Posts Tagged 'Wave Motion'

Hokusai’s Great Wave and Roguish Behaviour

Hokusai’s woodcut “The Great Wave off Kanagawa”.

“The Great Wave off Kanagawa”, one of the most iconic works of Japanese art, shows a huge breaking wave with foam thrusting forward at its crest, towering over three fishing boats, with Mt Fuji in the background [TM158 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Hokusai’s Great Wave and Roguish Behaviour’

Don’t be Phased by Waveform Distortions

For many years there has been an ongoing debate about the importance of phase changes in music. Some people claim that we cannot hear the effects of phase errors, others claim that we can. Who is right? The figure below shows a waveform of a perfect fifth, with components in the ratio {3 : 2} for various values of the phase-shift. Despite the different appearances, all sound pretty much the same.

Continue reading ‘Don’t be Phased by Waveform Distortions’

Gravitational Waves & Ringing Teacups

Newton’s law of gravitation describes how two celestial bodies orbit one another, each tracing out an elliptical path. But this is imprecise: the theory of general relativity shows that two such bodies radiate energy away in the form of gravitational waves (GWs), and spiral inwards until they eventually collide.

GW-Warning-Sign

Warning sign, described by Thomas Moore as a “geeky insider GR joke” [image from Moore, 2013].

Continue reading ‘Gravitational Waves & Ringing Teacups’

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.

Hovmoeller-Arrows

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Wavelets: Mathematical Microscopes

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.

Wavelets-CWT-Example-BOTTOM

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Yves Meyer wins 2017 Abel Prize

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].

Yves-Meyer-Wide

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Modelling Rogue Waves

BBC-FreakWave

Rogue wave [image from BBC Horizons, 2002]

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].

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For Good Comms, Leaky Cables are Best

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].

Atlantic-Telegraph-Map Continue reading ‘For Good Comms, Leaky Cables are Best’

How Big was the Bomb?

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).

US army soldiers watching the first test of an atomic weapon, the Trinity Test.

US army soldiers watching the first test of an atomic weapon, the Trinity Test.

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The Biggest Harp in Ireland

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”.

Image from TIger Dublin Fringe Festival website: http://fringefest.com/programme/harp-a-river-cantata Photo Credit: Ciara Corrigan

Image from Tiger Dublin Fringe Festival website.
Photo Credit: Ciara Corrigan

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White Holes in the Kitchen Sink

A tidal bore is a wall of water about a metre high travelling rapidly upstream as the tide floods in. It occurs where the tidal range is large and the estuary is funnel-shaped (see previous post on this blog). The nearest river to Ireland where bores can be regularly seen is the Severn, where favourable conditions for these hydraulic jumps occur a few times each year.

But you do not have to leave home to observe hydraulic jumps. Continue reading ‘White Holes in the Kitchen Sink’

Interesting Bores

This week’s That’s Maths column in the Irish Times ( TM036 ) is about bores. But don’t be put off: they are very interesting.

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Ducks & Drakes & Kelvin Wakes

The theme of this week’s That’s Maths column in the Irish Times ( TM021 ) is Kelvin Wakes, the beautiful wave patterns generated as a duck or swan swims through calm, deep water or in the wake of a ship or boat.
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