JEE Main · Physics · Waves

Waves on Strings: JEE Main previous year questions

Name: Waves on Strings: JEE Main previous year questions
Creator: Lumi

33 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 6 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 33; in 32 of 108 shifts
Years asked: 7/8; last asked 2026
Chance in a shift: 30%; calibrated model, how we compute it
Weighted estimate: 0.3; model; history: 0.3 a shift on average, typically 0.1–0.4

Key findings

01
Asked in 7 of 8 years with analysed shifts and in 32 of 108 shifts: 33 questions, #104 of 196 topics.
02
48% of its questions since 2020 tested an idea no earlier year had asked; 12 repeated an idea from the year before.
03
The most repeated idea is Wave Speed on String, asked 9 times in 9 shifts (2020, 2021, 2022, 2023, 2025), most often as “wave speed from wave equation”.
04
JEE Main has asked 14 of the 58 ideas in this topic; 41 have never been asked, directly or inside another question.
05
Mostly asked as numerical value (52%); 52% need a numerical answer, 55% are easy and 0% hard.
06
The skill tested most is calculation (67%), then multi-step (21%).

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.

Raw count: 2017: 0 in 1 shift · 2020: 6 in 12 shifts · 2021: 7 in 24 shifts · 2022: 8 in 24 shifts · 2023: 6 in 12 shifts · 2024: 2 in 18 shifts · 2025: 3 in 8 shifts · 2026: 1 in 9 shifts.

Up to 2023: 0.3; a shift, of 25
Since 2024: 0.2; -0.1
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 32/108; 30% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 33 questions on Waves on Strings since 2017.

Difficulty

QUESTIONS

1815

Easy18 · 55%
Medium15 · 45%
Hard0 · 0%

Format

Numerical value · 17 Q52%
Single correct · 16 Q48%

Skill tested

Calculation · 22 Q67%
Multi-step · 7 Q21%
Application · 3 Q9%
Conceptual · 1 Q3%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 14 of the 58 ideas in this topic. 41 have never been asked yet.

1441

Asked directly14 · 24%
Touched inside another question3 · 5%
Never asked41 · 71%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Idea, year, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

ideaAskedShareYears’17’20’21’22’23’24’25’26

OpenRepeated9 · 27%27%5/8223
- 8 Apr ’25 S2 · Q34
  Two 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
- 10 Apr ’23 S1 · Q52
  A transverse harmonic wave on a string is given by $y(x,t) = 5\sin(6t + 0.003\,x)$ where $x$ and $y$ are in cm and $t$ in sec. The wave…
  easyNumerical valueAsked the year before
- 11 Apr ’23 S2 · Q51
  A wire of density $8\times10^{3}\ \mathrm{kg/m^3}$ is stretched between two clamps $0.5\ \mathrm{m}$ apart. The extension developed in the…
  mediumNumerical valueAsked the year before
- 15 Apr ’23 S1 · Q51
  The 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 valueAsked the year before
- 28 Jul ’22 S1 · Q39
  In the wave equation $y=0.5\sin\frac{2\pi}{\lambda}(400\,t-x)\ \mathrm{m}$ the velocity of the wave will be :
  easySingle correctAsked the year before
- 29 Jul ’22 S2 · Q56
  The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 $\mathrm{ms^{-1}}$ . The area of cross-section…
  mediumNumerical valueAsked the year before
- 25 Feb ’21 S2 · Q23
  The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be…
  easyNumerical valueAsked the year before
- 26 Feb ’21 S1 · Q24
  The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form $y=-0.21\sin(x+30t)$ is produced in it, where $x$ …
  mediumNumerical valueAsked the year before
- 8 Jan ’20 S2 · Q9
  A transverse wave travels on a taut steel wire with a velocity of $v$ when tension in it is $2.06\times10^{4}\ \mathrm{N}$ . When the…
  easySingle correctNew idea
OpenRepeated6 · 18%18%4/822
OpenRepeated4 · 12%12%3/82
OpenRepeated3 · 9%9%3/8
OpenRepeated2 · 6%6%2/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8

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

Every idea inside this topic

14 different ideas were tested; 5 came more than once.

Wave Speed on String9×
wave speed from wave equation
Numerical value · 9 shifts · 6 numerical
Sonometer Laws6×
sonometer mass from frequencies
Numerical value · 6 shifts · 3 numerical
Particle Velocity vs Wave Velocity4×
wave speed from wave equation
Single correct · 4 shifts
Superposition of Traveling Waves3×
resultant amplitude and phase of two waves
Single correct · 3 shifts · 1 numerical
Harmonics and Overtones2×
linear mass density from consecutive harmonics
Numerical value · 2 shifts · 2 numerical
Beat Frequency in Sonometer Experiments1×
tuning fork frequency from beats and tension change
Numerical value · 1 shift · 1 numerical
Phase Difference in Traveling Waves1×
wave speed from wave equation
Numerical value · 1 shift · 1 numerical
Direction of Wave Propagation1×
equation of travelling wave from wavelength and frequency
Single correct · 1 shift
Interference Amplitude on Strings1×
resultant amplitude of two waves
Single correct · 1 shift
Standing Wave Equation1×
amplitude at a point in standing wave
Numerical value · 1 shift · 1 numerical
Linear Wave Differential Equation1×
identify equation of a travelling wave
Single correct · 1 shift
Nodes and Antinodes1×
node position from standing wave equation
Numerical value · 1 shift · 1 numerical
Wave Speed in Elastic Strings1×
fundamental frequency of strained wire
Numerical value · 1 shift · 1 numerical
Wave Speed on a Hanging String1×
wavelength change along hanging rope with load
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Wave Speed on Stringwave speed from wave equation	9	9	Numerical valueCalculation	6
Sonometer Lawssonometer mass from frequencies	6	6	Numerical valueCalculation	3
Particle Velocity vs Wave Velocitywave speed from wave equation	4	4	Single correctCalculation	–
Superposition of Traveling Wavesresultant amplitude and phase of two waves	3	3	Single correctCalculation	1
Harmonics and Overtoneslinear mass density from consecutive harmonics	2	2	Numerical valueCalculation	2
Beat Frequency in Sonometer Experimentstuning fork frequency from beats and tension change	1	1	Numerical valueMulti-step	1
Phase Difference in Traveling Waveswave speed from wave equation	1	1	Numerical valueCalculation	1
Direction of Wave Propagationequation of travelling wave from wavelength and frequency	1	1	Single correctApplication	–
Interference Amplitude on Stringsresultant amplitude of two waves	1	1	Single correctCalculation	–
Standing Wave Equationamplitude at a point in standing wave	1	1	Numerical valueCalculation	1
Linear Wave Differential Equationidentify equation of a travelling wave	1	1	Single correctConceptual	–
Nodes and Antinodesnode position from standing wave equation	1	1	Numerical valueCalculation	1
Wave Speed in Elastic Stringsfundamental frequency of strained wire	1	1	Numerical valueCalculation	1
Wave Speed on a Hanging Stringwavelength change along hanging rope with load	1	1	Single correctMulti-step	–

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Waves on Strings questions, year by year

The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.

Key findings

Questions a shift, year by year

Difficulty, format and skill

Difficulty

Format

Skill tested

New idea, or one asked before?

Coverage of the topic

Idea, year, question

Every idea inside this topic

Waves on Strings questions, year by year

JEE Main 20261 question in 1 shift

JEE Main 20253 questions in 2 shifts

JEE Main 20242 questions in 2 shifts

JEE Main 20236 questions in 6 shifts

JEE Main 20228 questions in 8 shifts

JEE Main 20217 questions in 7 shifts

JEE Main 20206 questions in 6 shifts

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