Waves Revision Notes for NEET Physics PDF Download
🌊 WAVES · Mechanical Waves & Sound
Wave motion • Wave equation • Speed of wave • Superposition • Standing waves • Beats • Doppler effect • NEET problems
📐 WAVE MOTION
Mechanical wave – requires medium (e.g., sound, water).
Electromagnetic wave – no medium needed (light).
Transverse wave – displacement ⊥ propagation direction (string waves).
Longitudinal wave – displacement ∥ propagation direction (sound).
Wave parameters: wavelength λ, frequency f, period T, amplitude A, speed v = fλ = ω/k.
📈 Transverse wave (sine wave)
📝 WAVE EQUATION & SPEED
General travelling wave: y = f(x ± vt) or y = A sin(kx ∓ ωt + φ) (where k = 2π/λ, ω = 2πf).
Speed on a string: v = √(T/μ) (T = tension, μ = linear mass density)
Speed of sound in gas: v = √(γRT/M) (γ = Cp/Cv)
For air at STP: v ≈ 330–340 m/s.
Speed of sound in solid: v = √(Y/ρ) (Young's modulus)
In liquid: v = √(B/ρ) (Bulk modulus)
🌀 SUPERPOSITION PRINCIPLE
Resultant displacement = vector sum of individual displacements.
Interference: For two waves y₁ = A sin(kx–ωt), y₂ = A sin(kx–ωt+φ)
Resultant amplitude = 2A cos(φ/2). Constructive: φ = 0,2π,…; Destructive: φ = π,3π,…
🎸 STANDING WAVES (String & Air Columns)
Formed by superposition of two identical waves travelling in opposite directions.
Fixed ends (string)
Boundary conditions: node at both ends.
λn = 2L/n, fn = n v/(2L), n = 1,2,3,…
Fundamental: f₁ = v/(2L)
Open organ pipe
Pressure node at ends (displacement antinode).
λn = 2L/n, fn = n v/(2L), n = 1,2,3,…
All harmonics present.
Closed organ pipe
Closed end: displacement node; open end: antinode.
λn = 4L/(2n–1), fn = (2n–1)v/(4L), n=1,2,…
Only odd harmonics.
🎵 Standing wave patterns (fundamental & overtones)
🔊 BEATS
When two waves of nearly equal frequencies superpose, amplitude varies periodically → beats.
Beat frequency: fbeat = |f₁ – f₂|
🚗 DOPPLER EFFECT
Apparent frequency change due to relative motion between source and observer.
General formula (for sound):
f' = f × (v ± vo) / (v ∓ vs)
Sign convention: +vo if observer moves toward source; +vs if source moves away from observer.
For light (relativistic): Δλ/λ = v/c (redshift/blueshift).
🚨 Doppler effect – source moving towards observer
💡 NEET TIPS & SHORTCUTS
- For string fixed at both ends, wavelength = 2L/n, frequency = n v/(2L).
- In open pipe, all harmonics; in closed pipe, only odd harmonics.
- Beat frequency formula: fbeat = |f₁ – f₂|.
- Doppler effect: relative speed determines change; use sign carefully.
⚠️ COMMON MISTAKES
- Confusing transverse vs longitudinal wave motion.
- Using λ = v/f incorrectly when wave speed changes with medium.
- Forgetting that standing waves require specific boundary conditions.
- Applying Doppler formula without correct sign convention.
📌 QUICK REVISION CARD
Wave speed: v = fλ
String wave: v = √(T/μ)
Sound speed (gas): v = √(γRT/M)
Fixed string harmonics: fn = n v/(2L)
Open pipe: fn = n v/(2L)
Closed pipe: fn = (2n–1) v/(4L)
Beat frequency: fbeat = |f₁ – f₂|