Waves, Sound, Light, and Optics
Core concepts
Wave properties: wavelength, frequency, amplitude, speed (v = fλ), superposition, interference, standing waves, resonance, and the Doppler effect. Sound: intensity and decibels, harmonics of strings and open/closed pipes, beats. Light: reflection, refraction and Snell's law, total internal reflection, lenses and mirrors (thin-lens equation, magnification), diffraction and double-slit interference, and polarization.
Traps to watch
- Frequency is set by the source and does not change when a wave enters a new medium; speed and wavelength change.
- Pipe boundary conditions: an open end is a pressure node/displacement antinode; a closed end is the reverse. Open-open pipes support all harmonics; closed-open pipes support only odd harmonics.
- Sign conventions in optics: real images have positive image distance for lenses; virtual images are negative. Keep one convention throughout.
- Snell's law bends toward the normal entering a denser medium (higher index), away when leaving.
- Total internal reflection requires going from higher to lower index and exceeding the critical angle.
- Doppler: approaching source raises observed frequency; the shift depends on relative motion.
Rule of thumb
For standing-wave problems, sketch nodes and antinodes first, then set the length equal to the appropriate fraction of a wavelength (½λ for a fundamental string or open pipe, ¼λ for a closed-open pipe).
Worked example
A string fixed at both ends is 1.5 m long and its fundamental frequency is 100 Hz. Wave speed? Fundamental: L = λ/2, so λ = 3.0 m. v = fλ = 100 × 3.0 = 300 m/s.