Materials (Unit 1) covers mechanical properties of solids — Hooke\'s law, stress-strain curves, Young\'s modulus. Waves (Units 2 and 5) covers wave behaviour — superposition, diffraction, interference, and standing waves.
Density ρ = m/V. Hooke\'s law: F = kx (up to the limit of proportionality). Spring constant k (N/m). Elastic: returns to original shape. Plastic: permanent deformation. Stress σ = F/A (Pa). Strain ε = ΔL/L (no units). Young\'s modulus E = σ/ε = (FL)/(AΔL) (Pa). Measured by stretching a wire: use Searle\'s apparatus or similar. Stress-strain graph: gradient in linear region = E. Area under curve = energy per unit volume. Ductile (e.g., copper): large plastic region. Brittle (e.g., glass): fractures with little plastic deformation.
Progressive wave: transfers energy without transferring matter. Transverse (EM, water) vs longitudinal (sound). v = fλ. Period T = 1/f. Phase difference: measured in degrees or radians. Superposition: when waves meet, displacements add. Constructive interference: in phase (path difference = nλ). Destructive: antiphase (path difference = (n+½)λ). Young\'s double slit: λ = ax/D (a = slit spacing, x = fringe spacing, D = distance to screen). Diffraction grating: nλ = d sinθ (d = slit spacing, n = order). Standing waves: formed when two waves of same frequency travel in opposite directions. Nodes (zero displacement), antinodes (maximum). For string fixed at both ends: L = nλ/2. Frequencies: harmonics f₁, 2f₁, 3f₁...
Progressive waves transfer energy from source to surroundings — every point oscillates with the same amplitude (but different phase). Standing (stationary) waves do NOT transfer energy — they\'re formed by superposition of two identical waves travelling in opposite directions. Key differences: (1) Energy: progressive → transfers energy; standing → stores energy (no net transfer). (2) Amplitude: progressive → same everywhere; standing → varies from zero (nodes) to maximum (antinodes). (3) Phase: progressive → adjacent points have different phases; standing → all points between two adjacent nodes oscillate in phase. (4) Wavelength: progressive → distance between consecutive identical points; standing → distance between alternate nodes = λ/2. Standing waves are seen on strings (instruments) and in pipes (organ pipes, wind instruments).
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