Topic 9.610 min read
Stationary Waves (Standing Waves)
A stationary or standing wave is produced when identical waves of the same speed, amplitude and frequency travel in opposite directions and superpose. Its pattern has fixed nodes and antinodes and transfers no energy from one part of the medium to another.
Choose Your Level
Beginner Level
Shake a rope while its far end reflects the wave back. The outgoing and reflected waves can combine to make a pattern that seems fixed. Some points never move, while other points move the most.
Recommended for Class 11
Overview
A stationary or standing wave is produced when identical waves of the same speed, amplitude and frequency travel in opposite directions and superpose. Its pattern has fixed nodes and antinodes and transfers no energy from one part of the medium to another.
Learning Outcomes
- A stationary wave is formed by identical waves travelling in opposite directions and superposing.
- The interfering waves have the same speed, amplitude and frequency.
- Nodes are fixed points where displacement is always zero.
- Antinodes are fixed points where particles oscillate with maximum amplitude.
- The standing-wave pattern does not travel through the medium.
- A stationary wave transfers no energy from one particle to the next.
- Successive nodes or successive antinodes are separated by half a wavelength.
- A node and its nearest antinode are separated by one quarter of a wavelength.
Intermediate Level
How a Stationary Wave Is Formed
A wave travelling through a medium is reflected at a boundary. The reflected wave travels back through the incoming wave. If the two waves are identical and have the same speed, amplitude and frequency, their superposition produces a stationary-wave pattern. The two component waves continue travelling in opposite directions, but the resultant pattern does not move along the medium.
Changing Shape During One Period
The textbook shows the resultant at several instants during one cycle, including t=0, T/4, T/2, 3T/4 and T. The particles between neighboring nodes oscillate up and down, so the shape changes with time. However, the positions of the nodes and antinodes remain fixed, which is why the pattern is called stationary.
Nodes and Antinodes
| Feature | Node (N) | Antinode (A) |
|---|---|---|
| Displacement | Always zero | Maximum |
| Particle motion | Particle does not vibrate | Particle oscillates rapidly |
| Cause | Continuous destructive interference | Continuous constructive interference |
| Position | Fixed | Fixed |
At a node, the two component waves always cancel, so the particle remains at rest. At an antinode, their displacements reinforce, so the oscillation amplitude equals the sum of the component amplitudes.
Why the Pattern Does Not Carry Energy
In a progressive wave, the disturbance and energy travel from particle to particle. In a stationary wave, each section of the medium oscillates within a fixed region bounded by nodes. Since the pattern does not advance, there is no net transfer of energy from one part of the medium to another.
Characteristic Distances
The distance from one node to the next node is the same as the distance from one antinode to the next antinode. Each equals half a wavelength.
A node lies halfway between its two neighboring antinodes, so the distance from a node to the nearest antinode is one quarter of a wavelength.
Spacing in a Standing Wave
A stationary wave has wavelength 0.80 m. Find the distance between successive nodes and the distance from a node to the nearest antinode.
- λ=0.80m
dNN=λ2=0.802=0.40m
dNA=λ4=0.804=0.20m
Final answer: Successive nodes are 0.40 m apart, and a node is 0.20 m from the nearest antinode.
Progressive Wave and Stationary Wave
| Property | Progressive wave | Stationary wave |
|---|---|---|
| Pattern | Travels through the medium | Remains fixed |
| Amplitude | Generally the same at equivalent points | Varies from zero at nodes to maximum at antinodes |
| Energy | Transferred through the medium | No net transfer from particle to particle |
| Fixed nodes and antinodes | Absent | Present |
Common Mistakes
- Do not say that the component waves stop moving; they travel in opposite directions while their resultant pattern remains fixed.
- Do not confuse a node with an antinode: node means zero displacement, antinode means maximum displacement.
- Successive nodes are separated by λ/2, not λ/4.
- A node and the nearest antinode are separated by λ/4.
- Stationary waves do not transfer energy along the medium.
Short-Question Preparation
Q. What is a stationary wave?
A. It is the resultant of identical waves of the same speed, amplitude and frequency travelling in opposite directions and superposing.
Q. What is a node?
A. A node is a fixed point of a stationary wave where displacement is always zero.
Q. What is an antinode?
A. An antinode is a fixed point where particles oscillate with maximum amplitude.
Q. What is the distance between successive nodes?
A. The distance is λ/2.
Q. Why is no energy transferred by a stationary wave?
A. The resultant pattern does not travel; particles oscillate only within fixed sections between nodes.
Sticky Notes
- A stationary wave is formed by identical waves travelling in opposite directions and superposing.
- The interfering waves have the same speed, amplitude and frequency.
- Nodes are fixed points where displacement is always zero.
- Antinodes are fixed points where particles oscillate with maximum amplitude.
- The standing-wave pattern does not travel through the medium.
- A stationary wave transfers no energy from one particle to the next.
- Successive nodes or successive antinodes are separated by half a wavelength.
- A node and its nearest antinode are separated by one quarter of a wavelength.
60-Second Revision
Two identical opposite-travelling waves superpose to form a fixed standing-wave pattern. Nodes have zero displacement and antinodes have maximum displacement. The pattern transfers no energy along the medium. Node-to-node and antinode-to-antinode spacing is λ/2; node-to-nearest-antinode spacing is λ/4.
Summary
A stationary or standing wave is produced when identical waves of the same speed, amplitude and frequency travel in opposite directions and superpose. Its pattern has fixed nodes and antinodes and transfers no energy from one part of the medium to another.
Ask-the-Tutor Modes
- Explain standing waves with a rope example.
- Compare nodes and antinodes.
- Explain why the pattern is stationary.
- Solve a wavelength-spacing question.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- Definition and formation conditions.
- Node: zero displacement.
- Antinode: maximum displacement.
- No energy transfer along the medium.
- dNN=dAA=λ/2 and dNA=λ/4.
Important formulas
- dNN=dAA=λ2
- dNA=λ4
Common exam traps
- Do not exchange the λ/2 and λ/4 distances.
- The resultant pattern is stationary even though the component waves travel.
Long question structure
Definition → formation → fixed pattern → nodes and antinodes → energy → characteristic distances
Common Mistakes
Common Mistakes
- Mistake
A node has zero displacement; an antinode has maximum displacement.
- Mistake
Successive nodes are λ/2 apart.
- Mistake
A nearest node-antinode pair is λ/4 apart.
- Mistake
The component waves travel, but the resultant pattern stays fixed.
- Mistake
No net energy is transferred along a stationary wave.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
A stationary wave is formed by identical waves travelling in opposite directions and superposing.
The interfering waves have the same speed, amplitude and frequency.
Nodes are fixed points where displacement is always zero.
Antinodes are fixed points where particles oscillate with maximum amplitude.
A stationary or standing wave is produced when identical waves of the same speed, amplitude and frequency travel in opposite directions and superpose. Its pattern has fixed nodes and antinodes and transfers no energy from one part of the medium to another.
- Definition
- A stationary or standing wave is produced when identical waves of the same speed, amplitude and frequency travel in opposite directions and superpose. Its pattern has fixed nodes and antinodes and transfers no energy from one part of the medium to another.
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Exam Practice
Important Question
Q1. Define a stationary wave.
Important Question
Q2. Differentiate between a node and an antinode.
Important Question
Q3. State three characteristics of stationary waves.
Important Question
Q4. Why does a stationary-wave pattern not travel?
Important Question
Q5. A stationary wave has wavelength 0.80 m. Find node-to-node and node-to-antinode distances.