)

What is the phase relationship between all points lying between two adjacent nodes on a stationary wave?

They are all in phase with each other.

Give three experimental setups used to demonstrate stationary waves.

A stretched string under tension, driven by an oscillator Microwaves reflected off a metal plate, sampled with a moveable detector An air column with a loudspeaker at the open end, using fine powder to show node positions

For a stationary wave to form in an air column, there must be a node at one end and a(n) .......... at the end with the loudspeaker.

For a stationary wave to form in an air column, there must be a node at one end and a(n) antinode at the end with the loudspeaker.

True or False? The nodes of a stationary wave move up and down over time, while the antinodes remain fixed in position.

False. It is the opposite: nodes are fixed in position, while antinodes move in the vertical direction only.

Define the first harmonic (fundamental mode) of a string fixed at both ends.

The first harmonic is the simplest possible stationary wave pattern: a single loop made up of two nodes and one antinode.

For a stationary wave on a string fixed at both ends, the n th harmonic has n antinodes and .......... nodes.

For a stationary wave on a string fixed at both ends, the n th harmonic has n antinodes and n + 1 nodes.

In an air column closed at one end, why can only odd harmonics form?

A node must always form at the closed end and an antinode at the open end. Each successive harmonic adds one extra node and one extra antinode, so only odd-numbered harmonics keep this node–antinode pattern correct.

Why can both odd and even harmonics form in an air column that is open at both ends?

An antinode forms at each open end, and this pattern is maintained as extra nodes and antinodes are added with increasing frequency, so both odd and even harmonics satisfy the boundary conditions.

True or False? For an air column open at both ends, the fundamental mode consists of a quarter wavelength.

False. For a column open at both ends, the fundamental mode is a half wavelength (a quarter wavelength applies to a column with one end closed and one end open).

A LevelPhysicsCambridge (CIE)Flashcards8. SuperpositionStationary Waves

Stationary Waves (Cambridge (CIE) A Level Physics): Flashcards

Exam code: 9702

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FrontThe Principle of Superposition
Define superposition.

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Cards in this collection (19)

Define superposition.
Superposition occurs when two or more waves arrive at the same point and overlap, so that their displacements combine to give a resultant displacement.
The principle of superposition states that when two or more waves overlap at a point, the displacement at that point is equal to the .......... of the displacements of the individual waves.
The principle of superposition states that when two or more waves overlap at a point, the displacement at that point is equal to the sum of the displacements of the individual waves.
How should individual wave displacements be combined when applying the principle of superposition?
As vector quantities, since individual displacements may be positive or negative.
True or False?
After two pulses meet and overlap, each pulse continues travelling on as normal, unaffected by the interaction.
True.
Once the pulses have passed through each other, they carry on with their original shape and direction, as if the interaction had not occurred.
What is the name given to the effect produced by the overlap of waves through superposition?
Interference.
On a diagram showing the superposition of two water waves, what does a region of zero resultant displacement indicate about the individual waves there?
The individual wave displacements at that point are equal and opposite, so they cancel to give a flat (zero) resultant.
Define a stationary wave.
A stationary wave is produced by the superposition of two waves of the same frequency and amplitude travelling in opposite directions (usually a travelling wave and its reflection), forming a wave pattern whose peaks and troughs do not move.
Define a node and an antinode on a stationary wave.
- A node is a point of zero amplitude (no vibration)
- An antinode is a point of maximum amplitude (maximum vibration)
What is the phase relationship between all points lying between two adjacent nodes on a stationary wave?
They are all in phase with each other.
Give three experimental setups used to demonstrate stationary waves.
- A stretched string under tension, driven by an oscillator
- Microwaves reflected off a metal plate, sampled with a moveable detector
- An air column with a loudspeaker at the open end, using fine powder to show node positions
For a stationary wave to form in an air column, there must be a node at one end and a(n) .......... at the end with the loudspeaker.
For a stationary wave to form in an air column, there must be a node at one end and a(n) antinode at the end with the loudspeaker.
True or False?
The nodes of a stationary wave move up and down over time, while the antinodes remain fixed in position.
False.
It is the opposite: nodes are fixed in position, while antinodes move in the vertical direction only.
Define the first harmonic (fundamental mode) of a string fixed at both ends.
The first harmonic is the simplest possible stationary wave pattern: a single loop made up of two nodes and one antinode.
For a string of length L fixed at both ends, what is the wavelength of the nth harmonic?
$λ_{n} = \frac{2 L}{n}$
For a stationary wave on a string fixed at both ends, the nth harmonic has n antinodes and .......... nodes.
For a stationary wave on a string fixed at both ends, the nth harmonic has n antinodes and n + 1 nodes.
In an air column closed at one end, why can only odd harmonics form?
A node must always form at the closed end and an antinode at the open end. Each successive harmonic adds one extra node and one extra antinode, so only odd-numbered harmonics keep this node–antinode pattern correct.
Why can both odd and even harmonics form in an air column that is open at both ends?
An antinode forms at each open end, and this pattern is maintained as extra nodes and antinodes are added with increasing frequency, so both odd and even harmonics satisfy the boundary conditions.
True or False?
For an air column open at both ends, the fundamental mode consists of a quarter wavelength.
False.
For a column open at both ends, the fundamental mode is a half wavelength (a quarter wavelength applies to a column with one end closed and one end open).
For an air column closed at one end, what is the length of the column at the fundamental frequency, in terms of wavelength λ?
$L = \frac{λ}{4}$

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