SHM Essentials
| Formula | Key Note |
|---|---|
| x = A sin(ωt + φ) | ω = 2π/T |
| v = ω√( − ) | v_max = Aω at x = 0 |
| a = −ω^{2}x | a_max = Aω^{2} at x = ±A |
| E = ½mω^{2} | Constant; KE = PE at x = A/√2 |
| T_spring = 2π√(m/k) | Independent of A and g |
| T_pendulum = 2π√(L/g) | Independent of mass; valid θ < 15° |
Wave Speed
| Medium | Formula | Order |
|---|---|---|
| String | v = √(T/μ) | — |
| Air (sound) | v = √(γRT/M) ∝ √T_K | v_solid > v_liquid > v_gas |
Pipes Quick Reference
| Type | f_{1} | Harmonics |
|---|---|---|
| Open pipe | v/(2L) | All: 1, 2, 3… |
| Closed pipe | v/(4L) = ½ × open | Odd: 1, 3, 5… |
NEET Traps — Must Memorise
- KE = PE at x = A/√2, NOT A/2
- Closed pipe 1st overtone = 3rd harmonic (not 2nd)
- Doppler: toward → − in denominator, not +
- Spring: works in zero gravity; pendulum does NOT
- Node spacing = λ/2 (not λ)
- Beat frequency = |f_{1} − f_{2}| (difference, not sum)
- f_closed = ½ × f_open for same length
Doppler Sign Guide
f' = f × (v + v_O) / (v − v_S) ← TOWARD: + top, − bottom
f' = f × (v − v_O) / (v + v_S) ← AWAY: − top, + bottom