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Travelling Waves

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is...

Modes of Standing Waves: II

Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end....

Modes of Standing Waves - I

Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...

Propagation of Waves

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...

Reflection of Waves

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...

Wave Parameters

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...

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Related Experiment Video

Updated: Sep 16, 2025

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

Rigidity of Stratospheric Travelling Waves.

Adrian Constantin¹, Hua Shao^1,2, Hao Zhu^1,3

¹Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

Communications in Mathematical Physics

|July 7, 2025

Summary

This study reveals rigidity properties of atmospheric waves on outer planets. Wave speeds are constrained by zonal flow velocities, with potential symmetry breaking due to planetary rotation.

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Last Updated: Sep 16, 2025

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

Magnetically Induced Rotating Rayleigh-Taylor Instability

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Thermocapillary Convection Space Experiment on the SJ-10 Recoverable Satellite

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Published on: March 11, 2020

Area of Science:

Planetary Science
Atmospheric Dynamics
Fluid Mechanics

Background:

Zonally propagating waves are observed in the stratosphere of outer planets.
These waves are perturbations of background zonally sheared flows.

Purpose of the Study:

To investigate rigidity results for travelling waves in the stratosphere of outer planets.
To analyze wave speed constraints in different planetary atmospheric models.

Main Methods:

Utilizing f-plane and beta-plane approximations for Jupiter and Saturn.
Employing spherical coordinates for the broad zonal jets of Uranus and Neptune.

Main Results:

Wave speeds are confined within the range of zonal flow velocities in the f-plane approximation.
In the beta-plane setting, wave speeds are bounded by the maximum zonal velocity and can be slightly less than the minimum.
A rigidity result for travelling waves near zonal flow is established using spherical coordinates.

Conclusions:

The study provides constraints on the speeds of atmospheric travelling waves on outer planets.
Rotation can induce symmetry breaking in these zonally travelling waves, even if they are not zonally symmetric.