Let's see: (1) Make some progress learning
to play violin. I did. E.g., I made it through
not all of but over half of the Bach "Chaconne",
regarded as great music and challenging by nearly all
violinists. (2) Learn some Fourier theory,
pure and applied. I did that, for work with the
fast Fourier transform on sonar problems for the
US Navy and other problems. Also I took some
grad math courses that covered Fourier theory
carefully, right, based on measure theory.

I wrote the material here quickly, and better
explanations could be possible:

For a
violin, when tuning, and really also for much of the
playing, to get the frequency ratios correct,
which is most of what playing a violin with
good innotation is about, use overtones, that is,
the terms of a Fourier series expansion of
a periodic (not necessarily sine or cosine)
signal. In particular, when bow two strings
together, i.e., at the same time,
say, the A and the E, with the A
already at 440 Hz from, say, a tuning fork,
and slowly adjust the frequency of the E string,
then are, in part, adding
an overtone of the A string with
the signal of the E string and, really,
as adjust the E string,
sweeping in frequency, as in the terms
of a Fourier series, a sine wave overtone
of the E string the terms of the
Fourier series of the A string. When
that overtone of the E string gets close
to the frequency of a term in the Fourier
series of the A string, get beats,
that is, an amplitude modulation which
violin students learn to listen for and hear.
When the beats go from a few a second down to
less than one a second and basically go away,
then have found the frequency of the desired
overtone of the Fourier series of the A string,
that is, have essentially part of the Fourier series of
the A string.

As do other cases of bowing two strings together,
get to find more overtones:
E.g., want to use
a finger of the left hand on the A string to
play B, C, C#, D and E. E.g., Beethoven's
9th Symphony has "Ode to Joy" and can
play that in A Major with C# C# D E E
D C#, .... Well, to get the B correct,
bow it with the E string and look for
a perfect 4th. For the C, look for a
perfect major third. For the C#, look
for a perfect minor third. For the D,
bow with the open D string an look
for an octave. For the E, bow with the
E string and look for unison.
In eadh case, as adjust finger on the
A string, will be doing a sweep
in frequency looking for a term in the
Fourier series of the other string.

For the bridge, treat it as a linear system.
Then given and input signal, to get the
output, take the Fourier transform of the
input, multiply it by the impulse response
of the bridge, and then take the inverse
transform. The impulse response is
what get when hit the bridge with an
impulse, that is, a signal with all
frequencies with equal power. If the
bridge has a resonant frequency
and the troops march with that frequency,
then the product of the two Fourier transforms and the inverse transform
will be large and the bridge might fail.
Fourier transforms win again.

My comments on Fourier theory are fine and
should be entertaining for the HN audience.

I wrote the remarks quickly and kept
the content intuitive. If I wrote it
all out in terms of measure theory,
then I'd be still more difficult to read.
That you found something objectionable
with what I wrote is absurd.

Your remarks are ignorant about Fourier
theory and/or just hostile to me.
A guess is that I wrote something you
didn't understand and, thus, you got
hostile. Such hostility is not appropriate
on HN.

Put the two together and the criticize what I
wrote about where essentially Fourier theory
pops up playing a violin. There's more, e.g.,
the image through a lens of a point source
and, then, much of antenna theory, right, also
for sonar, especially the phased array case.
And there's the issued of power spectral
estimation -- did quite a lot of that via
Blackman and Tukey.

Right, the Michelson-Morley interferometer,
like Young's double slit, is basically
antenna theory and, thus, also Fourier theory.
I omit the details of the math.

What I wrote was supposed to be fun reading.

There's nothing wrong with what I wrote.
Maybe you don't like it; and of course
it was not a full course in Fourier theory;
and I omitted the math; but for much of
a STEM technical audience it should have been
easy to read.

Your medical diagnosis is totally wacko
nonsense,
incompetent, irresponsible, erroneous,
inappropriate, insulting, and provocative.

Here's your logic: You know some sick people
who write. You observe that I write.
So, you conclude that I must be sick.
Erroneous. Nonsense.