Error Analysis — Common Mistakes in Waves & SHM — Notes

#	Error	Correct Understanding
1	KE = PE at x = A/2	KE = PE at x = A/√2 ≈ 0.707A, not at x = A/2
2	Closed pipe has same harmonics as open pipe	Closed pipe: ODD harmonics only (1, 3, 5…); open pipe: all harmonics
3	Doppler: adding $v_S$ to denominator when source approaches	When source moves toward observer, subtract $v_S$ from denominator: f' = f· $\frac{v}{v − v_S}$
4	Spring period depends on amplitude	T = 2π $\sqrt{m/k}$ is completely independent of amplitude
5	Pendulum period depends on mass	T = 2π $\sqrt{L/g}$ has no mass term; only L and g matter
6	$v_{sound}$ > $v_{solid}$	Actually: $v_{solid}$ > $v_{liquid}$ > $v_{gas}$ ; solids have highest elastic modulus
7	Node–node distance = λ	Consecutive nodes are λ/2 apart, not λ. Full wavelength = 2 × (node-to-node distance)
8	Free-fall pendulum oscillates faster	$g_{eff}$ = 0 in free fall → T = ∞ → pendulum does NOT oscillate
9	First overtone of closed pipe = 2nd harmonic	First overtone of closed pipe = 3rd harmonic (3 $f_{1}$ ), since even harmonics absent
10	Total energy in SHM varies with x	Total energy E = ½mω^{2} $A^{2}$ is CONSTANT regardless of position x