Wave Phenomena Overview

Jul 6, 2025

Overview

This lecture covers wave superposition, stationary waves, diffraction, interference, and diffraction gratings, detailing concepts, equations, and key experimental applications for each.

Superposition of Waves

  • Superposition is when wave displacements combine at a point to produce a resultant displacement.
  • Constructive superposition happens when waves are in phase (phase difference of 0, 2π, 4π...), resulting in maximum amplitude.
  • Destructive superposition occurs when waves are in antiphase (phase difference π, 3π, 5π...), resulting in minimum or zero amplitude.

Stationary (Standing) Waves

  • Stationary waves are formed by the superposition of two identical waves traveling in opposite directions.
  • Nodes occur at points of destructive interference (zero amplitude); antinodes at constructive interference (maximum amplitude).
  • On a string of length L: fundamental wavelength λ = 2L, first harmonic f = v/2L.
  • For higher harmonics: nth harmonic wavelength λ = 2L/n, frequency f_n = n·(v/2L).
  • In pipes: closed-end pipes have fundamental λ = 4L, f = v/4L; open-end pipes have fundamental λ = 2L, f = v/2L.

Diffraction

  • Diffraction is the spreading of waves when they pass through a gap or around an obstacle.
  • Maximum diffraction occurs when gap/obstacle size ≈ wavelength.
  • For light, significant diffraction at slits < 0.1 mm; longer wavelengths diffract more than shorter ones.

Interference of Waves

  • Interference is the pattern from two coherent waves overlapping, forming nodes (destructive) and antinodes (constructive).
  • Coherence requires constant phase difference and same frequency/wavelength.
  • Path difference for nodes: (n+½)λ; for antinodes: nλ.
  • In Young's double slit: fringe spacing x = λD/a (λ=wavelength, D=distance to screen, a=slit separation).

Diffraction Gratings

  • A diffraction grating contains many closely spaced slits producing sharp, bright maxima.
  • Maxima occur at angles θ where d·sinθ = nλ (d=grating spacing, n=order).
  • Number of observable maxima depends on grating lines per mm and wavelength.
  • Grating spacing d = 1/number of lines per unit length.

Key Terms & Definitions

  • Superposition — Combination of displacements from two or more waves at a point.
  • Node — Point on a stationary wave with zero amplitude.
  • Antinode — Point on a stationary wave with maximum amplitude.
  • Coherent Waves — Waves with constant phase difference and same frequency.
  • Diffraction — Spreading of waves past obstacles or through gaps.
  • Diffraction Grating — Optical device with many slits for creating interference patterns.

Action Items / Next Steps

  • Practice calculating fundamental and harmonic frequencies for strings and air columns.
  • Solve problems using double slit and diffraction grating equations.
  • Review definitions and distinguish between constructive and destructive interference.