Archive for September 22, 2015

Hat and Beard

Posted in Jazz with tags , , , , on September 22, 2015 by telescoper

I haven’t posted much Jazz recently, and was reminded of this fact when I listened to the following track on my iPod yesterday while travelling back from Cardiff to Brighton.  Hat and Beard is an original composition by one of my favourite jazz artists, saxophonist Eric Dolphy and was written in honour of another of my favourite jazz artists, Thelonious Monk, who not only sported a splendid beard but also had a famously eccentric taste in headgear…

hat and beard

Anyway, Hat and Beard is taken from the pioneering free jazz album Out to Lunch. This album is without doubt one of the high points of 1960s avant-garde jazz, primarily because of Dolphy’s extraordinary playing (in this case on bass clarinet) but also because of the brilliance of the other musicians: Freddie Hubbard on trumpet; Bobby Hutcherson on vibes; Richard Davis on bass; and the superb Tony Williams on drums (who was only 18 when this track was recorded).


Amplitude & Energy in Electromagnetic Waves

Posted in Cute Problems, The Universe and Stuff with tags , , , on September 22, 2015 by telescoper

Here’s a little physics riddle. As you all know, electromagnetic radiation consists of oscillating electric and magnetic fields rather like this:

Figure10.1(Graphic stolen from here.) The polarization state of the wave is defined by the direction of the Electric field, in this case vertically upwards.

Now the energy carried by an electromagnetic wave of a given wavelength is proportional to the square of its amplitude, denoted in the Figure by A, so the energy is of the form kA2 in this case with k constant. Two separate electromagnetic waves with the same amplitude and wavelength would thus carry an energy = 2kA2.

But now consider what happens if you superpose two waves in phase, each having the same wavelength, polarization and amplitude to generate a single wave with amplitude 2A. The energy carried now is k(2A)2 = 4kA2, which is twice the value obtained for two separate waves.

Where does the extra energy come from?

Answers through the Comments Box please!