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Waves and Sound

NEET > Physics > Oscillations and Waves

Unit Progress

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Overview content

Chapter Snapshot - Waves and Sound

Waves and Sound is one of the highest-scoring chapters in NEET physics, covering the full lifecycle of mechanical wave motion — from the wave equation y = a sin(ωt − kx) and types of waves, through the speed of sound in different media, interference, standing waves in strings and organ pipes, beats, and the Doppler effect. You will also encounter intensity and loudness (decibels), musical characteristics, and acoustics of buildings. The chapter blends conceptual understanding with formula-intensive numericals.

✓ Use This To Plan Your First 2–3 Hours
Expected Questions (Typical)
Q
3-4
NEET regularly tests Doppler effect (apparent frequency formula), organ pipe harmonics (open vs closed), standing wave nodes/antinodes, beats frequency, and speed of sound temperature dependence. Past papers show 3-4 questions from this chapter almost every year.
Time Required (Practical)
⏱
10-12 hrs
Theory and derivations take ~4 hrs; organ pipe + string numericals ~3 hrs; Doppler effect problems ~2 hrs; beats + interference + MCQ revision ~2-3 hrs.
Difficulty Level
⚡
Moderate
Wave equation and basic frequency–wavelength–speed relations are straightforward. Doppler sign conventions and identifying open vs closed pipe harmonics are the main difficulty zones. Standing wave node/antinode positions cause frequent errors.
Most Asked Style: Numerical — apply Doppler formula to find apparent frequency; find fundamental frequency of a string or pipe given length and tension; calculate beat frequency. Also frequent: conceptual MCQs on harmonic series in closed vs open organ pipes.Biggest Trap: Applying Doppler formula with wrong sign convention — in f' = f(v ± v_observer)/(v ∓ v_source), the observer velocity goes in the numerator (+ for approach) and source velocity in the denominator (− for approach toward observer). Swapping numerator/denominator is the #1 error.Fast Win: Memorise: (i) Open pipe → all harmonics, max wavelength = 2L; (ii) Closed pipe → only odd harmonics, max wavelength = 4L; (iii) Beat frequency = |f₁ − f₂|. These three facts alone account for ~40% of this chapter's NEET marks.Revision-Friendly: The Doppler effect sign convention table (Case 1–6 from the textbook) is the single best revision diagram. Draw it once and it anchors all apparent frequency scenarios.

Subtopics - Waves and Sound (NEET)

Wave motion, sound propagation, resonance and the Doppler effect — from ripples to seismic waves

Revision tip: Build your revision around three pillars: (1) wave equation y = a sin(ωt − kx) with all coefficient identifications; (2) open vs closed organ pipe harmonic table; (3) Doppler formula with sign convention. Everything else hangs off these three anchors.
NCERT LinesMCQsQuick Test

1) Wave Motion Fundamentals

Characteristics of wave motion, classification of waves (mechanical vs non-mechanical, transverse vs longitudinal, progressive vs stationary, 1D/2D/3D), audible/infrasonic/ultrasonic/shock waves, and all key wave terms: amplitude, wavelength, frequency, time period, wave function, harmonic wave, wave velocity, phase.

Transverse WavesLongitudinal WavesProgressive WaveStationary WaveUltrasonic > 20 kHzInfrasonic < 20 HzMach Number
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Characteristics of Wave MotionParticles vibrate about mean position without net transport of matter. Velocity of particles differs at different positions; wave velocity is constant for a given medium. Medium requires elasticity, inertia, minimum friction, and uniform density.
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Types of WavesMechanical vs non-mechanical; transverse (crests/troughs, solids and liquid surface only, polarisable) vs longitudinal (compressions/rarefactions, all media, not polarisable); progressive vs stationary; 1D, 2D, 3D.
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Wave Terms and Wave FunctionAmplitude a; wavelength λ = distance between two same-phase points; frequency n (Hz); time period T = 1/n; wave function y = f(x, t); group velocity v_g = dω/dk; phase φ = ωt − kx; intensity I = 2π²n²a²ρv ∝ a².
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Audible, Infrasonic and UltrasonicAudible: 20 Hz – 20 kHz. Infrasonic: < 20 Hz (earthquakes, ocean). Ultrasonic: > 20 kHz; λ < 1.66 cm in air; used in SONAR and ultrasonography. Shock waves: supersonic sources (Mach > 1), conical disturbance.

2) Equation of a Plane Progressive Wave

Mathematical representation of a harmonic travelling wave, identification of all wave parameters from the equation, particle velocity, phase and path difference relations, and pressure wave vs displacement wave.

y = a sin(ωt − kx)v = ω/kλ = 2π/kT = 2π/ωv_p(max) = aωΔP₀ = akB
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Wave Equation and Formsy = a sin(ωt − kx); six equivalent forms. ω = coefficient of t; k = coefficient of x; v = ω/k; λ = 2π/k; T = 2π/ω; n = ω/2π. Minus sign between t and x terms means +x direction propagation.
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Particle Velocityv_p = ∂y/∂t = aω cos(ωt − kx); max = aω. Relation: v_p = −v × (∂y/∂x) = −v × slope.
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Phase and Path DifferenceΔφ = (2π/λ) × Δx (path difference). Δφ = (2π/T) × Δt (time difference). Argument of sin/cos = phase.
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Pressure WaveIf y = a sin(ωt − kx), then ΔP = ΔP₀ cos(ωt − kx); ΔP₀ = akB. Pressure wave leads displacement by π/2. Pressure maximum where displacement is minimum.

3) Speed of Sound

Newton's formula and Laplace correction for speed of sound in gases; factors affecting speed (pressure, temperature, density, humidity, wind); comparison across media; speed of transverse wave in a stretched string.

v = √(γP/ρ)v = √(γRT/M)v₀ = 332 m/s at 0°Cvₜ = v₀ + 0.61tv ∝ √Tv_solid > v_liquid > v_gas
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Newton's Formula and Laplace CorrectionNewton: v = √(P/ρ) = 280 m/s (isothermal, incorrect). Laplace: v = √(γP/ρ) = √(γRT/M) = 332 m/s for air (adiabatic, correct). For air γ = 1.41.
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Factors Affecting SpeedPressure: no effect at constant T. Temperature: v ∝ √T; vₜ = v₀ + 0.61t (v₀ = 332 m/s, t in °C, small changes). Density: v ∝ 1/√ρ. Humidity: moist air < dry air density → faster in humid. Wind: v' = v + w cosθ.
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Comparison Across MediaSolids most elastic → fastest (~5000 m/s for steel). Liquids moderate (~1500 m/s for water). Gases least elastic → slowest (332 m/s in air at 0°C). E_solid > E_liquid > E_gas.
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Transverse Wave in Stringv = √(T/m); T = tension, m = mass per unit length. If weight immersed: T = Mg(1 − σ/ρ). If temperature diff: T = YAαΔθ.

4) Superposition, Interference and Standing Waves

Principle of superposition and its four applications; constructive and destructive interference with path/phase difference conditions; standing wave equation y = 2a cos(kx)sin(ωt); nodes, antinodes, and energy in stationary waves; Quink's tube experiment.

Constructive: Δ = nλDestructive: Δ = (2n−1)λ/2y = 2a cos(kx)sin(ωt)Node: A_SW = 0Antinode: A_SW = 2aI_max/I_min = (a₁+a₂)²/(a₁−a₂)²
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Superposition PrincipleResultant displacement = vector sum of individual displacements. Applications: interference (phase difference), stationary waves (direction difference), beats (frequency difference), Lissajous figures (perpendicular SHMs). Energy conserved, redistributed.
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InterferenceConstructive: φ = 2nπ; path diff = nλ; A_max = a₁ + a₂; I_max = (√I₁ + √I₂)². Destructive: φ = (2n−1)π; path diff = (2n−1)λ/2; A_min = a₁ − a₂; I_min = (√I₁ − √I₂)². For equal amplitudes: I_max = 4I₀, I_min = 0.
›
Standing WavesFormed by two identical waves travelling in opposite directions. y = 2a cos(kx)sin(ωt) (free end reflection) or y = 2a sin(kx)cos(ωt) (rigid end). Nodes (A=0): separation λ/2. Antinodes (A_max=2a): separation λ/2. Node-antinode distance = λ/4. Energy confined; not transmitted across nodes.
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Quink's TubeTwo U-tubes to demonstrate interference. Pulling tube B by distance x changes path by 2x. For successive maxima: 2x = λ; λ = 2x. Speed of sound v = n₀ × 2x.

5) Vibration of Strings

Stationary waves on stretched strings; fundamental mode and overtones; formula for pth harmonic; laws of string vibration; Sonometer and its applications; composite strings.

f₁ = (1/2L)√(T/m)fₚ = p/(2L)√(T/m)All harmonics presentn ∝ 1/Ln ∝ √Tn ∝ 1/√m
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Fundamental Mode and HarmonicsFixed at both ends: nodes at ends, antinodes between. Fundamental (p=1): λ₁ = 2L; f₁ = (1/2L)√(T/m). pth harmonic: λ_p = 2L/p; f_p = p×f₁. All even and odd harmonics present. Ratio 1:2:3:...
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Laws of String VibrationLaw of length: n ∝ 1/L (n₁L₁ = n₂L₂). Law of tension: n ∝ √T. Law of mass: n ∝ 1/√m. Law of density: n ∝ 1/√d. Sonometer applies all four laws.
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SonometerHollow box with a wire; n = (1/2l)√(T/m) = (1/2l)√(T/πr²d). Resonance when n_fork = n_string → rider thrown off. Transverse arrangement: n_fork = n_string; longitudinal: n_fork = 2×n_string.
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Composite StringsTwo strings joined end-to-end vibrate at matching harmonics. (p/2l₁)√(T/m₁) = (q/2l₂)√(T/m₂). Ratio p/q = (l₁/l₂)√(m₁/m₂).

6) Vibration of Organ Pipes

Longitudinal standing waves in closed and open organ pipes; all harmonics vs odd-only; formulae for frequency; end correction; resonance tube experiment to find speed of sound; Kundt's tube; tuning fork properties.

Open: f_n = nv/2L (all)Closed: f_n = (2n−1)v/4L (odd only)End correction e = 0.6rResonance tube: v = 2n(l₂−l₁)Overtone vs Harmonic
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Closed Organ PipeClosed end = node, open end = antinode. Only odd harmonics: 1st, 3rd, 5th… f_n = (2N−1)v/4L. Max wavelength = 4L. Ratio of harmonics 1:3:5. pth overtone = (2p+1)th harmonic. Ratio of overtones 3:5:7.
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Open Organ PipeBoth ends = antinodes. All harmonics: f_n = Nv/2L. Max wavelength = 2L. Ratio of harmonics 1:2:3. pth overtone = (p+1)th harmonic. Sweeter sound than closed pipe (richer harmonics). Open pipe half-submerged = closed pipe of length L/2; same fundamental frequency.
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End CorrectionAntinode forms slightly outside open end. e = 0.6r (r = radius). Effective length: open pipe l' = l + 2e; closed pipe l' = l + e.
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Resonance TubeClosed pipe with variable water column. First resonance at l₁ + e = λ/4; second at l₂ + e = 3λ/4. λ = 2(l₂ − l₁); v = 2n(l₂ − l₁). Also l₂ = 3l₁ + 2e.
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Kundt's TubeMetal rod vibrates longitudinally → standing waves in gas column. Lycopodium powder heaps at nodes (spacing = λ_air/2). v_air/v_rod = λ_air/λ_rod. Used to compare velocities, density of gases, and find γ.
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Tuning ForkU-shaped metallic device producing single frequency. n ∝ t/l² × √(Y/ρ). Loading (wax) near tip → lower frequency. Filing near tip → higher frequency. Breaking one prong → stops vibrating. Temperature rise → frequency decreases.

7) Beats

Formation of beats by superposition of two sound waves of slightly different frequencies; beat frequency; beat period; determination of unknown frequency using loading/filing method; practical limit of distinguishable beats.

f_beat = |f₁ − f₂|T_beat = 1/|f₁−f₂|≤10 beats/sec audibleLoading → ↓ frequencyFiling → ↑ frequency
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Formation and Equation of BeatsTwo waves y₁ = a sin 2πn₁t, y₂ = a sin 2πn₂t superimpose. Resultant: y = A sin π(n₁+n₂)t where A = 2a cos π(n₁−n₂)t (amplitude varies). Beat frequency = n₁ − n₂. Beat period T = 1/(n₁−n₂). Persistence of hearing = 0.1 s → max ~10 distinct beats/sec.
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Determining Unknown FrequencyKnown fork A (nₐ), unknown fork B (n_B), x beats/sec. Load B with wax (nB decreases): if beats increase → nB = nA − x; if beats decrease → nB = nA + x; if beats = 0 → nB = nA + x. File B (nB increases): if beats increase → nB = nA + x; if decrease → nB = nA − x.

8) Doppler Effect

Apparent change in frequency of sound due to relative motion between source and observer; general formula and sign convention; all six standard cases; special cases (crossing, moving target, SONAR, rotating source); conditions for no Doppler effect.

f' = f(v ± v_O)/(v ∓ v_S)+ observer approaching− source approachingCrossing: Δf = 2nv_Sv/(v²−v_S²)SONAR: f' = (1 ± 2v_sub/v)f
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General Formula and Sign Conventionf' = f[(v + v_m) − v_O]/[(v + v_m) − v_S]. For stationary medium: f' = f(v − v_O)/(v − v_S). Direction v is from source to observer. Velocities in the direction of v are positive. Observer in numerator, source in denominator. Approach → frequency increases; recession → decreases.
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Standard CasesSource moving toward observer: f' = fv/(v−vS). Source away: f' = fv/(v+vS). Observer toward source: f' = f(v+vO)/v. Observer away: f' = f(v−vO)/v. Both approach: f' = f(v+vO)/(v−vS). Both recede: f' = f(v−vO)/(v+vS).
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Crossing and Moving TargetSource crosses stationary observer: Δf = 2nvSv/(v²−vS²) ≈ 2nvS/v when vS << v. Moving target (toward): receiver gets f'' = f(v+vT)/(v−vT); away: f'' = f(v−vT)/(v+vT). Moving car toward wall: f' = f(v+vC)/(v−vC) using image method.
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No Doppler EffectNo effect when: (1) S and L both at rest; (2) only medium moves; (3) S-L distance remains constant; (4) S and L move perpendicular to wave direction; (5) velocities ≥ speed of sound.

9) Sound Characteristics and Acoustics

Intensity, loudness and decibel scale; pitch, quality/timbre, loudness as musical characteristics; musical sound vs noise; Echo, reverberation and Sabine's law; conditions for echo; reflection/refraction of sound waves.

I = P/4πr²β = 10 log(I/I₀)I₀ = 10⁻¹² W/m²Echo: d > 17 mReverberation: t = KV/αSThreshold of pain: 120 dB
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Intensity and Decibel ScaleI = P/(4πr²); I ∝ 1/r². I ∝ a². I₀ = 10⁻¹² W/m² (threshold of hearing). β = 10 log₁₀(I/I₀) dB. At threshold pain β = 120 dB. Doubling intensity → +3 dB; 10× intensity → +10 dB.
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Musical CharacteristicsPitch: related to frequency (high freq = shrill pitch). Loudness: related to intensity. Quality/timbre: determined by overtones present (distinguishes sitar from violin). Noise = irregular variations; musical sound = regular harmonic waves.
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Echo and ReverberationEcho: persistence of hearing = 0.1 s; t = 2d/v > 0.1 → d > v/20 = 17 m (at 340 m/s). Reverberation = prolongation of sound after source stops. Reverberation time t = KV/αS (Sabine's law). Controlled by curtains, carpets, large audience, absorbing wall materials.
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Reflection and RefractionFrequency unchanged in reflection and refraction. Rigid end → phase change π (crest→trough); free end → no phase change. For sound in medium denser than surroundings (slow medium), wave bends toward normal. Longitudinal waves: compression reflects as compression from rigid end.

Waves and Sound Download Notes & Weightage Plan

For each topic in the Waves and Sound chapter below, you get (2) the exact resources to download and how to use them, and (3) a simple importance & time plan so NEET students know what to do first and what to revise last.

2 Downloads

Wave Motion Fundamentals

Types of waves, key definitions, frequency ranges, wave function, intensity formula.

Transverse vs LongitudinalProgressive vs StationaryAudible/Infrasonic/UltrasonicMach NumberIntensity ∝ a²

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)Mechanical waves need medium (sound, seismic); EM waves do not (light, radio). Transverse: ⊥ vibration, crests/troughs, solids + liquid surface, polarisable. Longitudinal: ∥ vibration, compressions/rarefactions, all media, not polarisable. Audible: 20 Hz–20 kHz; Infrasonic < 20 Hz; Ultrasonic > 20 kHz (λ < 1.66 cm in air). Intensity I = 2π²n²a²ρv = P/4πr²; I ∝ a²; I ∝ 1/r². Phase: ωt − kx; phase diff = (2π/λ)(path diff). Wave function y = f(x−vt) for +x direction.
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Make a transverse vs longitudinal comparison table from Table 17.1 (p.759). Then write all 15 key wave terms with their symbols and units. Solve 5 MCQs identifying wave type from given scenario.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions0-1Conceptual classification MCQs; occasionally a question on intensity formula or decibel.
Time Required1.5 hrs45 min reading definitions, 45 min classification MCQs.
DifficultyEasyMostly classification and definition; no complex calculation required.
  • Scoring Focus: Polarisation difference (transverse can be polarised, longitudinal cannot); mechanical medium requirement; intensity vs amplitude relation.
  • High-risk Area: Students think sound in water behaves as electromagnetic wave (cannot be — it is mechanical). Also confuse rarer/denser medium for sound vs light.
  • Best Practice Style: Single-correct MCQs with classification or comparison.
Priority rule: Cover first as it provides vocabulary for all other topics.

Equation of a Plane Progressive Wave

Reading wave parameters from the equation; particle velocity vs wave velocity; phase and path difference.

y = a sin(ωt − kx)ω = coeff of tk = coeff of xv = ω/kv_p(max) = aωPressure wave ⊥ phase to displacement

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)y = a sin(ωt − kx): ω = coeff of t, k = coeff of x, v = ω/k, λ = 2π/k, T = 2π/ω, n = ω/2π. (v_p)_max = aω. v_p = −v × (∂y/∂x). Phase = (ωt − kx). Path diff Δx ↔ phase diff Δφ = (2π/λ)Δx. Pressure wave: ΔP = ΔP₀ cos(ωt − kx); ΔP₀ = akB; pressure leads displacement by π/2. y = (x²−v²t²) does NOT represent a wave (not of form f(x±vt)).
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Given an equation like y = 5 sin(200t − 2.5x), extract a, ω, k, v, λ, T, n, (v_p)_max. Practice 8–10 such extraction problems. Then do 3 problems on phase difference given two positions or two times.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions1NEET frequently asks to identify wave velocity or particle velocity amplitude from a given wave equation.
Time Required1.5 hrs30 min learning extraction rules, 1 hr numericals.
DifficultyEasy-ModerateStraightforward once the five coefficient identifications are memorised; confusing v_wave (= ω/k) vs v_particle (= aω) is the main trap.
  • Scoring Focus: v = ω/k (wave speed) vs (v_p)_max = aω (max particle speed); direction of propagation from sign between t and x.
  • High-risk Area: Students read v = aω (particle speed max) as the wave speed — wrong. Wave speed v = ω/k.
  • Best Practice Style: Numerical extraction from equation + phase difference calculation.
Priority rule: High priority — foundation for all wave problems.

Speed of Sound

Speed of sound in different media, Newton and Laplace formulae, temperature effects, factors that do not affect speed.

v = √(γP/ρ) = √(γRT/M)v₀ = 332 m/s at 0°Cvₜ = 332 + 0.61tv ∝ √T; v independent of Pv_solid > v_liquid > v_gas

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)Newton: v = √(P/ρ) = 280 m/s (wrong — isothermal). Laplace: v = √(γP/ρ) = √(γRT/M) = 332 m/s for air at 0°C (adiabatic, correct). v_rms/v_sound = √(3/γ). Effect of P at constant T: no effect (P↑ → ρ↑ proportionally). T: v ∝ √T; vₜ = v₀ + 0.61t (small t); 1°C rise → +0.61 m/s. Density: v ∝ 1/√ρ. Humidity: moist air less dense → faster. Wind: v' = v + w cosθ. Steel ≈ 5000 m/s; water ≈ 1500 m/s; air at 0°C = 332 m/s.
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Write the Laplace formula derivation in 4 lines. Then solve 5 temperature-effect problems: given speed at 0°C = 332 m/s, find speed at T°C or t°C. Memorise the three media speeds.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions0-1Speed comparison across media or temperature-effect numerical are common.
Time Required1 hr30 min Newton-Laplace theory, 30 min numerical practice.
DifficultyEasy-ModerateFormulae are clean; the conceptual trap is that pressure has no effect on v at constant T.
  • Scoring Focus: v independent of pressure at constant T (NEET 2015 type); temperature effect: v ∝ √T; compare media speeds.
  • High-risk Area: Thinking pressure increase → speed increase (it does not, because density increases proportionally). Also confusing v_rms of gas with v_sound.
  • Best Practice Style: Short numerical + conceptual MCQs (effect of conditions on speed).
Priority rule: Medium priority — frequently tested as a one-liner or data-extraction question.

Superposition, Interference and Standing Waves

Superposition principle applied to interference and standing waves; constructive/destructive conditions; standing wave equation; nodes and antinodes; energy confinement.

Constructive: Δ = nλDestructive: Δ = (2n−1)λ/2I_max = (√I₁+√I₂)²y_SW = 2a cos(kx)sin(ωt)Node-antinode: λ/4Energy not transmitted past nodes

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)Resultant: A = √(a₁²+a₂²+2a₁a₂cosφ). I = I₁+I₂+2√(I₁I₂)cosφ. Constructive: φ=2nπ; Δ=nλ; I_max=(√I₁+√I₂)². Destructive: φ=(2n−1)π; Δ=(2n−1)λ/2; I_min=(√I₁−√I₂)². For equal amp: I_max=4I₀, I_min=0. Standing wave (free end): y=2a cos(kx)sin(ωt). Nodes (A=0): x = λ/4, 3λ/4... Antinodes (A=2a): x = 0, λ/2, λ... Successive node/antinode separation = λ/2; node-antinode = λ/4. Energy does NOT propagate past nodes. Total SW energy = 2× each component.
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Derive y₁+y₂ = 2a cos(kx)sin(ωt) step by step. List node and antinode positions for both free-end and rigid-end cases. Solve 5 problems on I_max/I_min when a₁/a₂ ratio is given.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions0-1Node/antinode position MCQs; I_max/I_min ratio given amplitude ratio.
Time Required1.5 hrs45 min derivation of SW equation, 45 min node/antinode + interference MCQs.
DifficultyModerateDerivation is moderately complex; most errors come from using wrong node/antinode positions for rigid vs free boundary.
  • Scoring Focus: I_max/I_min = (a₁+a₂)²/(a₁−a₂)²; node-antinode spacing = λ/4; energy confinement in segments.
  • High-risk Area: Interchanging node and antinode positions for rigid vs free boundary; forgetting the ½ in path-to-phase conversion.
  • Best Practice Style: Graph-based MCQs (identify nodes/antinodes from standing wave diagram); ratio-based intensity problems.
Priority rule: Medium priority — important conceptual foundation for organ pipes.

Vibration of Strings

String harmonics, laws of vibration, Sonometer application; composite strings.

f₁ = (1/2L)√(T/m)All harmonics: 1:2:3n ∝ 1/L ∝ √T ∝ 1/√mSonometer resonanceComposite: p·√(T/m₁)/l₁ = q·√(T/m₂)/l₂

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)v = √(T/m); f_p = (p/2L)√(T/m) = pf₁. All even and odd harmonics: ratio 1:2:3. Pluck at l/2p for p loops. Law of length: nl=const. Law of tension: n/√T=const. Law of mass: n√m=const. Law of density: n√d=const. Sonometer: n=(1/2l)√(T/πr²d); resonance when n_fork=n_string → rider thrown off. Transverse mounting: n_fork = n_string; longitudinal: n_fork = 2n_string (fork vibrates at twice the string frequency).
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Practice the four laws by solving 3 problems each (e.g., doubling tension → what happens to frequency?). Memorise f₁=(1/2L)√(T/m) with all substitution cases. Draw the first three modes for a string with node/antinode positions.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions0-1Frequency calculation given length, tension, and linear density; or comparing two strings.
Time Required1.5 hrs45 min theory + 45 min numericals.
DifficultyModerateFormula application is systematic; the main trap is forgetting the factor of 2 for longitudinal sonometer mounting.
  • Scoring Focus: f₁=(1/2L)√(T/m); doubling T → f becomes √2 times; halving L → f doubles.
  • High-risk Area: Confusing mass per unit length m and total mass M. Linear density m = M/L (not the same as bulk density). Also confusing transverse vs longitudinal sonometer setups.
  • Best Practice Style: Short numerical MCQs with one variable changed.
Priority rule: Medium priority — 0-1 question in NEET; master f₁ formula first.

Vibration of Organ Pipes

Open and closed organ pipe harmonic series, end correction, resonance tube, Kundt's tube.

Open: f_n=nv/2L (all)Closed: f_n=(2n−1)v/4L (odd)End correction e=0.6rResonance: v=2n(l₂−l₁)Closed: 1st overtone=3rd harmonicOpen: 1st overtone=2nd harmonic

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)Closed pipe: node at closed end, antinode at open end. Only odd harmonics n₁:n₃:n₅=1:3:5. Max λ=4L. pth overtone=(2p+1)th harmonic. Open pipe: antinodes at both ends. All harmonics 1:2:3. Max λ=2L. pth overtone=(p+1)th harmonic. End correction e=0.6r; effective length_open=l+2e; effective length_closed=l+e. Resonance tube: λ=2(l₂−l₁); v=2n(l₂−l₁). Second resonance not at 3×first resonance but at 3l₁+2e. Kundt's tube: v_air/v_rod=λ_air/λ_rod. Open pipe sweeter sound (more harmonics). Frequency of tuning fork n∝t/l²×√(Y/ρ).
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Draw the first three modes of both open and closed pipes side by side, labelling nodes (N) and antinodes (A). List harmonics and overtones in parallel columns. Solve 5 frequency-of-pipe questions and 3 resonance tube problems.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions1-2NEET heavily tests organ pipes — identifying which harmonics are present, finding frequency from length, or comparing open vs closed pipes.
Time Required2 hrs1 hr drawing pipe modes + 1 hr numericals.
DifficultyModerateThe odd-only vs all-harmonics rule is simple but students confuse overtone numbering vs harmonic numbering.
  • Scoring Focus: Closed pipe → odd harmonics only; open pipe → all harmonics; overtone-to-harmonic conversion formula.
  • High-risk Area: Saying 'second harmonic of closed pipe' — closed pipe has no even harmonics! Also confusing end correction direction (always adds to effective length).
  • Best Practice Style: Table-based MCQs on harmonic identification; calculation of fundamental frequency.
Priority rule: Highest priority in Waves — covers 1-2 NEET questions annually. Must master.

Beats

Beat formation, frequency, period, and using beats to identify unknown tuning fork frequency.

f_beat = |f₁−f₂|Max ~10 beats/sec audibleLoading → ↓fFiling → ↑fBeats > x after loading → fB = fA−x

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)Beats: periodic variation of intensity when two nearly equal frequencies superimpose. y = A sin π(n₁+n₂)t; A = 2a cos π(n₁−n₂)t. Beat freq = n₁−n₂; Beat period = 1/(n₁−n₂). Max audible beats ≈10 (persistence of hearing 0.1 s). Unknown frequency determination: load known/unknown fork (decreases f); count new beats x'. If B loaded and beats increase: n_B = n_A − x. If beats decrease: n_B = n_A + x. If beats = 0: n_B = n_A + x. Three tuning forks n, n+x, n+2x in equal amplitudes → beat freq = x.
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Study Table 17.7 (p.772) — all four loading/filing cases. Practice 4 problems on finding unknown frequency using the table. Memorise: loading always DECREASES frequency.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions0-1Beats questions are common — usually finding unknown frequency by loading/filing logic.
Time Required1 hr30 min theory + 30 min beat frequency determination problems.
DifficultyModerateThe loading/filing logic table is confusing; must practise all four cases until automatic.
  • Scoring Focus: Beat frequency formula; loading→decrease rule; Table 17.7 logic for unknown frequency.
  • High-risk Area: Students reverse the loading logic — when B is loaded and beats increase, n_B is BELOW n_A (not above). This is the most frequently missed beats question.
  • Best Practice Style: Logic-based MCQs on loading/filing to identify unknown frequency.
Priority rule: Medium priority — usually 0-1 question; beats logic takes only 30 min to master.

Doppler Effect

Apparent frequency formula; all six standard cases; crossing, moving target, SONAR, rotating source; conditions for no Doppler effect.

f' = f(v±v_O)/(v∓v_S)Observer numerator, Source denominatorBoth approach → max f'Crossing: Δf = 2nv_Sv/(v²−vS²)SONAR: f' = (1±2v_sub/v)f

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)General: f' = f[(v+vm)−vO]/[(v+vm)−vS]. Stationary medium: f' = f(v−vO)/(v−vS). Sign convention: direction of v from S to O. Velocities in direction of v = positive. Approach always increases apparent freq; recession decreases. 6 standard cases memorised from Table on p.773-775. Crossing source: Δf_before-after = 2nv_Sv/(v²−vS²) ≈ 2nvS/v for vS<<v. Moving target (approaching): f'' = f(v+vT)/(v−vT). Car → wall: f' = f(v+vC)/(v−vC) [image method]. No Doppler: both at rest; medium-only moving; S-L distance constant; perpendicular motion; velocity ≥ v_sound. Doppler in sound is asymmetric; in light it is symmetric.
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Write the general formula. Apply it to all 6 cases from scratch to derive specific expressions. Solve 10 Doppler numericals of varying type (source moving, observer moving, both moving, crossing). Special attention to car-wall problem and moving target.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions1-2Doppler is the highest-frequency NEET topic in this chapter — 1-2 questions nearly every year. Focuses on finding apparent frequency in numerical or conceptual form.
Time Required2 hrs45 min formula + sign convention; 1 hr 15 min numericals covering all cases.
DifficultyModerate-HighThe formula itself is simple but sign errors at source/observer denominator/numerator cause systematic mistakes. Car-wall and moving-target problems add complexity.
  • Scoring Focus: Sign convention mastery; source in denominator (−v_S for approach); observer in numerator (+v_O for approach). Crossing frequency change formula.
  • High-risk Area: Swapping observer and source positions in the formula — putting observer's velocity in the DENOMINATOR (it must go in numerator). Also forgetting the factor of 2 in Δf formula for crossing.
  • Best Practice Style: Multi-case numericals; select-the-correct-formula MCQs; apparent frequency ratio problems.
Priority rule: HIGHEST priority in the chapter — 1-2 NEET questions every year. Spend the most time here after organ pipes.

Waves and Sound Chapter NEET Traps & Common Mistakes (Topic-Wise)

Each subtopic below is of the Waves and Sound chapter and shows what NEET students usually do wrong in NEET examination, a short example of the mistake, and how NEET frames the question to trick you with close options are given below.

! Avoid Easy Negatives
Doppler Formula Sign Convention
Doppler EffectApparent FrequencySign Errors

Mistake Snapshot (What Students Do Wrong)

  • Observer velocity in denominator: Students write f' = f(v−vS)/(v±vO) putting observer velocity in denominator instead of numerator — wrong standard form.
  • Wrong sign for approach: For observer approaching source: numerator is (v + vO); for source approaching observer: denominator is (v − vS). Students reverse these signs.
2–3 Line Example (Typical Error)

A car (source) approaches a stationary observer at 20 m/s; v_sound = 340 m/s; f = 500 Hz. Correct: f' = 500×340/(340−20) = 531 Hz. Wrong (denominator swap): f' = 500×(340+20)/340 = 529 Hz but formula was applied incorrectly.

How NEET Frames The Trap

NEET options always include the 'reversed sign' answer as a distractor. Always ask: is it source or observer moving? Source goes in denominator, observer in numerator.

NEET-Style Trap Question Format

Q. A train moving at 20 m/s toward a stationary observer sounds a whistle of frequency 400 Hz. Speed of sound = 340 m/s. The frequency heard by the observer is:
A. 400 × 360/340   B. 400 × 340/360   C. 400 × 340/320   D. 400 × 320/340  
Trick: Source approaching → denominator decreases → f' increases. f' = 400×340/(340−20) = 400×340/320. Answer = option C.

Quick rule: Observer in NUMERATOR (+ approaching); Source in DENOMINATOR (− approaching). A source moving toward you raises pitch — denominator decreases, f' goes up.
Closed vs Open Organ Pipe Harmonics
Organ PipesHarmonicsOvertonesClosed Pipe Odd Only

Mistake Snapshot (What Students Do Wrong)

  • Closed pipe produces all harmonics: Students forget that a closed pipe has a node at one end (asymmetric boundary conditions) which forces only odd harmonics (1, 3, 5…).
  • Overtone ≠ Harmonic numbering: In a closed pipe: 1st overtone = 3rd harmonic (NOT 2nd harmonic). Students add 1 instead of going to the next ODD harmonic.
2–3 Line Example (Typical Error)

Closed pipe of length 1 m; v = 340 m/s. Fundamental f₁ = v/4L = 85 Hz. The SECOND harmonic does NOT exist. First overtone = 3rd harmonic = 3×85 = 255 Hz.

How NEET Frames The Trap

Questions ask 'what is the second harmonic of a closed pipe?' — there is no second harmonic! The answer must invoke the odd-harmonic restriction.

NEET-Style Trap Question Format

Q. For a closed organ pipe of length L, which frequencies are present in its harmonic series?
A. v/4L, v/2L, 3v/4L, v/L   B. v/4L, 3v/4L, 5v/4L, 7v/4L   C. v/2L, v/L, 3v/2L, 2v/L   D. v/4L, v/2L, 5v/4L, 7v/4L  
Trick: Only odd harmonics: f_n = (2N−1)v/4L for N = 1,2,3,4: gives v/4L, 3v/4L, 5v/4L, 7v/4L. Answer B.

Quick rule: Closed pipe: ONLY odd harmonics (v/4L, 3v/4L, 5v/4L…). Open pipe: ALL harmonics (v/2L, 2v/2L, 3v/2L…). Never even harmonics for closed pipe.
Wave Speed vs Particle Speed
Wave Equationv = ω/kv_p = aωParameter Identification

Mistake Snapshot (What Students Do Wrong)

  • Using aω as wave speed: Students see ω in the equation y = a sin(ωt − kx) and calculate aω as the wave speed — but aω is the MAXIMUM PARTICLE speed, not the wave speed.
  • Wave speed = amplitude × frequency: Confusing v_wave = λf = ω/k with v_particle_max = aω. The 'a' has no role in wave propagation speed.
2–3 Line Example (Typical Error)

y = 0.02 sin(200t − 4x) (SI units). Wave speed v = ω/k = 200/4 = 50 m/s. Max particle speed = aω = 0.02 × 200 = 4 m/s. These are completely different quantities.

How NEET Frames The Trap

NEET gives a wave equation and asks 'what is the speed of this wave?' — the answer is ω/k but distractor option is always aω.

NEET-Style Trap Question Format

Q. A wave is represented by y = 0.05 sin(300t − 6x) m. What is the speed of the wave and the maximum speed of a particle?
A. Wave speed = 50 m/s, particle speed max = 15 m/s   B. Wave speed = 15 m/s, particle speed max = 50 m/s   C. Wave speed = 300 m/s, particle speed max = 0.3 m/s   D. Wave speed = 6 m/s, particle speed max = 300 m/s  
Trick: v_wave = ω/k = 300/6 = 50 m/s. v_p_max = aω = 0.05 × 300 = 15 m/s. Answer A.

Quick rule: Wave speed = ω/k (NOT related to amplitude). Particle max speed = aω (involves amplitude). They are different concepts entirely.
Beats and Loading Logic
BeatsUnknown FrequencyLoadingFiling

Mistake Snapshot (What Students Do Wrong)

  • Loading increases frequency: Students mix up filing (increases frequency) and loading/waxing (decreases frequency). Loading adds mass → lowers natural frequency.
  • Wrong direction of beats reasoning: If B is loaded and beats INCREASE, students say nB > nA — actually nB < nA (extra reduction pushed it further from nA).
2–3 Line Example (Typical Error)

Forks A (known, 256 Hz) and B (unknown) give 4 beats/sec. B is loaded → beats become 6/sec. Loading decreased nB further from nA, so nB was already below nA. Therefore nB = 256 − 4 = 252 Hz.

How NEET Frames The Trap

The table-based logic (Table 17.7) is counter-intuitive: when loading INCREASES beats, that means nB was BELOW nA, not above.

NEET-Style Trap Question Format

Q. Forks A (512 Hz) and B (unknown) give 4 beats/sec. When B is loaded with wax, beats increase to 6/sec. The frequency of B before loading is:
A. 516 Hz   B. 508 Hz   C. 512 Hz   D. 520 Hz  
Trick: Loading decreases nB. Beats increased → nB moved further from nA = 512. So nB was already < 512. nB = 512 − 4 = 508 Hz. Answer B.

Quick rule: Loading fork B: beats increase → nB = nA − x (B was below A). Beats decrease → nB = nA + x (B was above A, loading brought it closer). Loading ALWAYS lowers frequency.
Effect of Pressure and Temperature on Speed of Sound
Speed of SoundPressure EffectTemperature EffectConstant Temperature

Mistake Snapshot (What Students Do Wrong)

  • Increasing pressure increases sound speed: Students assume more pressure → more molecular collisions → faster sound. False: at constant T, as P increases, ρ increases proportionally, so v = √(γP/ρ) stays constant.
  • Confusing v ∝ √T (Kelvin) with t (°C): v ∝ √T where T is ABSOLUTE temperature (Kelvin). For small changes use vₜ = v₀ + 0.61t (t in °C), but for ratio problems use T₁ and T₂ in Kelvin.
2–3 Line Example (Typical Error)

Doubling pressure at constant temperature: ρ also doubles. v = √(γP/ρ) = √(γ × 2P/2ρ) = √(γP/ρ) = unchanged. Speed of sound is independent of pressure at constant T.

How NEET Frames The Trap

NEET options include a 'speed doubles when pressure doubles' option — this is wrong and is the trap. The correct answer is speed is unchanged.

NEET-Style Trap Question Format

Q. If the pressure of a gas is doubled at constant temperature, the speed of sound in the gas becomes:
A. Doubled   B. Halved   C. √2 times the original   D. Unchanged  
Trick: At constant T, P/ρ = constant (ideal gas). v = √(γP/ρ) = constant. Answer D.

Quick rule: Speed of sound is INDEPENDENT of pressure at constant temperature. It depends on temperature via v ∝ √T (Kelvin).

Topics

Characteristics of Wave Motion

Waves

Types of Waves

Important Terms Regarding Wave Motion

Velocity of Transverse Wave

Factors Affecting Velocity of Sound in Gaseous Medium

Velocity of Longitudinal Wave (Sound Wave)

Equation of a Plane Progressive Wave

Pressure Waves

Reflection and Refraction of Waves

Echo

Interference of Sound Waves

Principle of Superposition

Quink's Tube

Standing Waves or Stationary Waves

Terms Related to the Application of Stationary Wave

Standing Waves on a String

Sonometer

Standing Wave in an Organ Pipe

Vibration of Composite Strings

Tuning Fork

End Correction

Kundt's Tube

Resonance Tube

Beats

Determination of Unknown Frequency

Doppler's Effect

Musical Sound and Acoustics

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Characteristics of Wave Motion

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