Theme C · Wave Behaviour

Transverse (oscillation ⟂ travel, e.g. light); longitudinal (∥ travel, e.g. sound).

$\omega = 2\pi f = 2\pi/T$. Force toward equilibrium.

Max speed at equilibrium; max accel at extremes.

Independent of mass and (small) amplitude.

Continuously swaps between KE and PE.

Max $v=\omega x_0$ at $x=0$; $v=0$ at $x=\pm x_0$.

Amplitude (max displacement), wavelength λ (m), frequency f (Hz), period T (s), speed v (m s⁻¹).

Doubling amplitude ⇒ ×4 intensity; inverse-square with distance from a point source.

Reflection: i = r (from the normal). Refraction: bends TOWARD the normal entering a slower/denser medium; $n_1\sin\theta_1=n_2\sin\theta_2$.

Fringe spacing; $d$ = slit separation, $D$ = distance to screen.

$\lambda$: m · $f$: Hz · $T$: s · $v$: m s⁻¹ · $\omega$: rad s⁻¹ · $x, x_0$: m. Angles in equations: radians.

Mixing s–t with v–t graphs; using f in place of ω (ω = 2πf); degrees vs radians in SHM.

Two identical waves travelling opposite ways superpose: fixed nodes (no motion) and antinodes (max motion).

Odd harmonics only ($n = 1, 3, 5$).

Driving a system at its natural frequency → large amplitude (e.g. bridges, instruments).

Source approaching (−) → higher pitch; receding (+) → lower pitch.

Waves bend around gaps; overlapping waves add (constructive) or cancel (destructive).

Constructive: path difference = $n\lambda$. Destructive: $(n+\tfrac12)\lambda$.

Standing wave: adjacent nodes are $\lambda/2$ apart; antinode↔node is $\lambda/4$.

All harmonics, like a string.

Approaching source ⇒ $v-v_s$ (smaller denominator ⇒ HIGHER f). Receding ⇒ $v+v_s$ (lower f).

$f$: Hz · $v$: m s⁻¹ · $L$: m · $\lambda$: m. Speed of sound ≈ 340 m s⁻¹ in air.

Using 4L for a string (it's 2L); forgetting closed pipes only have ODD harmonics; wrong Doppler sign.