PhysicsPHY 06
Oscillations & Waves
SHM energy, spring-mass, simple pendulum, Doppler effect, organ pipes, beats
NCERT XI Ch.14–15
NCERT Ref
Concept Core
Essential theory — everything NCERT tests on Oscillations & Waves
SIMPLE HARMONIC MOTION
a = −ω²x. F = −kx (restoring force ∝ displacement, opposite direction).
x = A sin(ωt + φ). v = Aω cos(ωt + φ). vmax = Aω at x=0. amax = Aω² at x = ±A.
Energy: PE = ½kx² = ½mω²x². KE = ½m(vmax²−ω²x²). Total E = ½kA² = constant.
TIME PERIODS
Spring-mass: T = 2π√(m/k). Independent of amplitude (for small oscillations).
Simple pendulum: T = 2π√(L/g). Independent of mass AND amplitude (small θ). Increases on Moon (g smaller), increases at height.
LC oscillator: T = 2π√(LC).
WAVES & SOUND
vsound = √(γP/ρ) = √(γRT/M). Increases with temperature (v ∝ √T).
Beats: fbeat = |f₁ − f₂|. Audible up to ~10 Hz.
Doppler effect: f' = f(v + vo)/(v − vs). Source approaching = higher frequency. Moving away = lower.
ORGAN PIPES
Open pipe: harmonics at L = nλ/2 → fn = nv/(2L). All harmonics present.
Closed pipe: only odd harmonics. L = (2n−1)λ/4 → fn = (2n−1)v/(4L). Fundamental freq = v/4L.
Open pipe fundamental = 2× closed pipe fundamental (same L).
Fact & Formula Vault
High-yield facts, numbers, and formulas
SHM Formulae
x = A sin(ωt + φ)
v_max = Aω (at x=0)
a_max = Aω² (at x=±A)
Total E = ½kA² (constant)
Time Periods
Spring: T = 2π√(m/k)
Pendulum: T = 2π√(L/g)
T ∝ 1/√g (pendulum)
Independent of amplitude
Waves
v_sound ∝ √T
Beats = |f₁ − f₂|
Doppler: f'=f(v+v_o)/(v−v_s)
Open pipe: all harmonics
Worked Examples
NEET-style questions solved step-by-step
EASYA pendulum of length L has time period T. At what length will T double?▾
A pendulum of length L has time period T. At what length will T double?
T = 2π√(L/g). For T to double: 2T = 2π√(L'/g) → L' = 4L. Length must be quadrupled (4L).
MEDIUMTwo tuning forks of 256 Hz and 260 Hz are sounded together. Beat frequency?▾
Two tuning forks of 256 Hz and 260 Hz are sounded together. Beat frequency?
Beat frequency = |260 − 256| = 4 Hz. The listener hears 4 loud pulses per second.
HARDAn ambulance siren (700 Hz) approaches at 20 m/s. Speed of sound = 340 m/s. Observed frequency?▾
An ambulance siren (700 Hz) approaches at 20 m/s. Speed of sound = 340 m/s. Observed frequency?
f' = f(v)/(v−v_s) = 700 × 340/(340−20) = 700 × 340/320 = 743.75 Hz ≈ 744 Hz. Source approaching → higher freq.
Mistake DNA
Common NEET traps for this chapter
⚠ Pendulum mass independence
Pendulum period is independent of BOTH mass and amplitude (for small angles). Only L and g matter.
✓ Fix: T_pendulum = 2π√(L/g). No mass, no amplitude.
⚠ Closed vs open pipe
Closed pipe: only ODD harmonics (1st, 3rd, 5th). Open pipe: ALL harmonics. Closed fundamental = v/4L. Open = v/2L.
✓ Fix: Closed = odd harmonics only. Open = all harmonics.
⚠ Doppler formula signs
If source moves toward observer: v−v_s (denominator decreases → f increases). If observer moves toward source: v+v_o (numerator increases → f increases).
✓ Fix: Toward = higher frequency. Away = lower.
Chapter Intelligence
Exam data and last-minute strategy
NEET Frequency
3–4 Q/year. SHM energy, pendulum period, beats, Doppler effect, organ pipe harmonics are standard every year.
High-Yield
Total E = ½kA² (constant). T_spring = 2π√(m/k). Beats = |f₁−f₂|. Closed pipe = odd harmonics. Doppler: approaching → higher f.
Strategy
Memorise time period formulae for spring and pendulum. Doppler problems: set up formula carefully with signs. Beats are straightforward subtraction.
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