Stationary vs Travelling Waves: Difference and Comparison

Stationary waves are formed by the interference of two waves with the same frequency and amplitude traveling in opposite directions, resulting in nodes and antinodes that remain fixed in space. Conversely, traveling waves propagate through a medium, transferring energy from one point to another without interference, characterized by continuously changing crests and troughs as they move forward.

Key Takeaways

1. Stationary waves remain fixed, whereas traveling waves propagate through a medium.
2. Nodes and antinodes characterize stationary waves while traveling waves have peaks and troughs.
3. In stationary waves, energy remains confined to a specific location, but energy transfers from one point to another in traveling waves.

Stationary vs Travelling Waves

The movement of two waves in the opposite directions whose frequencies and amplitudes are the same form stationary waves. These waves do not transmit energy. The movement of waves from one point to the other is called a travelling wave. There are no nodes or antinodes in a travelling wave. These waves transmit energy.

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Comparison Table

Feature	Stationary Wave	Travelling Wave
Movement	Does not travel – particles vibrate around a fixed position	Travels through a medium – particles oscillate and transfer energy
Formation	Superposition of two identical travelling waves moving in opposite directions	Occurs when a travelling wave encounters a boundary (reflection) or travels through a medium with non-uniform properties
Energy Transfer	Does not transfer energy – energy oscillates at fixed points	Transfers energy along the direction of propagation
Nodes and Antinodes	Has points of zero displacement (nodes) and points of maximum displacement (antinodes)	Does not have nodes and antinodes
Examples	Vibrating guitar string, sound waves in a pipe closed at one end	Water waves in a lake, sound waves travelling through air

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What are Stationary Waves?

Formation and Characteristics:

When two waves of identical frequency and amplitude traveling in opposite directions meet, they superimpose upon each other. At certain points along the medium, the two waves reinforce each other, creating regions of maximum constructive interference known as antinodes. Conversely, at other points, the waves cancel each other out, resulting in regions of minimum or zero amplitude called nodes.

Mathematical Representation:

Stationary waves can be mathematically described using the principle of superposition, where the displacement of the medium at any point and time is the sum of the individual wave displacements. This leads to the formation of standing wave equations, such as those governing vibrations in strings, membranes, and other oscillating systems. The equations involve sine or cosine functions, with coefficients determined by the boundary conditions of the system.

Applications and Examples:

Stationary waves have numerous practical applications across various fields. In acoustics, they are responsible for the resonance phenomena observed in musical instruments, where the standing waves produced determine the instrument’s timbre and pitch. In optics, interference patterns generated by stationary waves are utilized in devices like interferometers for precise measurements. Moreover, in quantum mechanics, stationary waves play a central role in the wave-particle duality concept, describing the behavior of particles like electrons within atomic orbitals.

 

What are Travelling Waves?

Characteristics of Travelling Waves

1. Propagation: Travelling waves move through a medium by causing particles in the medium to oscillate back and forth as the wave passes. The motion of these particles is parallel to the direction of wave propagation.
2. Continuous Transmission of Energy: Travelling waves transport energy from one location to another without any net displacement of the medium. As the wave moves, energy is transferred from one particle to the next, allowing the wave to propagate over distance.
3. Wavefronts: Travelling waves exhibit wavefronts, which are surfaces of constant phase that propagate through the medium. These wavefronts represent the leading edge of the disturbance as it moves through space.
4. Amplitude and Frequency: Travelling waves possess characteristics such as amplitude (the maximum displacement of particles from their equilibrium positions) and frequency (the number of oscillations per unit time). These properties determine the intensity and pitch of the wave, respectively.
5. Types of Travelling Waves: Travelling waves can be classified into two main types: transverse waves and longitudinal waves. In transverse waves, particles of the medium oscillate perpendicular to the direction of wave propagation, while in longitudinal waves, particles oscillate parallel to the direction of propagation.
6. Examples: Examples of travelling waves include electromagnetic waves (such as light and radio waves), water waves, sound waves, seismic waves, and waves on strings or springs.

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Main Differences Between Stationary Waves and Travelling Waves

1. Propagation:
   • Stationary waves do not propagate through a medium; instead, they result from the interference of two waves traveling in opposite directions.
   • Travelling waves propagate through a medium, transferring energy from one point to another without interference.
2. Particle Motion:
   • In stationary waves, particles of the medium oscillate in a fixed pattern, with nodes and antinodes remaining stationary.
   • In travelling waves, particles oscillate back and forth in the direction of wave propagation, transferring energy as the wave moves.
3. Formation:
   • Stationary waves are formed by the superposition of two waves with the same frequency and amplitude traveling in opposite directions.
   • Travelling waves are generated by a disturbance that propagates through a medium, causing particles to oscillate as the wave moves forward.
4. Energy Transfer:
   • Stationary waves do not transport energy; instead, they represent a redistribution of energy within the medium.
   • Travelling waves continuously transmit energy from one point to another as they propagate through the medium.
5. Characteristic Patterns:
   • Stationary waves exhibit nodes (points of no displacement) and antinodes (points of maximum displacement) that remain fixed in space.
   • Travelling waves feature continuously changing crests and troughs as they move forward, with no fixed pattern of nodes and antinodes.

References

1. https://yakari.polytechnique.fr/Django-pub/documents/matteo2004rp-1pp.pdf
2. https://arxiv.org/pdf/0901.1026
3. https://arxiv.org/pdf/patt-sol/9701007