JEE Main Waves and Oscillations: SHM, Sound & Superposition Guide
Waves and Oscillations is a 2-3 question block in JEE Main Physics. It tests both conceptual understanding of wave behavior and formula application for SHM calculations.
Simple Harmonic Motion (1-2 questions)
Displacement: x = A sin(ωt + φ). Velocity: v = ω√(A²-x²). Acceleration: a = -ω²x. Time period of: spring (T = 2π√(m/k)), pendulum (T = 2π√(L/g)). Energy in SHM: KE = ½mω²(A²-x²), PE = ½mω²x². Total E = ½mω²A².
Damped and Forced Oscillations
Resonance condition: driving frequency = natural frequency. At resonance: amplitude is maximum, phase difference = π/2. Q factor = ω₀/2β (sharpness of resonance). JEE Main: given under/over/critically damped — identify type from given equation.
Wave Motion (1 question)
Wave equation: y = A sin(kx - ωt). Wave speed v = ω/k = λf. Speed of sound in gas = √(γRT/M). Transverse vs longitudinal waves. Intensity of wave ∝ A².
Standing Waves and Resonance
Strings: f_n = n/(2L) × √(T/μ). Open pipe: all harmonics. Closed pipe: odd harmonics only. Resonance in pipes — length of air column for 1st, 2nd resonance. Beats: f_beat = |f₁ - f₂|.
Doppler Effect
f_observed = f_source × (v ± v_observer)/(v ∓ v_source). Sign convention: approach → higher frequency. JEE Main: moving source approaching/receding stationary observer. Also: red shift for receding stars (light Doppler).
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