Define stationary wave .

A stationary wave is formed by the superposition of two waves of the same frequency and amplitude travelling in opposite directions, usually a travelling wave and its reflection.

What is the key difference between how a stationary wave and a progressive wave handle energy?

A stationary wave stores energy, whereas a progressive wave transfers energy.

A node is a point on a stationary wave with no vibration (zero amplitude).

An antinode is a point on a stationary wave where the vibration is at its maximum amplitude.

Do the nodes and antinodes of a stationary wave move along its length?

No. The nodes are fixed in position, and the antinodes only move vertically (in amplitude), not along the length of the wave.

Two points on a stationary wave with an .......... number of nodes between them are out of phase, while two points with an .......... number of nodes between them are in phase.

Two points on a stationary wave with an odd number of nodes between them are out of phase, while two points with an even number of nodes between them are in phase.

True or False? Two points on a stationary wave with one node between them are in phase.

False. Points separated by an odd number of nodes (such as one) are out of phase ; only an even number of nodes between two points gives points that are in phase.

Define the principle of superposition .

The principle of superposition states that when two or more waves with the same frequency arrive at a point, the resultant displacement is the sum of the displacements of each wave.

What happens when two waves of the same frequency and amplitude superpose in phase ?

Constructive interference occurs: the peaks and troughs of both waves line up, and the resultant wave has double the amplitude.

What happens when two waves of the same frequency and amplitude superpose in anti-phase ?

Destructive interference occurs: the peaks of one wave line up with the troughs of the other, and the resultant wave has no amplitude.

What conditions must two waves meet to form a stationary wave ?

The two waves must travel in opposite directions along the same line, and have the same frequency, the same wavelength, and a similar amplitude.

Why does a node form at a particular point on a stationary wave?

At a node , the two component waves are in anti-phase, so destructive interference causes them to cancel each other out.

Why does an antinode form at a particular point on a stationary wave?

At an antinode , the two component waves are in phase, so constructive interference causes them to add together.

On a stretched string, stationary waves (resonant frequencies) form when a .......... number of half wavelengths fits exactly onto the length of the string.

On a stretched string, stationary waves (resonant frequencies) form when a whole number of half wavelengths fits exactly onto the length of the string.

True or False? Like a stationary wave, every point on a progressive wave has a different amplitude.

False. On a progressive wave , every point has the same amplitude. It is on a stationary wave that each point has a different amplitude, ranging from zero at the nodes to maximum at the antinodes.

Define the first harmonic (fundamental frequency).

The first harmonic is the simplest stationary wave pattern on a string fixed at both ends: a single loop consisting of two nodes and one antinode.

How many nodes and antinodes does the second harmonic of a string fixed at both ends have?

The second harmonic has three nodes and two antinodes .

How many nodes and antinodes does the third harmonic of a string fixed at both ends have?

The third harmonic has four nodes and three antinodes .

For the nth harmonic on a string fixed at both ends, how many antinodes and nodes are there?

The nth harmonic has n antinodes and n + 1 nodes.

How is the frequency of the nth harmonic related to the frequency of the first harmonic ?

The frequency of the nth harmonic is n times the frequency of the first harmonic.

For a string of length L fixed at both ends, the wavelength of the first harmonic is ..........

For a string of length L fixed at both ends, the wavelength of the first harmonic is 2L .

True or False? The third harmonic of a stationary wave on a string has three nodes and four antinodes.

False. The third harmonic has four nodes and three antinodes — following the rule that the nth harmonic has n antinodes and n + 1 nodes.

What is the aim of this required practical?

To investigate how the frequency of the first harmonic on a stretched string is affected by changing the length of the string, the tension in the string, or the mass per unit length of the string.

What is the independent variable and what is the dependent variable in this experiment?

Independent variable: length, tension, or mass per unit length of the string (whichever is being investigated) Dependent variable: frequency of the first harmonic

How is the mass per unit length, μ , of the string determined?

Measure the mass of a known length of the string (1 m is ideal) on a balance, then calculate μ = mass of string ÷ length of string.

A graph of frequency f against 1/ L is plotted for this experiment. What does the gradient of this graph represent, and how is the wave speed found from it?

The gradient of the graph is equal to v /2, so the wave speed is found by doubling the gradient: v = 2 × gradient.

What is the main source of random error when identifying the first harmonic in this experiment, and how can it be minimised?

The sharpness of resonance makes it difficult to judge exactly when the first harmonic has been reached. This is minimised by adjusting the frequency while watching a node closely, to find the position of largest response.

In this experiment, a .......... string should be used instead of a metal wire, to avoid injury if it snaps under tension.

In this experiment, a rubber string should be used instead of a metal wire, to avoid injury if it snaps under tension.

True or False? The amplitude of vibration is the most reliable way to judge exactly when the first harmonic has been reached.

False. Looking at the amplitude is less reliable, since the string is moving very fast at resonance. A more reliable technique is to adjust the frequency while watching a node closely, to find the position of largest response.

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Stationary Waves (AQA A Level Physics): Flashcards

Exam code: 7408

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Define stationary wave.

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Cards in this collection (31)

Define stationary wave.
A stationary wave is formed by the superposition of two waves of the same frequency and amplitude travelling in opposite directions, usually a travelling wave and its reflection.
What is the key difference between how a stationary wave and a progressive wave handle energy?
A stationary wave stores energy, whereas a progressive wave transfers energy.
Define node.
A node is a point on a stationary wave with no vibration (zero amplitude).
Define antinode.
An antinode is a point on a stationary wave where the vibration is at its maximum amplitude.
Do the nodes and antinodes of a stationary wave move along its length?
No. The nodes are fixed in position, and the antinodes only move vertically (in amplitude), not along the length of the wave.
Two points on a stationary wave with an .......... number of nodes between them are out of phase, while two points with an .......... number of nodes between them are in phase.
Two points on a stationary wave with an odd number of nodes between them are out of phase, while two points with an even number of nodes between them are in phase.
True or False?
Two points on a stationary wave with one node between them are in phase.
False.
Points separated by an odd number of nodes (such as one) are out of phase; only an even number of nodes between two points gives points that are in phase.
Define the principle of superposition.
The principle of superposition states that when two or more waves with the same frequency arrive at a point, the resultant displacement is the sum of the displacements of each wave.
What happens when two waves of the same frequency and amplitude superpose in phase?
Constructive interference occurs: the peaks and troughs of both waves line up, and the resultant wave has double the amplitude.
What happens when two waves of the same frequency and amplitude superpose in anti-phase?
Destructive interference occurs: the peaks of one wave line up with the troughs of the other, and the resultant wave has no amplitude.
What conditions must two waves meet to form a stationary wave?
The two waves must travel in opposite directions along the same line, and have the same frequency, the same wavelength, and a similar amplitude.
Why does a node form at a particular point on a stationary wave?
At a node, the two component waves are in anti-phase, so destructive interference causes them to cancel each other out.
Why does an antinode form at a particular point on a stationary wave?
At an antinode, the two component waves are in phase, so constructive interference causes them to add together.
On a stretched string, stationary waves (resonant frequencies) form when a .......... number of half wavelengths fits exactly onto the length of the string.
On a stretched string, stationary waves (resonant frequencies) form when a whole number of half wavelengths fits exactly onto the length of the string.
True or False?
Like a stationary wave, every point on a progressive wave has a different amplitude.
False.
On a progressive wave, every point has the same amplitude. It is on a stationary wave that each point has a different amplitude, ranging from zero at the nodes to maximum at the antinodes.
Define the first harmonic (fundamental frequency).
The first harmonic is the simplest stationary wave pattern on a string fixed at both ends: a single loop consisting of two nodes and one antinode.
How many nodes and antinodes does the second harmonic of a string fixed at both ends have?
The second harmonic has three nodes and two antinodes.
How many nodes and antinodes does the third harmonic of a string fixed at both ends have?
The third harmonic has four nodes and three antinodes.
For the nth harmonic on a string fixed at both ends, how many antinodes and nodes are there?
The nth harmonic has n antinodes and n + 1 nodes.
How is the frequency of the nth harmonic related to the frequency of the first harmonic?
The frequency of the nth harmonic is n times the frequency of the first harmonic.
For a string of length L fixed at both ends, the wavelength of the first harmonic is ..........
For a string of length L fixed at both ends, the wavelength of the first harmonic is 2L.
What equation gives the speed of a wave travelling along a stretched string?
$v = \sqrt{\frac{T}{μ}}$
Where T is the tension in the string (N) and μ is the mass per unit length of the string (kg m^-1).
True or False?
The third harmonic of a stationary wave on a string has three nodes and four antinodes.
False.
The third harmonic has four nodes and three antinodes — following the rule that the nth harmonic has n antinodes and n + 1 nodes.
What is the aim of this required practical?
To investigate how the frequency of the first harmonic on a stretched string is affected by changing the length of the string, the tension in the string, or the mass per unit length of the string.
What is the independent variable and what is the dependent variable in this experiment?
- Independent variable: length, tension, or mass per unit length of the string (whichever is being investigated)
- Dependent variable: frequency of the first harmonic
How is the tension in the string calculated in this experiment?
$T = m g$
Where m is the mass attached to the string and g is the gravitational field strength (9.81 N kg^-1).
How is the mass per unit length, μ, of the string determined?
Measure the mass of a known length of the string (1 m is ideal) on a balance, then calculate μ = mass of string ÷ length of string.
A graph of frequency f against 1/L is plotted for this experiment. What does the gradient of this graph represent, and how is the wave speed found from it?
The gradient of the graph is equal to v/2, so the wave speed is found by doubling the gradient: v = 2 × gradient.
What is the main source of random error when identifying the first harmonic in this experiment, and how can it be minimised?
The sharpness of resonance makes it difficult to judge exactly when the first harmonic has been reached. This is minimised by adjusting the frequency while watching a node closely, to find the position of largest response.
In this experiment, a .......... string should be used instead of a metal wire, to avoid injury if it snaps under tension.
In this experiment, a rubber string should be used instead of a metal wire, to avoid injury if it snaps under tension.
True or False?
The amplitude of vibration is the most reliable way to judge exactly when the first harmonic has been reached.
False.
Looking at the amplitude is less reliable, since the string is moving very fast at resonance. A more reliable technique is to adjust the frequency while watching a node closely, to find the position of largest response.

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