JEE Main & Advanced / Physics / Chapter 16

Waves on String

Study transverse waves, superposition, reflection, and string harmonics in a way that links formulas directly to JEE patterns.

Original Notes2 Core SectionsJEE Revision Style
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JEE Intro

How to Think About Waves on String

Study transverse waves, superposition, reflection, and string harmonics in a way that links formulas directly to JEE patterns.

This chapter is written as original Learn at My Place teaching copy. The aim is to give you the JEE decision-making layer: what equation to trust, what approximation is valid, and where exam traps usually appear.

Read the full note once, then revisit the quick revision block before solving your own practice questions.

Problem Method

How to Solve Waves on String Questions

1. Model the Situation

Draw the body, path, field, graph, or interaction first. Label known quantities and choose sign convention before writing equations.

2. Pick the Governing Law

Decide whether the problem is about conservation, force balance, energy, momentum, fields, or graph interpretation.

3. Check the Edge Case

Verify units, limiting values, direction, and whether approximation assumptions are valid for JEE Main and Advanced options.

Section A

Notes: Waves on String

Original teaching copy for Learn at My Place

1. Speed and Superposition on a String

For a stretched string, wave speed is:

v=Tμv = \sqrt{\frac{T}{\mu}}
where TT is tension and μ\mu is linear mass density. Higher tension increases speed; higher linear density reduces it.

Reflection at a fixed end inverts a pulse, while reflection at a free end does not. Superposition remains the master rule behind pulse overlap and interference.

2. Standing Waves and Harmonics

Standing waves form by superposition of two equal-frequency waves traveling in opposite directions. Nodes have zero amplitude; antinodes have maximum amplitude.

For a string fixed at both ends:

fn=nv2L,n=1,2,3,f_n = \frac{nv}{2L}, \qquad n=1,2,3,\dots
The fundamental is the first harmonic, and every higher mode is an integer multiple of it.

Quick Revision

Last 5-Minute Recall

JEE exam rule: First identify the governing principle. Most errors happen because students choose the wrong framework before they start the algebra.
Wave speed on a stretched string
Superposition and pulse reflection
Standing-wave formation
Harmonics and normal modes
Verified question bank

Waves on String questions with answers

Open any of these 91 quality-checked JEE questions to review all four options, the correct answer, and the worked explanation.

  1. Question 1 · EasyWave Speed
  2. Question 2 · EasyWave Speed
  3. Question 3 · EasyWave Equation
  4. Question 4 · MediumWave Speed
  5. Question 5 · MediumWave Speed
  6. Question 6 · MediumReflection
  7. Question 7 · MediumReflection
  8. Question 8 · MediumPower in Waves
  9. Question 9 · MediumWave Speed
  10. Question 10 · MediumWave Equation
  11. Question 11 · HardPower in Waves
  12. Question 12 · HardWave Speed
  13. Question 13 · HardReflection
  14. Question 14 · HardPower in Waves
  15. Question 15 · HardWave Equation
  16. Question 16 · HardWave Equation
  17. Question 17 · HardWave Speed
  18. Question 18 · HardPower in Waves
  19. Question 19 · EasyStanding Waves
  20. Question 20 · EasyHarmonics
  21. Question 21 · EasyHarmonics
  22. Question 22 · MediumStanding Wave Equation
  23. Question 23 · MediumHarmonics
  24. Question 24 · MediumSonometer
  25. Question 25 · MediumSonometer
  26. Question 26 · MediumStanding Waves
  27. Question 27 · MediumSonometer
  28. Question 28 · MediumHarmonics
  29. Question 29 · HardSonometer
  30. Question 30 · HardStanding Wave Equation
  31. Question 31 · HardResonance Frequency
  32. Question 32 · HardSonometer
  33. Question 33 · HardEnergy in Standing Waves
  34. Question 34 · HardHarmonics
  35. Question 35 · HardSonometer
  36. Question 36 · HardStanding Waves
  37. Question 37 · HardHarmonics
  38. Question 38 · HardBeats with Sonometer
  39. Question 39 · EasyOne End Fixed
  40. Question 40 · EasyOne End Fixed
  41. Question 41 · MediumOne End Fixed
  42. Question 42 · MediumMelde's Experiment
  43. Question 43 · MediumMelde's Experiment
  44. Question 44 · MediumSpeed of Wave
  45. Question 45 · MediumFundamental Frequency
  46. Question 46 · MediumTension Variation
  47. Question 47 · HardEnergy
  48. Question 48 · HardSonometer
  49. Question 49 · HardOne End Fixed
  50. Question 50 · HardMelde's Experiment
  51. Question 51 · HardString with Mass
  52. Question 52 · HardHarmonics
  53. Question 53 · HardPhase Velocity
  54. Question 54 · HardSonometer
  55. Question 55 · HardWave Speed
  56. Question 56 · HardEnergy Density
  57. Question 57 · HardSonometer
  58. Question 58 · EasyWave Speed
  59. Question 59 · EasyHarmonics
  60. Question 60 · MediumBeats
  61. Question 61 · MediumStanding Waves
  62. Question 62 · MediumResonance
  63. Question 63 · MediumSonometer
  64. Question 64 · MediumWave Equation
  65. Question 65 · HardStanding Waves
  66. Question 66 · HardPower
  67. Question 67 · HardHarmonics
  68. Question 68 · HardReflection
  69. Question 69 · HardSonometer
  70. Question 70 · HardWave Equation
  71. Question 71 · HardStanding Waves
  72. Question 72 · HardHarmonics
  73. Question 73 · HardMelde's Experiment
  74. Question 74 · HardSonometer
  75. Question 75 · HardReflection
  76. Question 76 · HardHarmonics
  77. Question 77 · HardWave Speed Variation
  78. Question 78 · HardTime for Pulse
  79. Question 79 · HardNonlinear Superposition
  80. Question 80 · HardImpedance Matching
  81. Question 81 · HardNormal Modes
  82. Question 82 · HardEnergy Transport
  83. Question 83 · HardSoliton
  84. Question 84 · HardCoupled Strings
  85. Question 85 · HardWave Speed Variation
  86. Question 86 · HardMode Mixing
  87. Question 87 · HardDispersion
  88. Question 88 · HardQuantum Analogy
  89. Question 89 · HardAmplitude in Resonance
  90. Question 90 · HardPolarisation
  91. Question 91 · HardHarmonics Advanced
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