IB Physics Topic C.4.1 Formation and Properties of Standing Waves Revision Notes (SL/HL)

IB Physics Topic C.4.1 Formation and Properties of Standing Waves Revision Notes (SL/HL) | RevisionDojo

Written by official IB examiners

Formation of Standing Waves through Superposition

Definition

Standing wave

Standing wave is a combination of two waves moving in opposite directions, each having the same amplitude and frequency.

To understand this, let's break down the process:

Two identical waves:
1. Imagine two waves with the same speed, wavelength, and amplitude.
2. One wave travels to the right, while the other travels to the left.
Superposition:
1. When these waves meet, they overlap and combine according to the principle of superposition.
2. This means the displacement of the resulting wave is the sum of the displacements of the two individual waves.
Interference:
1. The waves interfere with each other, creating regions of constructive and destructive interference.
2. In constructive interference, the displacements add up, resulting in a larger amplitude.
3. In destructive interference, the displacements oppose each other, reducing the amplitude and producing zero displacement only when the displacements are equal in magnitude and opposite in direction.

Tip

The principle of superposition states that when two or more waves overlap, the resulting displacement is the sum of the individual displacements.

Nodes and Antinodes

In a standing wave, certain points remain fixed while others oscillate with maximum amplitude.
These points are called nodes and antinodes.

Nodes: Points of Zero Displacement

Definition

Nodes

Nodes are points on a standing wave where the displacement is always zero.

This occurs because of destructive interference between the two waves.

Example

The nodes are located at positions where the two waves meet crest-to-trough, cancelling each other out completely.

Antinodes: Points of Maximum Displacement

Definition

Antinodes

Antinodes are points on a standing wave where the displacement reaches its maximum value.

This occurs due to constructive interference, where the crests or troughs of the two waves align.

Example

The antinodes are located halfway between the nodes, where the amplitude is largest.

Relationship Between Nodes and Antinodes

Distance: The distance between two consecutive nodes (or two consecutive antinodes) is half a wavelength ($\frac{\lambda}{2}$).
Position: Antinodes are always located halfway between two nodes.

Note

Nodes and antinodes are fixed in space.
Unlike travelling waves, the crests and troughs of a standing wave do not move along the medium.

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Formation of Standing Waves through Superposition

Definition

Standing wave

Standing wave is a combination of two waves moving in opposite directions, each having the same amplitude and frequency.

To understand this, let's break down the process:

Two identical waves:
1. Imagine two waves with the same speed, wavelength, and amplitude.
2. One wave travels to the right, while the other travels to the left.
Superposition:
1. When these waves meet, they overlap and combine according to the principle of superposition.
2. This means the displacement of the resulting wave is the sum of the displacements of the two individual waves.
Interference:
1. The waves interfere with each other, creating regions of constructive and destructive interference.
2. In constructive interference, the displacements add up, resulting in a larger amplitude.
3. In destructive interference, the displacements oppose each other, reducing the amplitude and producing zero displacement only when the displacements are equal in magnitude and opposite in direction.

Tip

The principle of superposition states that when two or more waves overlap, the resulting displacement is the sum of the individual displacements.

Nodes and Antinodes

In a standing wave, certain points remain fixed while others oscillate with maximum amplitude.
These points are called nodes and antinodes.

Nodes: Points of Zero Displacement

Definition

Nodes

Nodes are points on a standing wave where the displacement is always zero.

This occurs because of destructive interference between the two waves.

Example

The nodes are located at positions where the two waves meet crest-to-trough, cancelling each other out completely.

Antinodes: Points of Maximum Displacement

Definition

Antinodes

Antinodes are points on a standing wave where the displacement reaches its maximum value.

This occurs due to constructive interference, where the crests or troughs of the two waves align.

Example

The antinodes are located halfway between the nodes, where the amplitude is largest.

Relationship Between Nodes and Antinodes

Distance: The distance between two consecutive nodes (or two consecutive antinodes) is half a wavelength ($\frac{\lambda}{2}$).
Position: Antinodes are always located halfway between two nodes.

Note

Nodes and antinodes are fixed in space.
Unlike travelling waves, the crests and troughs of a standing wave do not move along the medium.

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

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Duis aute irure dolor in reprehenderit

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Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
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Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics C.4.1 Formation and Properties of Standing Waves Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Formation of Standing Waves through Superposition

Nodes and Antinodes

Nodes: Points of Zero Displacement

Antinodes: Points of Maximum Displacement

Relationship Between Nodes and Antinodes

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Formation of Standing Waves through Superposition

Nodes and Antinodes

Nodes: Points of Zero Displacement

Antinodes: Points of Maximum Displacement

Relationship Between Nodes and Antinodes

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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