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Oscillations & Waves

SHM, sound waves, Doppler effect, standing waves

Key Concepts
  • SHM: restoring force F = −kx; acceleration proportional to and opposite to displacement
  • Resonance: maximum amplitude when driving frequency = natural frequency
  • Sound is a longitudinal mechanical wave; light is a transverse EM wave
  • Standing waves: nodes (zero amplitude) and antinodes (maximum amplitude)
  • Doppler effect: apparent frequency changes with relative motion of source/observer
Important Formulae
Angular frequency (spring) ω = √(k/m); T = 2π√(m/k)
Simple pendulum period T = 2π√(L/g)
Wave speed v = fλ
Speed of sound (air) v = √(γP/ρ) ≈ 331 m/s at 0°C
Doppler formula f' = f (v ± v_o) / (v ∓ v_s)
SHM energy E = ½mω²A²
Quick Tips
  • In Doppler formula: upper signs when source/observer approach, lower signs when receding.
  • Beats frequency = |f₁ − f₂|; used to tune musical instruments.
  • For a pipe open at both ends: harmonics are n = 1, 2, 3…; closed at one end: only odd harmonics.
Sample Practice Questions

  1. Standing waves are formed by superposition of two waves with:

    • Different frequencies, same direction
    • Same frequency, opposite directions
    • Different amplitudes, same direction
    • Different phases, perpendicular directions
    Show answer

    Answer: Same frequency, opposite directions

  2. The velocity of sound in a medium of elasticity E and density ρ:

    • √(ρ/E)
    • √(E/ρ)
    • E/ρ
    • √(Eρ)
    Show answer

    Answer: √(E/ρ)

  3. In SHM, the acceleration is always directed towards:

    • Extreme position
    • Mean position
    • Perpendicular to velocity
    • Away from mean position
    Show answer

    Answer: Mean position

  4. In a transverse wave, particles vibrate:

    • Parallel to direction of propagation
    • Perpendicular to direction of propagation
    • At 45° to direction of propagation
    • In circular paths
    Show answer

    Answer: Perpendicular to direction of propagation

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Practice Questions

Practice 20 randomly selected NEET questions on Oscillations & Waves. Answers are revealed after each question.

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