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.