← Theme C · Wave Behaviour
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Theme C · Wave Behaviour

Chapter 1 · Wave foundations

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Wave equation
v=fλv = f\lambda
Frequency / period
f=1Tf = \frac{1}{T}
Wave types
Transverse (oscillation ⟂ travel, e.g. light); longitudinal (∥ travel, e.g. sound).
SHM defining condition
a=−ω2xa = -\omega^2 x
ω=2πf=2π/T\omega = 2\pi f = 2\pi/T. Force toward equilibrium.
SHM position
x=x0cos⁡(ωt)x = x_0\cos(\omega t)
Max speed at equilibrium; max accel at extremes.
Pendulum period
T=2πLgT = 2\pi\sqrt{\tfrac{L}{g}}
Independent of mass and (small) amplitude.
Mass-spring period
T=2πmkT = 2\pi\sqrt{\tfrac{m}{k}}
SHM energy
E=12mω2x02E = \tfrac{1}{2}m\omega^2 x_0^2
Continuously swaps between KE and PE.
SHM velocity
v=±ωx02−x2v = \pm\omega\sqrt{x_0^2 - x^2}
Max v=ωx0v=\omega x_0 at x=0x=0; v=0v=0 at x=±x0x=\pm x_0.
Wave quantities
Amplitude (max displacement), wavelength λ (m), frequency f (Hz), period T (s), speed v (m s⁻¹).
Intensity
I∝A2,I∝1r2I \propto A^2,\quad I \propto \tfrac{1}{r^2}
Doubling amplitude ⇒ ×4 intensity; inverse-square with distance from a point source.
Reflection / refraction
Reflection: i = r (from the normal). Refraction: bends TOWARD the normal entering a slower/denser medium; n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1=n_2\sin\theta_2.
Double-slit fringes
Δy=λDd\Delta y = \frac{\lambda D}{d}
Fringe spacing; dd = slit separation, DD = distance to screen.
Key SI units
λ\lambda: m · ff: Hz · TT: s · vv: m s⁻¹ · ω\omega: rad s⁻¹ · x,x0x, x_0: m. Angles in equations: radians.
Common traps
Mixing s–t with v–t graphs; using f in place of ω (ω = 2πf); degrees vs radians in SHM.