Superposition of waves: constructive and destructive interference on a string
Two travelling waves on a string add up. Change the amplitudes, the frequencies and the phase difference, or send them in opposite directions, and see constructive and destructive interference, standing waves with nodes and beats.
Also searched as: superposition of waves · superposition of waves · principle of superposition · constructive and destructive interference · interference of waves · standing waves formation
About this experiment
| Subject | Physics |
|---|---|
| Class | 11 |
| Chapter | 14. Waves |
| NCERT section | 14.5–14.6 |
| Level | NCERT level |
| Time | about 15 minutes |
| Access | Included in a PractiSci plan |
Aim
To see the principle of superposition: when two waves meet, the displacement is the sum of the displacements, which gives constructive or destructive interference, standing waves and beats.
Theory
Principle of superposition: when two or more waves travel through the same medium, the resultant displacement at any point is the algebraic sum of the displacements of the separate waves. After they cross, each continues unchanged.
Two waves of the same frequency travelling the same way give a wave of the same frequency whose amplitude depends on the phase difference φ: A = √(A₁² + A₂² + 2 A₁A₂ cos φ). When φ = 0 (crest on crest) the waves are in phase, A = A₁ + A₂: constructive interference. When φ = 180° (crest on trough) A = |A₁ − A₂|: destructive interference, and if A₁ = A₂ the string does not move at all. A path difference Δx corresponds to φ = 2πΔx/λ.
Two identical waves travelling in opposite directions give a standing wave y = 2A sin kx cos ωt. There are points that never move (nodes, a distance λ/2 apart) and points of the greatest motion (antinodes). This is what happens on a plucked string and in an organ pipe.
Formulas used
- y = y₁ + y₂ (superposition)
- y₁ = A₁ sin(kx − ωt), y₂ = A₂ sin(kx − ωt + φ)
- A = √(A₁² + A₂² + 2A₁A₂ cos φ)
- φ = 2π Δx / λ
- standing wave: y = 2A sin kx cos ωt; nodes λ/2 apart
- beat frequency = |f₁ − f₂|
Procedure: what to do in the virtual lab
- Set equal amplitudes and frequencies and φ = 0. Check that the resultant amplitude is 2A.
- Set φ = 180°. What is the resultant? Try different amplitudes.
- Try φ = 90° and compare the amplitude with the formula.
- Choose the opposite direction and find the nodes and antinodes of the standing wave. Measure the distance between two nodes.
- Make the frequencies slightly different (1.0 and 1.2 Hz) and look for beats.
Observations to make
- The resultant (white) is the sum of the blue and red waves at every point.
- For φ = 180° with equal amplitudes the string stays straight.
- The nodes of the standing wave are at fixed places, half a wavelength apart.
- When the frequencies differ the amplitude swells and fades regularly.
What you can change in this experiment
- Amplitude of wave 1 (0.2 to 1.5 cm)
- Amplitude of wave 2 (0.2 to 1.5 cm)
- Frequency of wave 1 (0.5 to 3 Hz)
- Frequency of wave 2 (0.5 to 3 Hz)
- Phase difference between the waves (0 to 360 °)
- Wave 2 travels: in the same direction as wave 1 / in the opposite direction (standing wave)
Viva questions on Superposition of waves
Questions an examiner may ask in the Class 11 physics practical. Run the experiment in the lab to find the answers yourself, then check them in the Learn tab.
- State the principle of superposition.
- What is the condition for constructive and for destructive interference?
- How is a standing wave formed? What are nodes and antinodes?
- What is the beat frequency of two notes of 256 Hz and 260 Hz?
Frequently asked questions
What is the aim of the Superposition of waves experiment?
To see the principle of superposition: when two waves meet, the displacement is the sum of the displacements, which gives constructive or destructive interference, standing waves and beats.
Which formulas are used in the Superposition of waves experiment?
y = y₁ + y₂ (superposition); y₁ = A₁ sin(kx − ωt), y₂ = A₂ sin(kx − ωt + φ); A = √(A₁² + A₂² + 2A₁A₂ cos φ); φ = 2π Δx / λ; standing wave: y = 2A sin kx cos ωt; nodes λ/2 apart
What viva questions are asked on Superposition of waves?
State the principle of superposition. What is the condition for constructive and for destructive interference? How is a standing wave formed? What are nodes and antinodes? What is the beat frequency of two notes of 256 Hz and 260 Hz?
How do I do the superposition of waves experiment for Class 11 online?
Open the Superposition of waves virtual lab on PractiSci, follow the procedure above, change the values and read the live graph. It matches the Class 11 physics practical, with the aim, theory, observations and viva questions on this page.
What is the resultant amplitude of two waves with a phase difference φ?
A = √(A₁² + A₂² + 2 A₁ A₂ cos φ). It is A₁ + A₂ for φ = 0 and |A₁ − A₂| for φ = 180°.
How is a standing wave formed?
Two identical waves travelling in opposite directions superpose. Nodes form every λ / 2, with antinodes between them.
What are beats?
When two waves of slightly different frequencies overlap, the amplitude rises and falls |f₁ − f₂| times per second.
Can I do the Superposition of waves experiment online?
Yes. Open it as a 3D virtual lab in your browser or on your phone, change the values and read the results from live graphs. It is part of a PractiSci plan.
Syllabus: Class XI Physics, Chapter 14 — Waves, §14.6 (principle of superposition), §14.7 (reflection and standing waves), §14.8 (beats)
What you do in the lab
Change the controls and watch the physics behave in real time in 3D. Live readouts and graphs show the numbers behind it, and the Learn tab has the theory, procedure, observations and viva questions. Works on a phone or a laptop, in English and Hindi.
Topics: superposition of waves · interference · constructive and destructive interference · phase difference · standing waves · beats · waves
Read the full guide: Oscillations and waves.
More from this chapter
- Beats from two close frequencies
- Doppler effect
- Melde's experiment: standing waves on a string
- Resonance tube (open and closed organ pipes)
- Resonance tube: speed of sound and end correction
- Sonometer: frequency, tension, length laws
- Sound intensity, inverse-square law and decibels
- Standing waves on a string and Melde's experiment