hammer weight penny cube

[Helmut Wabnig]

             excuse!
   excuse!    (bow)      excuse!
             excuse!

(For putting non- piano related stuff on the list.)
(Make sure the word *piano* occurs from time to time.)
(Twice, so far.)


Problem:

>one penny is five times as hot as the other when I >begin to monitor their
temperatures. Both of these >pennies are in a bath which is constantly taking
>away their heat energy in a way which does not change >the temperature of
the bath. I monitor the >temperatures until equilibrium occurs between the
>penny and the bath.  Which penny will arrive at the >equilibrium
temperature first?

answer:
nope.niemals.never!

>Next question: I have two ice cubes, one is removed >from a freezer with a
temperature of 0 c, the other >is removed at the same time from a freezer
with a
>temperature of  -15 c.  These cubes appear to be >identical in shape and
they are the same mass.  Which >ice cube will melt completely first?
>Michael.

answer: the -15 c cube.
        I will put it into my whisky and freeze
        the other down further.

                      Piano.
(third time)


We are generally not aware of the technical
functioning of things around us. Without Fourier
we would not be able to send us news on the
internet. Or to hear music. Or to see the text
on the screen. Fourier is *real life*, it's
our dayly bread.

The ear is a Fourier Analyzer. It takes apart
the components of a sound into its single
frequencies and sends them, with amplitude
and phase, to this jelly in my head.

Forget ray optics, talk real stuff:
The eye camera is a Fourier Synthesizer.
Any object, eg. a black/white transition from
a letter on my screen, sends its light rays
into all directions, separated into fundamentals
and harmonics, called *space frequencies*, because
they go off in slighty different angles.
The camera has to combine the space frequencies
back with correct amplitude and phase to produce
an image.

Sound: A flute is an almost pure sinus wave.
The Hammond organ sound is a triangle.
A violin is a unsymmetric triangle, like
a sawtooth. Clearly, the overtones, the harmonics,
are audible. They shape the envelope of the sound
wave. The more corners, the more edges, the wave
has, the more overtones ar needed to fill the shape.

This is quite easy, because we can *hear* it.
But what happens if there is a single event,
like a hammer striking or somebody knocking
on the door. The sound pulse will have a certain
shape if we make a drawing of the sound intensity.
It's not rounded, it is somewhat rough. That's
where the overtones sit. This applies to continuous
tones and to single events like the crack we hear
when we close the piano cover.
(the fourth)

Michael, I did not write this for you. It is just
an example how I would explain Fourier to somebody.

I live in Austria.
Yours
Helmut Wabnig
wabi@net4you.co.at