I am back in business as you can see my
hair has returned.
I can talk. I haven't needed to shave this
side of my face since September but I'm
doing okay with most of the... most of the
things, a little bit more regimented
kind of life.
The problem is that people are going to
be moving in upstairs and I may have to
change the - where I live. That would cause
a big disruption. And in the meantime, I
have been having some difficulty getting
the Sound In Air, the animations for
this to give an improvement on the old
animation. So i'll give you what I've
got and we'll see where we can go from there.
With the guitar, the complex vibration
patterns of the top and back plates move
air in and out of the sound hole.
Something like this. And now my thinking
is that for chords and multiple strings
the motion would be more complex, maybe
like this. And another idea is that the
spherical expansion of the sound wave
starts right here at the sound hole.
Demonstrated like this. The motion of
sound wave particles can't be observed in
detail.
They're too small. They're too fast. And
there are far too many of them. Zooming in
several times on the spherical sound wave
helps to give some idea of their very
microscopic nature.
Here's a visual model I created
I got permission from mega-nerd for this
one. It shows the random kinetic motion
organized into sound waves.
This one from Muehleisen models the start
of the wave as the cyclical motion of a
piston. It's a fairly common image for
the air particle motion. And for the
guitar it serves as an introductory and
very simplified model of the Helmholtz
resonation at the sound hole. And this
animation clearly shows how traveling
waves form standing wave patterns such
as those inside an acoustic guitar body
or those reverberating in a concert hall.
Now here is my main problem. I have to
provide a convincing visual model for a 12
year old guitarist which does not
require high school or college math. And
to do that I have tied two sets of Fourier
circles together and I now need to
demonstrate that it models the sound of a
chord as multiple strings played at the
same time. Now here is the simple harmonic
motion we've been using up to now. Here's
the complex Fourier motion of a single
string. And here is the motion for two
strings. Treating each of these
individually. Here is the vertical simple
harmonic motion. Turned to the horizontal
it represents the additional directional
motion a simple harmonic sound wave
imposes on to the random kinetic motion
of the air particles.
And here is the complex Fourier model for
the sound wave of the single string.
And finally, the average motion of an ideal
molecule of an ideal gas when the
octave is sounded on two guitar strings at the
same time.
Now the two sets of Fourier circles are
separated out
and their waves are added together to
reproduce the original curve. Positive
added to positive. Positives and negatives
added here.
And finally two negatives create larger
negative value. And the original curve is
reproduced. And this is all just a
simplified model. Next the two connected
circles are put on their side and the
horizontal motion drives the piston
image to generate the complex motion of
a sound wave produced by a two-string
octave. Down below the logarithmic
placement values of the octave are shown
on the basilar membrane.
And just to be clear, a melodic octave
interval sounds when you play the
fundamental first then double the
original frequency. A harmonic interval
when both frequencies are played at the
same time on two or more strings. The
appearance can change but the relative
proportions do not.
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