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.

Speed on a string: v = √(T/μ)   (T = tension, μ = linear mass density)

Speed of sound in gas: v = √(γRT/M)   (γ = C_p/C_v)

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)

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,…

General formula (for sound):
f' = f × (v ± v_o) / (v ∓ v_s)
Sign convention: +v_o if observer moves toward source; +v_s if source moves away from observer.

For light (relativistic): Δλ/λ = v/c (redshift/blueshift).

💡 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: f_beat = |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.

Wave speed: v = fλ

String wave: v = √(T/μ)

Sound speed (gas): v = √(γRT/M)

Fixed string harmonics: f_n = n v/(2L)

Open pipe: f_n = n v/(2L)

Closed pipe: f_n = (2n–1) v/(4L)

Beat frequency: f_beat = |f₁ – f₂|