Waves Packed in Envelopes

In this article we take a look at group velocity and at the extraction of the envelope of a wave packet using the ideas of the Hilbert transform. Interference of two waves A single sinusoidal wave is infinite in extent and periodic in space and time. When waves interact, the dynamics are more interesting. The … Continue reading Waves Packed in Envelopes →

Geodesics on the Spheroidal Earth-II

Geodesy is the study of the shape and size of the Earth, and of variations in its gravitational field. The Earth was originally believed to be flat, but many clues, such as the manner in which ships appear and disappear at the horizon, and the changed perspective from an elevated vantage point, as well as … Continue reading Geodesics on the Spheroidal Earth-II →

Geodesics on the Spheroidal Earth – I

Both Quito in Ecuador and Singapore are on the Equator. One can fly due eastward from Singapore and reach Quito in due course. However, this is not the shortest route. The equatorial trans-Pacific route from Singapore to Quito is not a geodesic on Earth! Why not? The General Equation for Geodesics Open a typical text … Continue reading Geodesics on the Spheroidal Earth – I →

Fourier’s Wonderful Idea – II

Solving PDEs by a Roundabout Route Joseph Fourier, born just 250 years ago, introduced a wonderful idea that revolutionized science and mathematics: any function or signal can be broken down into simple periodic sine-waves. Radio waves, micro-waves, infra-red radiation, visible light, ultraviolet light, X-rays and gamma rays are all forms of electromagnetic radiation, differing only … Continue reading Fourier’s Wonderful Idea – II →