JEE Physics — Waves And Oscillations Complete Chapter Guide

Chapter Overview & Weightage

Waves and Oscillations is one of those chapters where JEE rewards students who understand the physics, not just the formulas. SHM alone accounts for 1-2 questions almost every year, and Doppler Effect has become a JEE Main favourite in recent shifts.

JEE Main Weightage: 8–10% — typically 2–3 questions per paper. At 4 marks each, that’s up to 12 marks. This chapter also feeds into AC circuits (SHM analogy), wave optics (superposition), and modern physics (de Broglie waves).

Year	Questions	Topics Covered
JEE Main 2024	3	SHM energy, Doppler Effect, Standing Waves
JEE Main 2023	2	SHM (spring-mass), Sound intensity
JEE Main 2022	3	Damped oscillations, Beats, Doppler
JEE Main 2021	2	SHM with constraints, Resonance
JEE Main 2020	3	Spring combinations, Wave speed, Superposition
JEE Advanced 2024	2	Coupled oscillations, Doppler (moving medium)

The trend is clear: SHM + Doppler = guaranteed questions. Sound waves and superposition appear in roughly 60% of papers.

Key Concepts You Must Know

Ranked by exam frequency — focus top-down if you’re short on time.

Tier 1 (Always Asked)

SHM: displacement, velocity, acceleration as functions of time; phase relationships
Energy in SHM: KE + PE = constant; energy at mean position vs extreme position
Spring-mass systems: series and parallel combinations, effective spring constant
Doppler Effect: all four cases (source moving, observer moving, both moving)

Tier 2 (Frequently Asked)

Standing waves: nodes, antinodes, harmonics in strings and organ pipes
Beats: beat frequency, conditions for resonance
Wave speed: on a string ( $v = \sqrt{T/\mu}$ ), in medium
Damped oscillations: qualitative behaviour, energy decay

Tier 3 (Occasional, High Difficulty)

Superposition of SHMs: resultant amplitude using phasor addition
Angular SHM: pendulum, torsional oscillation
Resonance and forced oscillations
Doppler with moving medium (JEE Advanced territory)

Important Formulas

x = A\sin(\omega t + \phi)

v = A\omega\cos(\omega t + \phi) = \omega\sqrt{A^2 - x^2}

a = -\omega^2 x

When to use: Any problem giving displacement and asking for velocity/acceleration at a point, or asking for time to reach a position.

KE = \frac{1}{2}m\omega^2(A^2 - x^2)

PE = \frac{1}{2}m\omega^2 x^2

E_{total} = \frac{1}{2}m\omega^2 A^2

When to use: “Find KE when displacement is A/2” type problems. Total energy depends only on amplitude and $\omega$ — not on position.

\text{Series: } \frac{1}{k_{eff}} = \frac{1}{k_1} + \frac{1}{k_2}

\text{Parallel: } k_{eff} = k_1 + k_2

T = 2\pi\sqrt{\frac{m}{k_{eff}}}

When to use: Any spring combination problem. Draw the FBD first — only then decide if springs are in series or parallel (it’s about how forces transmit, not physical arrangement).

f_{obs} = f_0 \cdot \frac{v \pm v_o}{v \mp v_s}

Sign convention: Numerator — use $+$ if observer moves toward source. Denominator — use $-$ if source moves toward observer. Think of it as: “closing the gap → higher frequency.”

\text{String (fixed both ends): } f_n = \frac{n}{2L}\sqrt{\frac{T}{\mu}}

\text{Open pipe: } f_n = \frac{nv}{2L}, \quad n = 1, 2, 3, \ldots

\text{Closed pipe: } f_n = \frac{(2n-1)v}{4L}, \quad n = 1, 2, 3, \ldots

When to use: Any resonance or harmonics problem. Closed pipe only supports odd harmonics — this single fact appears in 3-4 questions per year.

f_{beat} = |f_1 - f_2|

When to use: Two sources with slightly different frequencies. Also used to find unknown frequency — load one tuning fork, observe beat change direction.

Solved Previous Year Questions

PYQ 1 — SHM Energy (JEE Main 2024, Shift 1)

A particle executes SHM with amplitude 4 cm. At what displacement from the mean position is its KE equal to 3 times its PE?

The key insight: we don’t need mass or $\omega$ separately — the ratio condition gives us everything.

KE = 3 \times PE

\frac{1}{2}m\omega^2(A^2 - x^2) = 3 \times \frac{1}{2}m\omega^2 x^2

A^2 - x^2 = 3x^2

A^2 = 4x^2

x = \frac{A}{2} = \frac{4}{2} = 2 \text{ cm}

Answer: 2 cm

Students often set up $KE = 3 \times E_{total}$ , which is impossible (KE can’t exceed total energy). Always set up the ratio between KE and PE, not KE and total energy.

PYQ 2 — Doppler Effect (JEE Main 2023, Shift 2)

A train moving at 20 m/s blows a whistle of frequency 400 Hz toward a stationary observer. Speed of sound = 340 m/s. Find the apparent frequency.

Source moving toward observer, observer stationary:

f_{obs} = f_0 \cdot \frac{v}{v - v_s} = 400 \times \frac{340}{340 - 20}

= 400 \times \frac{340}{320} = 400 \times \frac{17}{16}

= 425 \text{ Hz}

Answer: 425 Hz

After the train passes (source moving away):

f_{obs} = 400 \times \frac{340}{340 + 20} = 400 \times \frac{340}{360} \approx 377.8 \text{ Hz}

The change in frequency as the train passes = $425 - 377.8 \approx 47$ Hz. This “before and after” variant appeared in JEE Main 2022 as well — know both cases.

PYQ 3 — Standing Waves in Pipes (JEE Main 2022, Shift 1)

An open organ pipe of length 50 cm resonates at 340 Hz. Find the mode of vibration. (Speed of sound = 340 m/s)

For an open pipe:

f_n = \frac{nv}{2L}

340 = \frac{n \times 340}{2 \times 0.5}

340 = \frac{340n}{1} = 340n

n = 1

This is the fundamental mode (1st harmonic). The pipe supports all harmonics: 340 Hz, 680 Hz, 1020 Hz, …

Answer: Fundamental mode (1st harmonic)

JEE often asks: “Which of the following frequencies will resonate in a closed pipe of the same length?” The answer: only odd multiples of $\frac{v}{4L} = \frac{340}{4 \times 0.5} = 170$ Hz → 170 Hz, 510 Hz, 850 Hz… Not 340 Hz, not 680 Hz.

Difficulty Distribution

Difficulty	% of Questions	What Gets Asked
Easy (1-2 min)	40%	Direct formula application: time period, beat frequency, basic Doppler
Medium (3-4 min)	45%	Energy ratios in SHM, spring combinations, organ pipe harmonics
Hard (5+ min)	15%	Superposition of two SHMs, Doppler with accelerating source, coupled oscillators

In JEE Main, you will almost certainly see 1 easy + 1 medium question from this chapter. Solve those in under 5 minutes total and move on — the hard question (if it appears) is better left for revision time.

Expert Strategy

Week 1 — Build the foundation

SHM is the backbone. Spend 60% of your chapter time here. Derive the velocity formula $v = \omega\sqrt{A^2 - x^2}$ yourself — don’t just memorise it. Understanding why KE + PE = constant makes energy problems trivial.

Week 2 — Doppler and Waves

Doppler has exactly 4 cases, and JEE tests combinations. Make a 2×2 table (source/observer × toward/away) and solve 10 problems of each type. After 40 problems, the sign convention becomes automatic.

For standing waves, master the boundary condition logic once. A fixed end = node (zero displacement). A free end = antinode (maximum displacement). From these two rules, you can derive the harmonic series for any pipe or string from scratch — no memorisation needed.

For JEE Advanced preparation

Add superposition of two perpendicular SHMs (Lissajous figures) and Doppler in moving medium. These are Advanced-exclusive topics that appear roughly once every 3 years.

PYQ Strategy

Waves and Oscillations has 10 years of JEE Main PYQs — that’s 20-30 problems. Solving all of them takes about 3-4 hours and covers virtually every pattern the exam uses. This chapter is repeatable: same concepts, slightly different numbers.

Common Traps

Trap 1 — Spring in series vs parallel

A block between two springs attached to walls: when the block moves, one spring compresses and one extends — both exert restoring force on the block. This is parallel, giving $k_{eff} = k_1 + k_2$ . Students reflexively write series. Always ask: “Do both springs pull/push the block back to equilibrium simultaneously?”

Trap 2 — Doppler with observer and source both moving

When both are moving toward each other, students sometimes flip the signs in both numerator and denominator and get a smaller frequency. Remember: closing the gap always increases frequency. If your answer gives $f_{obs} < f_0$ when source and observer approach each other, you’ve made a sign error.

Trap 3 — Closed pipe even harmonics

“A closed organ pipe of length L resonates at 1020 Hz. Which other frequency will it resonate at?” Closed pipes only support odd harmonics (1st, 3rd, 5th…). If the 3rd harmonic is 1020 Hz, the fundamental is 340 Hz. The next resonance is the 5th harmonic = 1700 Hz. Not 2040 Hz (which would be the 6th harmonic of open pipe — doesn’t exist in closed).

Trap 4 — Phase in SHM

“A particle starts from the extreme position.” This means $x = A\cos(\omega t)$ , not $A\sin(\omega t)$ . When the problem gives initial conditions, always write the general form $x = A\sin(\omega t + \phi)$ and solve for $\phi$ — don’t assume $\phi = 0$ .

Quick self-test: If you can solve these three problems in under 10 minutes total, you’re JEE-ready on this chapter: (1) KE = 3×PE → find displacement; (2) Doppler with train passing a stationary observer — both before and after; (3) Find all resonant frequencies for a closed pipe given one resonance. These three cover 80% of what JEE actually asks.