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Sunday, 25 October

JEE Main · Physics · Class 11

Waves: JEE Main previous year questions

78 questions in 70 of the 108 JEE Main shifts Lumi analysed, asked in 7 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
78
in 70 of 108 shifts · 7 of 8 years
Average a shift
0.6
of 25 Physics · 0.5 since 2024 -0.1
Typical range
0.2–0.8
questions a shift; fewest 0.0, most 0.9
Weighted estimate
0.6
model, recent years count more · about 2.3 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Waves

Priority

Lower priority

One of the 7 Physics chapters that shared the last fifth of Physics questions in the 108 shifts analysed. How bands are set

Past questions
78in 70 of 108 shifts
Study plan gives it
11 hover 12 months; 8 h over 6
Study this chapter →

Ideas asked most often

  1. Wave Speed on String9×
  2. Sonometer Laws6×
  3. Particle Velocity vs Wave Velocity4×
  4. Closed Organ Pipe Harmonics4×
  5. Superposition of Traveling Waves3×

238 of the 286 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 36% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Waves at a glance

  1. 01

    64%

    of its 14 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    83%

    of the 286 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    53%

    of its questions asked for a numerical answer, 1.8 times the Physics average.

  4. 04

    3%

    of its questions were rated hard, against 5% across all Physics questions in the same shifts.

Questions a shift, year by year

Out of the 25 Physics questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

0240’170.8’200.6’210.7’220.8’230.4’240.9’250.2’26

Raw count: 2017: 0 in 1 shift · 2020: 10 in 12 shifts · 2021: 18 in 24 shifts · 2022: 20 in 24 shifts · 2023: 12 in 12 shifts · 2024: 9 in 18 shifts · 2025: 7 in 8 shifts · 2026: 2 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Numerical answer53%
  • Calculation24%
  • Application10%
  • Multi-step8%
  • Conceptual4%
  • Recall, single correct1%

Most common asks: wave speed from wave equation (4); original frequency when source and detector recede (1); resultant amplitude of two travelling waves (1).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#64
of 70 by weighted estimate
Rank in Physics
#26
of 28 chapters
Share of Physics
2.3%
of its questions, all shifts analysed
Busiest year
2025
0.9 questions a shift
Year to year
Swings a lot
varies by about 0.3 questions a shift
Long-run direction
+0.03
questions a shift, per year
Easy questions
44%
3% rated hard
Numerical answer
53%
1.8× the Physics rate
With a figure
0%
graph, diagram or structure
Study time
11 h
8 h on a 6-month plan
Marks per study hour
0.21
#60 of 70 chapters
Foundation for others
77%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 2017
  • 202010
  • 202118
  • 202220
  • 202312
  • 20249
  • 20257
  • 20262
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Calculation65%
  • Multi-step19%
  • Application10%
  • Conceptual4%
  • Recall1%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 286 ideas. In the 108 shifts analysed, JEE Main built a question around 38 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
38
Touched on in a question
10
Never asked
238

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. 7 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
08+questions in that year’s analysed shifts, shaded per shift
  • Waves on Strings

    As a topic: 33 questions in 7 of 8 years, most often numerical value, 52% numerical answer.

  • Resonance in Air Columns

    As a topic: 15 questions in 6 of 8 years, most often numerical value, 73% numerical answer.

  • Doppler Effect

    As a topic: 15 questions in 5 of 8 years, most often numerical value, 60% numerical answer.

  • Beats

    As a topic: 4 questions in 3 of 8 years, most often single correct, 25% numerical answer.

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open33 · 42%678623

    14 ideas inside

    • OpenRepeated9 · 27%223
    • OpenRepeated6 · 18%22
    • OpenRepeated4 · 12%2
    • OpenRepeated3 · 9%
    • OpenRepeated2 · 6%
    • Open1 · 3%
    • Open1 · 3%
    • Open1 · 3%
    • Open1 · 3%
    • Open1 · 3%
    • Open1 · 3%
    • Open1 · 3%
    • Open1 · 3%
    • Open1 · 3%
  • Open15 · 19%23324
  • Open13 · 17%453
  • Open4 · 5%2
  • Open3 · 4%
  • Open3 · 4%

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

The exact ideas JEE Main has asked

Inside the topics, 36 different ideas were tested; 12 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 78 Waves questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 20262 questions

  1. 2 Apr 2026, Shift 1 · Q35The equation of a plane progressive wave is given by y=5cos⁡π(200 t−x150)y=5\cos\pi\left(200\,t-\frac{x}{150}\right) where xx and yy are in cm and tt is…EasySingle correct
  2. 5 Apr 2026, Shift 1 · Q48A transverse wave on a string is described by y=3sin⁡(36t+0.018x+π/4)y = 3\sin(36t + 0.018x + \pi/4), where x,yx, y are in cm and tt in seconds. The least…MediumNumerical value

JEE Main 20257 questions

  1. 2 Apr 2025, Shift 2 · Q34A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the xx-direction in 0.3 sec. The crest P is at x=0x = 0 at…MediumSingle correct
  2. 3 Apr 2025, Shift 2 · Q35In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is…MediumSingle correct
  3. 4 Apr 2025, Shift 2 · Q34Displacement of a wave is expressed as x(t)=5cos⁡(628t+π2)x(t)=5\cos\left(628t+\frac{\pi}{2}\right) m. The wavelength of the wave when its velocity is 300…EasySingle correct
  4. 7 Apr 2025, Shift 1 · Q34Two harmonic waves moving in the same direction superimpose to form a wave x=acos⁡(1.5t)cos⁡(50.5t)x = a\cos(1.5t)\cos(50.5t) where t is in seconds. Find the…MediumSingle correct
  5. 7 Apr 2025, Shift 2 · Q35The equation of a wave travelling on a string is y=sin⁡[20πx+10πt]y=\sin[20\pi x+10\pi t], where xx and t are distance and time in SI units. The minimum…MediumSingle correct
  6. 8 Apr 2025, Shift 2 · Q34Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then…EasySingle correct
  7. 8 Apr 2025, Shift 2 · Q40The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y1(x,t)=4sin⁡(kx−ωt)y_1(x, t) = 4\sin(kx - \omega t)…MediumSingle correct

JEE Main 20249 questions

  1. 5 Apr 2024, Shift 2 · Q55A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of…EasyNumerical value
  2. 6 Apr 2024, Shift 2 · Q51Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th6^{\text{th}} and 5th5^{\text{th}} harmonics respectively. The difference of…EasyNumerical value
  3. 8 Apr 2024, Shift 1 · Q54A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is (a−1a)\left(\frac{a-1}{a}\right)…MediumNumerical value
  4. 8 Apr 2024, Shift 2 · Q44A plane progressive wave is given by y=2cos⁡2π(330t−x)y = 2\cos 2\pi(330t - x) m. The frequency of the wave is :EasySingle correct
  5. 1 Feb 2024, Shift 1 · Q54A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N. When the tension in the wire is changed to 54…MediumNumerical value
  6. 30 Jan 2024, Shift 1 · Q54In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the…HardNumerical value
  7. 30 Jan 2024, Shift 2 · Q54A point source is emitting sound waves of intensity 16×10−8 Wm−216\times 10^{-8}\ Wm^{-2} at the origin. The difference in intensity (magnitude…EasyNumerical value
  8. 31 Jan 2024, Shift 1 · Q49The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open…EasySingle correct
  9. 31 Jan 2024, Shift 2 · Q38The speed of sound in oxygen at S.T.P. will be approximately: (given, R=8.3 JK−1R=8.3\ \mathrm{JK^{-1}}, γ=1.4\gamma=1.4)MediumSingle correct

JEE Main 202312 questions

  1. 6 Apr 2023, Shift 1 · Q51A person driving car at a constant speed of 15 m/s is approaching a vertical wall. The person notices a change of 40 Hz in the frequency…MediumNumerical value
  2. 6 Apr 2023, Shift 2 · Q40The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:EasySingle correct
  3. 8 Apr 2023, Shift 1 · Q31The engine of a train moving with speed 10 ms−110\ \mathrm{ms^{-1}} towards a platform sounds a whistle at frequency 400 Hz400\ \mathrm{Hz}. The…EasySingle correct
  4. 8 Apr 2023, Shift 1 · Q51An organ pipe 40 cm40\ \mathrm{cm} long is open at both ends. The speed of sound in air is 360 ms−1360\ \mathrm{ms^{-1}}. The frequency of the…EasyNumerical value
  5. 8 Apr 2023, Shift 2 · Q51A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental…EasyNumerical value
  6. 10 Apr 2023, Shift 1 · Q52A transverse harmonic wave on a string is given by y(x,t)=5sin⁡(6t+0.003 x)y(x,t) = 5\sin(6t + 0.003\,x) where xx and yy are in cm and tt in sec. The wave…EasyNumerical value
  7. 11 Apr 2023, Shift 1 · Q56The equation of wave is given by Y=10−2sin⁡2π(160t−0.5x+π/4)Y = 10^{-2}\sin 2\pi(160t - 0.5x + \pi/4) where xx and YY are in m and tt in s. The speed of the…EasyNumerical value
  8. 11 Apr 2023, Shift 2 · Q31A car P travelling at 20 ms−120\ \mathrm{ms^{-1}} sounds its horn at a frequency of 400 Hz400\ \mathrm{Hz}. Another car Q is travelling behind the…MediumSingle correct
  9. 11 Apr 2023, Shift 2 · Q51A wire of density 8×103 kg/m38\times10^{3}\ \mathrm{kg/m^3} is stretched between two clamps 0.5 m0.5\ \mathrm{m} apart. The extension developed in the…MediumNumerical value
  10. 12 Apr 2023, Shift 1 · Q55For a certain organ pipe, the first three resonance frequencies are in the ratio of 1:3:5 respectively. If the frequency of fifth harmonic…MediumNumerical value
  11. 13 Apr 2023, Shift 2 · Q54In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a…EasyNumerical value
  12. 15 Apr 2023, Shift 1 · Q51The fundamental frequency of vibration of a string stretched between two rigid support is 50 Hz. The mass of the string is 18 g and its…EasyNumerical value

JEE Main 202220 questions

  1. 25 Jul 2022, Shift 1 · Q55An observer is riding on a bicycle and moving towards a hill at 18 km h−118\ \mathrm{km\,h^{-1}}. He hears a sound from a source at some distance…MediumNumerical value
  2. 25 Jul 2022, Shift 2 · Q44Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is 2\sqrt{2}…HardSingle correct
  3. 25 Jul 2022, Shift 2 · Q57Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The…EasyNumerical value
  4. 26 Jul 2022, Shift 1 · Q54When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50 Hz. If the observer moves…MediumNumerical value
  5. 26 Jul 2022, Shift 2 · Q43A transverse wave is represented by y=2sin⁡(ωt−kx)y = 2\sin(\omega t - kx) cm. The value of wavelength (in cm) for which the wave velocity becomes…MediumSingle correct
  6. 27 Jul 2022, Shift 2 · Q57A wire of length 30 cm, stretched between rigid supports, has it's nth^{th} and (n+1)th(n+1)^{th} harmonics at 400 Hz and 450 Hz, respectively.…MediumNumerical value
  7. 28 Jul 2022, Shift 1 · Q39In the wave equation y=0.5sin⁡2πλ(400 t−x) my=0.5\sin\frac{2\pi}{\lambda}(400\,t-x)\ \mathrm{m} the velocity of the wave will be :EasySingle correct
  8. 28 Jul 2022, Shift 1 · Q57The frequency of echo will be __________ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h…MediumNumerical value
  9. 29 Jul 2022, Shift 2 · Q56The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 ms−1\mathrm{ms^{-1}}. The area of cross-section…MediumNumerical value
  10. 24 Jun 2022, Shift 1 · Q42The equations of two waves are given by : y1=5sin⁡2π(x−vt)y_1=5\sin 2\pi(x-vt) cm y2=3sin⁡2π(x−vt+1.5)y_2=3\sin 2\pi(x-vt+1.5) cm These waves are simultaneously passing…EasySingle correct
  11. 24 Jun 2022, Shift 2 · Q54Standing Wave Equation · Easy · Numerical value
  12. 25 Jun 2022, Shift 1 · Q55Overlapping Resonances in Open and Closed Pipes · Medium · Numerical value
  13. 26 Jun 2022, Shift 2 · Q56Frequency Calculation in a Tuning Fork Series · Medium · Numerical value
  14. 27 Jun 2022, Shift 1 · Q46Moving Observer Cases · Easy · Single correct
  15. 28 Jun 2022, Shift 1 · Q50Beat Frequency Calculation · Medium · Single correct
  16. 28 Jun 2022, Shift 2 · Q57Closed Organ Pipe Harmonics · Medium · Numerical value
  17. 29 Jun 2022, Shift 1 · Q46Particle Velocity vs Wave Velocity · Medium · Single correct
  18. 29 Jun 2022, Shift 2 · Q53End Correction Calculation from Resonant Lengths · Medium · Numerical value
  19. 30 Jun 2022, Shift 1 · Q42Direction of Wave Propagation · Easy · Single correct
  20. 30 Jun 2022, Shift 1 · Q52Effect of Wind Velocity · Medium · Numerical value

JEE Main 202118 questions

  1. 3 Aug 2021, Shift 1 · Q9Collinear Superposition of SHMs · Medium · Single correct
  2. 4 Aug 2021, Shift 1 · Q1Open the question · Easy · Single correct
  3. 4 Aug 2021, Shift 2 · Q11Sonometer Laws · Easy · Single correct
  4. 26 Aug 2021, Shift 1 · Q24Nodes and Antinodes · Easy · Numerical value
  5. 26 Aug 2021, Shift 1 · Q30General Doppler Formula · Medium · Numerical value
  6. 26 Aug 2021, Shift 2 · Q30Superposition of Traveling Waves · Medium · Numerical value
  7. 27 Aug 2021, Shift 1 · Q25General Doppler Formula · Easy · Numerical value
  8. 27 Aug 2021, Shift 2 · Q25Closed Organ Pipe Harmonics · Easy · Numerical value
  9. 31 Aug 2021, Shift 1 · Q26Harmonics and Overtones · Medium · Numerical value
  10. 24 Feb 2021, Shift 2 · Q9Linear Wave Differential Equation · Easy · Single correct
  11. 24 Feb 2021, Shift 2 · Q25Doppler Beat Frequency Calculation · Medium · Numerical value
  12. 25 Feb 2021, Shift 1 · Q4End Correction Concept · Medium · Single correct
  13. 25 Feb 2021, Shift 2 · Q23Wave Speed on String · Easy · Numerical value
  14. 26 Feb 2021, Shift 1 · Q24Wave Speed on String · Medium · Numerical value
  15. 26 Feb 2021, Shift 2 · Q3Effect of Filing Fork · Easy · Single correct
  16. 16 Mar 2021, Shift 2 · Q30Harmonic Frequency Ratios · Medium · Numerical value
  17. 17 Mar 2021, Shift 2 · Q3Open the question · Medium · Single correct
  18. 18 Mar 2021, Shift 2 · Q27Light Doppler Approximation · Easy · Numerical value

JEE Main 202010 questions

  1. 8 Jan 2020, Shift 1 · Q23Gas Composition Effect on Frequency · Medium · Numerical value
  2. 8 Jan 2020, Shift 2 · Q9Wave Speed on String · Easy · Single correct
  3. 9 Jan 2020, Shift 1 · Q9Superposition of Traveling Waves · Medium · Single correct
  4. 9 Jan 2020, Shift 2 · Q11Sonometer Laws · Medium · Single correct
  5. 2 Sep 2020, Shift 1 · Q10Sonometer Laws · Easy · Single correct
  6. 2 Sep 2020, Shift 2 · Q23Wave Speed in Elastic Strings · Medium · Numerical value
  7. 3 Sep 2020, Shift 1 · Q9Wave Speed on a Hanging String · Medium · Single correct
  8. 4 Sep 2020, Shift 1 · Q9Open the question · Medium · Single correct
  9. 4 Sep 2020, Shift 2 · Q10Moving Reflector Echo · Medium · Single correct
  10. 5 Sep 2020, Shift 1 · Q20End Correction Concept · Easy · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

More Physics, Class 11

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