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.

## Posts Tagged 'Wave Motion'

### Waves Packed in Envelopes

Published April 26, 2018 Occasional Leave a CommentTags: Fluid Dynamics, Geophysics, Wave Motion

### Wavelets: Mathematical Microscopes

Published May 25, 2017 Occasional Leave a CommentTags: Applied Maths, Wave Motion

In the last post, we saw how Yves Meyer won the Abel Prize for his work with wavelets. Wavelets make it easy to analyse, compress and transmit information of all sorts, to eliminate noise and to perform numerical calculations. Let us take a look at how they came to be invented.

### Yves Meyer wins 2017 Abel Prize

Published May 18, 2017 Irish Times Leave a CommentTags: Applied Maths, Wave Motion

On 23 May King Harald V of Norway will present the Abel Prize to French mathematician Yves Meyer. Each year, the prize is awarded to a laureate for “outstanding work in the field of mathematics”. Comparable to a Nobel Prize, the award is named after the exceptional Norwegian, Niels Henrik Abel who, in a short life from 1802 to 1829, made dramatic advances in mathematics. Meyer was chosen for his development of the mathematical theory of *wavelets*. [See TM115 or search for “thatsmaths” at irishtimes.com].

### Modelling Rogue Waves

Published May 5, 2016 Irish Times Leave a CommentTags: Applied Maths, Fluid Dynamics, Wave Motion

There are many eyewitness accounts by mariners of gigantic waves – almost vertical walls of water towering over ocean-going ships – that appear from nowhere and do great damage, sometimes destroying large vessels completely. Oceanographers, who have had no way of explaining these ‘rogue waves’, have in the past been dismissive of these reports [TM090, or search for “thatsmaths” at irishtimes.com].

### For Good Comms, Leaky Cables are Best

Published April 16, 2015 Irish Times Leave a CommentTags: Applied Maths, History, Wave Motion

A counter-intuitive result of Oliver Heaviside showed how telegraph cables should be designed [see this week’s *That’s Maths* column (TM066) or search for “thatsmaths” at irishtimes.com].

### How Big was the Bomb?

Published September 18, 2014 Irish Times 1 CommentTags: Applied Maths, Fluid Dynamics, Physics, Wave Motion

By a brilliant application of dimensional analysis, G.I.Taylor estimated the explosive energy of the first atomic blast, the Trinity Test (see this week’s *That’s Maths* column in *The Irish Times, *TM053, or search for “thatsmaths” at irishtimes.com).

### The Biggest Harp in Ireland

Published September 4, 2014 Irish Times Leave a CommentTags: Geometry, Pythagoras, Wave Motion

This week’s *That’s Maths* column in *The Irish Times* (TM052, or search for “thatsmaths” at irishtimes.com) is about “Samuel Beckett Playing Bridge in Dublin”.