How much of JEE Main comes from Oscillations and Waves?

JEEGenie estimates about 4% of JEE Main marks come from Oscillations and Waves, based on recent papers. The share varies from year to year.

Which formulas matter most in Oscillations and Waves?

The Oscillations and Waves sheet on this page has 23 formula entries, starting with Simple Harmonic Motion (SHM), Differential Equation of SHM, General Solution of SHM, Velocity and Acceleration in SHM, Time Period of Spring-Mass System. Each one comes with when to use it and the trap to avoid.

What topics does Oscillations and Waves cover for JEE?

Oscillations and Waves covers Simple Harmonic Motion, Energy in SHM, Pendulums and Springs, Wave Motion, Superposition and Standing Waves, Doppler Effect.

How should I revise Oscillations and Waves before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Oscillations and Waves questions on JEEGenie.

How many previous-year questions are there on Oscillations and Waves?

JEEGenie has 360 previous-year questions on Oscillations and Waves, and this page shows a few with worked explanations.

Is practice on Oscillations and Waves free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Oscillations and Waves for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 4% of JEE Main marks come from Oscillations and Waves. This page covers 23 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Confusing SHM with uniform circular motion; SHM is projection of UCM.

Key points to know

Simple Harmonic Motion (SHM). SHM is a periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts opposite to it.
Damped Oscillations. Oscillations where amplitude decreases over time due to dissipative forces like friction.
Forced Oscillations and Resonance. When an external periodic force drives an oscillator, amplitude is maximum when driving frequency equals natural frequency (resonance).
Wave Motion. A wave is a disturbance that transfers energy through a medium without net transport of matter.
Interference of Waves. Constructive interference occurs when path difference is integer multiple of wavelength; destructive when half-integer.
Standing Waves. When two identical waves travel in opposite directions, they form standing waves with nodes and antinodes.

Formula sheet

Name	Formula	When to use
Simple Harmonic Motion (SHM)	$F = - k x$	Use when analyzing oscillating systems like springs, pendulums, or any system with linear restoring force.
Differential Equation of SHM	$\frac{d^{2} x}{d t^{2}} + ω^{2} x = 0$	Use to derive time period, angular frequency, or general solution for SHM systems.
General Solution of SHM	$x = A \sin (ω t + ϕ)$	Use to find displacement, velocity, acceleration at any time in SHM.
Velocity and Acceleration in SHM	$v = ω \sqrt{A^{2} - x^{2}}$ , $a = - ω^{2} x$	Use to compute velocity or acceleration at a given displacement in SHM.
Time Period of Spring-Mass System	$T = 2 π \sqrt{\frac{m}{k}}$	Use for any spring-mass system oscillating horizontally or vertically (vertical adds static extension but same $T$ ).
Time Period of Simple Pendulum	$T = 2 π \sqrt{\frac{L}{g}}$	Use for small-angle oscillations of a simple pendulum.
Energy in SHM	$E = \frac{1}{2} k A^{2} = \frac{1}{2} m ω^{2} A^{2}$	Use to find amplitude from energy or vice versa, or to find speed at a point.
Finding Time Period of Compound Systems	$T = 2 π \sqrt{\frac{I}{m g d}}$ (physical pendulum)	Use for rigid bodies oscillating about a pivot (e.g., rod, disc).
Damped Oscillations	$x = A e^{- b t / 2 m} \cos (ω^{'} t + ϕ)$	Use when friction or resistance is present in oscillatory systems.
Forced Oscillations and Resonance	$A = \frac{F_{0}}{m \sqrt{(ω_{0}^{2} - ω^{2})^{2} + (b ω / m)^{2}}}$	Use when analyzing systems with external periodic driving force.
Wave Motion	$y = f (x \pm v t)$	Use to describe propagation of disturbances in strings, sound, etc.
Wave Speed on a String	$v = \sqrt{\frac{T}{μ}}$	Use for transverse waves on a stretched string.
Speed of Sound in a Gas	$v = \sqrt{\frac{γ P}{ρ}} = \sqrt{\frac{γ R T}{M}}$	Use for speed of sound in gases, e.g., air.
Principle of Superposition	$y_{net} = y_{1} + y_{2}$	Use whenever waves overlap, leading to interference, beats, or standing waves.
Interference of Waves	$Δ x = n λ$ (constructive), $Δ x = (n + 1 / 2) λ$ (destructive)	Use for two-source interference problems (e.g., Young's double slit, sound waves).
Beats	$f_{beat} = ∣ f_{1} - f_{2} ∣$	Use when two sources of nearly equal frequency produce periodic loudness variation.
Standing Waves	$y = 2 A \cos (k x) \sin (ω t)$	Use for waves on strings fixed at both ends or in pipes.
Harmonics in a Stretched String	$f_{n} = \frac{n}{2 L} \sqrt{\frac{T}{μ}}$ , $n = 1, 2, 3, \dots$	Use for string instruments or any string fixed at both ends.
Harmonics in Organ Pipes	Open: $f_{n} = \frac{n v}{2 L}$ , $n = 1, 2, 3, \dots$ ; Closed: $f_{n} = \frac{n v}{4 L}$ , $n = 1, 3, 5, \dots$	Use for sound waves in pipes (e.g., flute, organ).
Doppler Effect in Sound	$f^{'} = f \frac{v \pm v_{o}}{v \mp v_{s}}$	Use when source or observer is moving relative to medium.
Phase Difference and Path Difference	$Δ ϕ = \frac{2 π}{λ} Δ x$	Use to relate path difference to phase difference in interference problems.
Intensity in Interference	$I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos Δ ϕ$	Use to find intensity at a point in interference pattern.
Lissajous Figures	$x = A \sin (ω_{1} t + ϕ_{1})$ , $y = B \sin (ω_{2} t + ϕ_{2})$	Use in problems involving two perpendicular oscillations (e.g., oscilloscope).

Open the Oscillations and Waves formula page

What JEE asks

Simple Harmonic Motion (SHM). JEE often tests SHM by asking for time period or amplitude from given force-displacement relation, or identifying SHM from equations.
Differential Equation of SHM. JEE may ask to derive time period from given differential equation or identify SHM from $a = - ω^{2} x$ .
General Solution of SHM. JEE often gives initial conditions to find $ϕ$ or asks for displacement at a specific time.
Velocity and Acceleration in SHM. JEE may ask for speed at a certain displacement or acceleration at an extreme position.
Time Period of Spring-Mass System. JEE often tests by combining springs in series/parallel to find effective $k$ and then $T$ .
Time Period of Simple Pendulum. JEE may ask effect of changing $L$ or $g$ (e.g., on a mountain or in lift) on $T$ .
Energy in SHM. JEE often asks ratio of KE to PE at a given displacement or fraction of energy.
Finding Time Period of Compound Systems. JEE may give a rod or disc and ask for time period, requiring $I$ calculation.
Damped Oscillations. JEE may ask for condition for critical damping or effect of damping on frequency.
Forced Oscillations and Resonance. JEE often tests resonance in context of sound or mechanical systems, e.g., Tacoma Narrows Bridge.
Wave Motion. JEE may ask to identify wave type from given equation or properties.
Wave Speed on a String. JEE often gives tension and mass/length to find wave speed or vice versa.
Speed of Sound in a Gas. JEE may ask effect of temperature or pressure on speed of sound.
Principle of Superposition. JEE often uses superposition to find resultant wave equation or amplitude.
Interference of Waves. JEE may ask for condition of maxima/minima or intensity at a point.
Beats. JEE often asks to find unknown frequency using beats with a tuning fork.
Standing Waves. JEE often asks for frequency of harmonics or number of nodes/antinodes.
Harmonics in a Stretched String. JEE may ask for frequency of a given harmonic or length for a specific frequency.
Harmonics in Organ Pipes. JEE often asks to find fundamental frequency or compare open vs closed.
Doppler Effect in Sound. JEE often gives velocities and asks for apparent frequency or speed of source.
Phase Difference and Path Difference. JEE may ask for phase difference given path difference or vice versa.
Intensity in Interference. JEE may ask ratio of maximum to minimum intensity or intensity at a given phase difference.
Lissajous Figures. JEE may ask to identify frequency ratio from given Lissajous pattern.

Common traps

Confusing SHM with uniform circular motion; SHM is projection of UCM. Simple Harmonic Motion (SHM)
Forgetting the $ω^{2}$ term; it's not $ω$ . Differential Equation of SHM
Forgetting the phase constant $ϕ$ ; initial conditions determine it. General Solution of SHM
Using $v = ω A$ for all positions; it's only maximum at $x = 0$ . Velocity and Acceleration in SHM
Including gravity; spring-mass system's $T$ is independent of $g$ . Time Period of Spring-Mass System
Using for large amplitudes; formula valid only for $θ < 10^{\circ}$ . Time Period of Simple Pendulum
Forgetting total energy is constant; only KE and PE change. Energy in SHM
Using simple pendulum formula for physical pendulum; need moment of inertia. Finding Time Period of Compound Systems
Forgetting exponential decay factor; amplitude is not constant. Damped Oscillations
Confusing resonance with natural frequency; resonance occurs at driving frequency near natural frequency. Forced Oscillations and Resonance
Thinking particles move with wave speed; they oscillate about mean position. Wave Motion
Using $T$ as tension in N, not including weight of string. Wave Speed on a String
Using isothermal bulk modulus; sound propagation is adiabatic. Speed of Sound in a Gas
Assuming superposition only for same frequency; it works for all waves. Principle of Superposition

Topics in Oscillations and Waves

Simple Harmonic Motion
Energy in SHM
Pendulums and Springs
Wave Motion
Superposition and Standing Waves
Doppler Effect

Previous-year questions on Oscillations and Waves

JEEGenie has 360 previous-year questions on Oscillations and Waves. A few worked examples follow.

Year	Questions
2026	9
2025	13
2024	13
2023	23
2022	19
2021	20
2020	15
2019	41
2018	11
2017	10
2016	9
2015	7
2014	14
2013	9
2012	7
2011	4
2010	6
2009	4
2008	5
2007	6
2006	10
2005	6
2004	2
2003	8
2002	8
2001	5
2000	6
1999	5
1998	5
1997	5
1996	3
1995	3
1994	2
1993	2
1992	4
1991	3
1990	4
1989	1
1988	3
1987	5
1986	2
1985	6
1984	8
1983	4
1982	1
1981	3
1979	1

Question 1 easy

The equation of a plane progressive wave is given by

y = 5 \cos π (200 t - \frac{x}{150})

where

x

and

y

are in cm and

t

is in second. The velocity of the wave is ________ m/s.

Answer: D

Explanation.

y = 5 \cos π (200 t - \frac{x}{150}) = 5 \cos (200 π t - \frac{π x}{150})

Compare with standard form:

y = A \cos (ω t - k x)

Thus,

ω = 200 π rad/s, k = \frac{π}{150} rad/cm

Wave speed:

v = \frac{ω}{k} = \frac{200 π}{π / 150} = 200 \times 150 = 30000 cm/s

Convert to m/s:

v = \frac{30000}{100} = 300 m/s

D) 300

From NTA/IIT papers: JEE Main 2026 · 2 Apr Shift 1

Question 2 medium

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the

x

-direction in 0.3 sec . The crest P is at

x = 0

t = 0 s e c

and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?

$y = 2 \cos (0.83 x - 3.35 t) c m$
$y = 2 \sin (0.83 x - 3.5 t) c m$
$y = 2 \cos (0.13 x - 0.5 t) c m$
$y = 2 \cos (3.35 x - 0.83 t) c m$

Answer: A

Explanation. Wave speed

v = \frac{1.2}{0.3} = 4 cm/s

. Wavelength

λ = 7.5 cm

, so

k = \frac{2 π}{λ} = \frac{2 π}{7.5} \approx 0.8378 rad/cm

. Angular frequency

ω = v k = 4 \times 0.8378 \approx 3.351 rad/s

. Crest at

x = 0

t = 0

means cosine form:

y = A \cos (k x - ω t)

. Amplitude

A = 2 cm

. Thus

y = 2 \cos (0.83 x - 3.35 t) cm

. The correct answer is option A.

From NTA/IIT papers: JEE Main 2025 · 2 Apr Shift 2

Question 3 easy

A sonometer wire of resonating length

90 c m

has a fundamental frequency of

400 H z

when kept under some tension. The resonating length of the wire with fundamental frequency of

600 H z

under same tension _______

c m

Answer: 60

Explanation. Since frequency is inversely proportional to length, f1*l1 = f2*l2. 400*90 = 600*l2, l2=60cm.

From NTA/IIT papers: JEE Main 2024 · 5 Apr Shift 2

Question 4 hard

A string of length

1

m and mass

2 \times 10^{- 5}

kg is under tension

T

. When the string vibrates, two successive harmonics are found to occur at frequencies

750

Hz and

1000

Hz. The value of tension

T

is ____ Newton.

Answer: 5

Explanation. For a string fixed at both ends, the harmonic frequencies are

f_{n} = \frac{n}{2 L} \sqrt{\frac{T}{μ}}, n = 1, 2, 3, \dots

where

L = 1 m

and

μ = \frac{m}{L} = 2 \times 10^{- 5} kg/m

. Two successive harmonics differ by the fundamental frequency:

f_{n + 1} - f_{n} = \frac{1}{2 L} \sqrt{\frac{T}{μ}} = f_{1} .

Given

f_{n + 1} = 1000 Hz

and

f_{n} = 750 Hz

f_{1} = 1000 - 750 = 250 Hz .

Thus

250 = \frac{1}{2 (1)} \sqrt{\frac{T}{2 \times 10^{- 5}}} .

500 = \sqrt{\frac{T}{2 \times 10^{- 5}}} .

Squaring:

250000 = \frac{T}{2 \times 10^{- 5}} ⟹ T = 250000 \times 2 \times 10^{- 5} = 5 N .

5

From NTA/IIT papers: JEE Advanced 2023

Question 5 hard

On a frictionless horizontal plane, a bob of mass

m = 0.1 k g

is attached to a spring with natural length

l_{0} = 0.1 m

. The spring constant is

k_{1} = 0.009 N m^{- 1}

when the length of the spring

l > l_{0}

and is

k_{2} = 0.016 N m^{- 1}

when

l < l_{0}

. Initially the bob is released from

l = 0.15 m

. Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is

T = (n π) s

, then the integer closest to

n

is _____.

Answer: 6

Explanation. For

l > l_{0}

, the spring constant is

k_{1} = 0.009 N / m

, and for

l < l_{0}

, it is

k_{2} = 0.016 N / m

. The motion is symmetric about

l_{0}

in terms of amplitude, but the time periods differ because the spring constants differ. **Step 1: Amplitude on each side** Released from

l = 0.15 m

, so maximum extension from

l_{0}

A = 0.15 - 0.10 = 0.05 m .

Since the spring force is conservative, the amplitude on the compression side is also

0.05 m

. **Step 2: Time period for extension side (

l > l_{0}

)** For SHM with spring constant

k_{1}

T_{1} = 2 π \sqrt{\frac{m}{k_{1}}} = 2 π \sqrt{\frac{0.1}{0.009}} = 2 π \sqrt{\frac{100}{9}} = 2 π \cdot \frac{10}{3} = \frac{20 π}{3} .

But this is the full period for that spring alone. Since the motion spends half the period on that side, the time for the extension half-cycle is

t_{1} = \frac{T_{1}}{2} = \frac{10 π}{3} .

**Step 3: Time period for compression side (

l < l_{0}

)** Similarly,

T_{2} = 2 π \sqrt{\frac{m}{k_{2}}} = 2 π \sqrt{\frac{0.1}{0.016}} = 2 π \sqrt{\frac{100}{16}} = 2 π \cdot \frac{10}{4} = 5 π .

Half-cycle time:

t_{2} = \frac{T_{2}}{2} = \frac{5 π}{2} .

**Step 4: Total period** The full oscillation consists of one extension half-cycle and one compression half-cycle:

T = t_{1} + t_{2} = \frac{10 π}{3} + \frac{5 π}{2} = \frac{20 π}{6} + \frac{15 π}{6} = \frac{35 π}{6} .

**Step 5: Compare with given form** Given

T = n π

, so

n = \frac{35}{6} \approx 5.833.

The integer closest to

5.833

6

6

From NTA/IIT papers: JEE Advanced 2022

Frequently asked questions

How much of JEE Main comes from Oscillations and Waves?: JEEGenie estimates about 4% of JEE Main marks come from Oscillations and Waves, based on recent papers. The share varies from year to year.
Which formulas matter most in Oscillations and Waves?: The Oscillations and Waves sheet on this page has 23 formula entries, starting with Simple Harmonic Motion (SHM), Differential Equation of SHM, General Solution of SHM, Velocity and Acceleration in SHM, Time Period of Spring-Mass System. Each one comes with when to use it and the trap to avoid.
What topics does Oscillations and Waves cover for JEE?: Oscillations and Waves covers Simple Harmonic Motion, Energy in SHM, Pendulums and Springs, Wave Motion, Superposition and Standing Waves, Doppler Effect.
How should I revise Oscillations and Waves before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Oscillations and Waves questions on JEEGenie.
How many previous-year questions are there on Oscillations and Waves?: JEEGenie has 360 previous-year questions on Oscillations and Waves, and this page shows a few with worked explanations.
Is practice on Oscillations and Waves free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.