Waves and Light: Stationary Waves

Waves and Light: Stationary Waves

Understanding Stationary Waves

  • Stationary waves, also known as standing waves, are the result of two waves of the same frequency, moving in opposite directions, superposing on each other.
  • These are the waves where certain points, known as nodes, appear to remain at rest, while others, called antinodes, undergo maximum displacement.
  • Stationary waves do not exhibit a net transfer of energy, unlike progressive waves.
  • Nodes are points of destructive interference where displacement is always zero.
  • Antinodes are points of constructive interference where displacement is maximum.

Node and Antinode Properties

  • Distances between consecutive nodes or antinodes represent half of a wavelength.
  • The distance between a node and an adjacent antinode is a quarter of a wavelength.
  • The distance between consecutive nodes or antinodes can also be considered as one period of the waveform.

Generation of Stationary Waves

  • Stationary waves are usually formed when waves are confined within a certain space, such as sound waves in an organ pipe or electromagnetic waves in a transmission line.
  • They can also be generated by the superposition of two identical waves travelling in opposite directions.
  • The two waves may be produced by reflection of a wave from a boundary or by simultaneously producing two waves from different sources.

Stationary Waves and Resonance

  • Resonance occurs when a system is driven at its natural frequency and the amplitude of oscillation increases.
  • It is a key concept in the generation of stationary waves.
  • It is due to resonance that a singer can break a glass with their voice, or that a radio can tune into a particular station.
  • The formation of stationary waves on a stringed musical instrument provides a visual demonstration of resonance.

Harmonics in Stationary Waves

  • Harmonics are whole number multiples of the fundamental frequency of a wave.
  • In the context of stationary waves, they give rise to different modes of vibration.
  • The first mode, or first harmonic, is called the fundamental or resonant frequency.
  • The second mode, or second harmonic, has twice the frequency of the fundamental.
  • Each mode corresponds to a specific pattern of nodes and antinodes.