Physics notesFluids & WavesWaves
Independent topic page
Name wave type and boundary conditions first; then superposition, harmonic formula or Doppler shift finishes the stem without formula thrash.
01. A plane progressive wave carries phase at speed v=fλ; transverse vs longitudinal is about particle motion relative to propagation, not about whether sound can exist in solids.
02. Superposition is linear addition of displacements. Beats: |f₁−f₂| intensity maxima per second when two close frequencies meet.
03. Stationary waves form from opposite travelling waves: nodes fixed, antinodes max amplitude. String harmonics need both ends’ boundary conditions; organ pipes need open/closed end rules.
04. Speed of sound in gases scales as √(γP/ρ)=√(γRT/M). Doppler for sound depends on source and observer motion relative to the air—sign discipline is mandatory.
05. Progressive waves: v=fλ always. Medium decides speed (string √(T/μ); sound √(γP/ρ) or √(γRT/M)). Particle speed ωA is not the wave speed.
06. Standing waves: draw boundaries. Both ends fixed ⇒ nλ/2=L; closed pipe ⇒ odd harmonics only. End correction when the stem gives diameter or asks for it.
07. Doppler for sound is classical and asymmetric—source and observer factors differ. Beats are |f₁−f₂|. Never import the light-Doppler formula.
Official · 2026
Official syllabus points for Waves & Sound only — not the full Fluids & Waves portion map. Portion hub: Fluids & Waves · Waves/SHM/Sound analysis.
Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf
Exam focusStanding waves on strings/air columns; beats; Doppler in sound.
Syllabus points
Do / check
2020–2026 paper weight
Topic match inside parent portion Waves/SHM/Sound (10.2% of Physics tags). Stats below are portion backdrop; matched subtopics show where Waves & Sound sits.
Portion-wide type/difficulty mix lives on the Waves/SHM/Sound analysis — not repeated here so this page stays on Waves.
01. Waves/SHM/Sound accounts for ~10.2% of tagged physics questions (2020–2026).
02. Dominant subtopics: Waves/Sound (13), SHM (11).
Cross-topic stems
Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch Waves & Sound — practise the knowledge bridge, not only the single-chapter drill.
Step 1: finish the rotation NUM with a clear MOI/energy chain. Step 2: switch mental model to interference/diffraction for the next NUM. Step 3: protect calculator/decimal hygiene across both.
Topic switch mid-numerical section drains working memory.
In NUM blocks, write a one-line topic label before each solve.
Step 1: for waves, check superposition/phase options individually. Step 2: for optics, ray-trace each claim (TIR, magnification, mirror/lens sign). Step 3: never assume ‘exactly two correct’ — mark only proven options.
Two consecutive MC items amplify partial-marking risk.
Practise MC pairs under a strict ‘prove or leave’ rule.
Why methods matter
Boundary sketches and a Doppler sign convention prevent harmonic and frequency mistakes.
Stops even-harmonic answers on closed pipes and wrong λ on strings.
Do thisMark fixed→node, free/open→antinode before writing f_n.
Stops even-harmonic answers on closed pipes and wrong λ on strings.
Closed pipe fundamental: L=λ/4 ⇒ f=v/(4L); next is 3v/(4L), not 2v/(4L).
Tuning-fork + variable-length column stems become counting, not guessing.
Do thisWrite allowed f as multiples of fundamental; match given resonance to the correct rung.
Tuning-fork + variable-length column stems become counting, not guessing.
Two successive resonances L₁, L₂: λ/2=L₂−L₁ for closed pipe.
Resolves ambiguous ‘beat decreases when tension increases’ statements.
Do thisTreat f_beat as |f−f₀|; ask whether tension/length change raised or lowered f.
Resolves ambiguous ‘beat decreases when tension increases’ statements.
If loading a fork drops its f and beats with a fixed fork fall, the loaded fork was originally above the fixed frequency.
Sign errors vanish when geometry is drawn once.
Do thisDraw v arrows for source, observer, wind; apply approach ⇒ numerator up / denominator down.
Sign errors vanish when geometry is drawn once.
Observer toward source: use v+v_o in numerator; source toward observer: v−v_s in denominator.
Processed examples
Read the impact line first. Then notice which family/model was chosen. The solution is written the way your rough sheet should look in the hall.
A string of length 1 m fixed at both ends vibrates in its first overtone with wave speed 40 m/s. Find the frequency.
This stem rewards early recognition of the standing waves on string / pipe model.
Model chosenFirst overtone is n=2; f=nv/(2L).
Answer40 Hz
Takeaway: Count harmonics from boundary conditions.
y=0.02 sin(4πt−0.02πx) (SI). Find wave speed.
This stem rewards early recognition of the progressive wave parameters model.
Model chosenv=ω/k.
Answer200 m/s
Takeaway: Match the standard sin(ωt−kx) form.
A source of frequency 680 Hz moves at 20 m/s toward a wall. An observer at rest near the source hears beats between direct and reflected sound. Take v=340 m/s. Find the beat frequency.
This Advanced-level variation couples hidden constraints with the doppler effect (sound) model.
Model chosenReflection: apply Doppler twice; direct frequency stays nearly f.
Answer85 Hz
Takeaway: Wall reflection uses an image source in the Doppler formula.
Reusable models
Advanced stems cluster. Name the family in 10–15s, write the fast model, then run the same path. Do not invent a new plan each time.
Looks likeRead ω, k, v, phase from y(x,t)
Fast modelMatch to A sin(ωt∓kx+φ); v=ω/k.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeHarmonics, nodes, end conditions
Fast modelSketch boundary nodes/antinodes; f_n = nv/(2L) or odd harmonics.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeTwo close frequencies or intensity interference (sound)
Fast modelf_beat = |f₁−f₂|; resultant amplitude depends on phase.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeMoving source/observer, wind
Fast modelUse f′ = f (v±v_o)/(v±v_s) with sign convention stated once.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Hall timing
Underline given/asked quantities, free/closed surface labels, idealisations and the exact target. Reject any formula whose assumptions are already violated.
Write the governing relation symbolically before substitution; define a control volume, free body, reference level, or thermodynamic path if the stem mixes regimes.
Keep ratios and differentials exact as long as possible. Carry signs, gauge/absolute pressures, degrees of freedom and units on the rough sheet instead of repairing them later.
Check dimensions, limiting cases and physical sense. For multi-correct, test every option independently rather than forcing one common conclusion.
After the model is locked
v=fλ; ω=2πf; k=2π/λ; y=A sin(ωt−kx+φ)
Progressive plane wave parameters
v=√(T/μ); f_n=n v/(2L) (both ends fixed)
Stretched string harmonics
f_n=n v/(2L), n=1,2,3… (ideal)
Both ends displacement antinodes
f_n=(2n−1)v/(4L), n=1,2,3…
One end closed: odd harmonics only
f_beat=|f₁−f₂|
Two close frequencies heard together
v=√(γP/ρ)=√(γRT/M)
Ideal gas; γ=C_P/C_V
f'=f (v±v_o)/(v±v_s) (signs: toward each other → higher f)
Source/observer moving through still air
Δφ=(2π/λ)Δx
Interference path difference
Make it automatic