Waves & Superposition
Wave properties, interference, diffraction and stationary waves
Progressive waves** transfer energy without transferring matter. **Transverse: oscillation perpendicular to direction (light, water). **Longitudinal:** oscillation parallel to direction (sound).
Wave equation: v = fλ (velocity = frequency × wavelength)
Electromagnetic spectrum (increasing frequency): Radio → Microwave → Infrared → Visible → UV → X-rays → Gamma. All travel at c = 3 × 10⁸ m/s in vacuum.
Superposition: When waves overlap, resultant displacement = sum of individual displacements.
Young's Double Slit: Light through two slits → interference pattern of bright and dark fringes. λ = ax/D (a = slit separation, x = fringe spacing, D = distance to screen). Proves wave nature of light.
Stationary (standing) waves: Formed when two progressive waves of same frequency travel in opposite directions. **Nodes** (zero amplitude) and **antinodes** (maximum amplitude). Examples: vibrating guitar string, organ pipes.
Key Points to Remember
- 1v = fλ (wave equation)
- 2Constructive: in phase; Destructive: antiphase
- 3Young's double slit proves wave nature of light
- 4Stationary waves have nodes and antinodes
Pakistan Example
FM Radio Waves Across Pakistan — From PTV to City FM
Pakistan's radio stations (FM 89, City FM 89) broadcast using electromagnetic waves in the FM band (88-108 MHz). Using v = fλ: at 89 MHz, wavelength = 3×10⁸/89×10⁶ ≈ 3.37m. Mountains in northern Pakistan cause diffraction of radio waves, which is why FM reception varies in valleys around Gilgit-Baltistan.