Common Errors & NEET Traps in Waves & SHM

Error 1 — KE = PE at x = A/2: The correct position is x = A/√2 ≈ 0.707A. Setting ½mω^{2}( $A^{2}$ − $x^{2}$ ) = ½mω^{2} $x^{2}$ gives x = A/√2. At x = A/2: KE = 3E/4, PE = E/4 — they are not equal.
Error 2 — Even harmonics in closed pipes: Closed organ pipes produce ONLY odd harmonics (1st, 3rd, 5th…). The asymmetric node-antinode boundary condition physically prevents even harmonics.
Error 3 — Doppler sign confusion: When source moves toward observer, subtract v_S from denominator (not add). Adding would give f' < f, which is wrong for an approaching source.
Error 4 — Spring period changes with amplitude: T = 2π√(m/k) has no amplitude term. Period is perfectly isochronous regardless of how far the spring is stretched.
Error 5 — Pendulum independent of gravity: Pendulum DOES depend on gravity (T = 2π√(L/g)). In zero gravity (free fall), T = ∞ and no oscillation occurs. The spring-mass system is gravity-independent.
Error 6 — Sound travels fastest in gases: Sound travels fastest in solids (highest elastic modulus), slowest in gases. v_solid > v_liquid > v_gas.
Error 7 — Node spacing is λ: Consecutive nodes are λ/2 apart, not λ. A full wavelength spans two node-to-node gaps.
Error 8 — First overtone of closed pipe = 2nd harmonic: The first overtone of a closed pipe is the 3rd harmonic (3f_{1}). There is no 2nd harmonic in a closed pipe.
Error 9 — Beat frequency = f_{1} + f_{2}: Beats arise from the frequency difference: f_beat = |f_{1} − f_{2}|. The sum gives the carrier frequency, not the beat rate.
Error 10 — Louder = higher frequency: Amplitude determines loudness (intensity ∝ $A^{2}$ ); frequency determines pitch. They are entirely independent quantities.