Joule Thief 101

[sm0ky2]

before I get into this, I will state some basic assumptions of the conditions involved.
These assumptions are to give quantities to the unknown factors necessary for such discussion to take place.

We will first assume that our wine glass is void of all defects, bubbles, cracks, stress-lines, and other such imperfections in the crystals

and since either two of the common methods of calculation are dependent upon temperature and other such factors,
(Young's Modulus or Shear Modulus)
We will further assume that these calculations take place at Sea Level, at SI "standard" temperature, pressure, humidity, etc.
We will also assume there is "standard" ratio of the components of the "air", such that the mathematical constants applied thereto,
   do not change throughout the mathematical analysis of the glass' resonance.

I will use Young's Modulus, as it pertains, with respect to glass-ceramics, directly to the velocity and propagation of the wave function.
This is derived using the Bulk Modulus K, and by a proportional constant of nature, both Shear Modulus and Poison's Ratio are defined.

Young's Modulus (defined by a capital "E", not to be confused with Energy) is therefore modified as:
E = pv^2
p is the density of the glass, and v is the longitudinal velocity of the pulse, or wavefront.

as you can see here, we must hold temperature constant, or we change the value of the modulus.
like sticking a tuning fork in the oven 


To further simplify the discussion, it will be assumed that the particular wine glass is of known composition.
let us assume this particular wine glass to be composed of a silicate
with a Young's modulus of 75

We will assume the speed of sound in air to be 343 Meters per Second

We will also assume that the wine glass is (mostly) cylindrical, and without odd curvatures.

[Note: there may be other obvious assumptions I may have forgotten,]
[ so the above list may be added to over the next short time]
[ while I attempt to fulfill what has been requested of me.]

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Now, what represents the resonant standing wave inside an (empty) glass, or glass filled with only air:
is considered in two parts.

There is the resonance of the cavity
and the shift in frequency caused by the elasticity of the glass material.

I will deal with the easy part first, the other half would probably take me most of a day to put into words.
The above Young's Modulus equation is already crunching half a page of math into a single line.
Do it again for the resonant cavity, and forgive me for needing a little time to plug both of them together.
it has been the better part of 15yrs since I've dealt with this particular issue.
Such is generally only required in theory, not in practice....
better yet, I have already done way more than necessary I think.
So let me just set this mess on my desk for now, I think you can see where it is leading.
I am not prepared at this moment to fully describe the wave interactions between the soundwave
and the vibrational wave through the glass material
in a coherent mathematical equation that represents both features.
this would be a lot easier if it were a flat, thin rectangle of glass.
Not a round goblet shape, its a mathematical blunder taking the tensor forces over a curvature.
(I think you have gotten the best of my patience on this one!! grr)

But what I will do instead is give you a footing by which you can change your own diaper.
(sorry, my babies are grown, I don't do that anymore)

So,. let us begin:

the frequency of the resonant cavity, formed by the dimensions of the wine glass is defined as:

f = v / 4(h + 0.4d)

where h is the height of the glass from the inside bottom to the rim
d is the diameter
v is the speed of sound

coincidentally:

v = f * wavelength
wavelength = 4(h + 0.4d)
v= f(4(h +0.4d))
and so forth and so on...

If the f represented by the resonant cavity were labeled as F1
the actual frequency resonating from the glass labeled as F2
then,

F1 - F2 = the shift in frequency caused by the glass material, as defined by Young's Modulus.

What you will find with your microphone or other testing apparatus, is both F2 resonating from the glass material
as well as F1 resonating inside the glass (with traces of F2 observable at certain locations therein)
as well as other (lower intensity) odd number harmonics.
these are defined as:


f = N(v) / 4(h + 0.4d)
  where N is an odd number.

Why an odd number?
  Because, much like our Joule Thief, the standing wave in the wineglass is a Half-Wave.
therefore, only the odd harmonics are not destroyed.

go ahead and test for these harmonic frequencies with your wine glass microphones.

If you find yourself unable to grasp these simple concepts,
you cannot understand what resonance "is".
everything that resonates, does so according to simple natural laws.

distances, velocities, intervals of time, rates of propagation
the things that define frequency

electricity and magnetism do not get a free pass on this one.
it is all the same

[sm0ky2]

four sentences.....

hmm.,..  I guess I fail your test then.

I require much more than that.

[MileHigh]

So you are talking about the resonance of the air cavity inside the wine glass.

I asked you about the resonance of the wine glass itself.  Is there a comprehension issue?

Now that you understand that I am asking you about the resonance of the wine glass itself (like if you were to flick your finger against the rim) please give clear and succinct answers to my questions:

How does a wine glass resonate, what is the mechanism?
How is the resonant frequency of a wine glass determined?

[sm0ky2]

So you are talking about the resonance of the air cavity inside the wine glass.

I asked you about the resonance of the wine glass itself.  Is there a comprehension issue?

Now that you understand that I am asking you about the resonance of the wine glass itself (like if you were to flick your finger against the rim) please give clear and succinct answers to my questions:

How does a wine glass resonate, what is the mechanism?
How is the resonant frequency of a wine glass determined?

your inability to comprehend overwhelms me.....

the resonance of the glass itself, is a function of BOTH the resonance of the cavity formed by the SHAPE and DIMENSIONS of the WINE GLASS and the materials constant caused by the change in frequency through the glass itself.

if you flick a flat piece of glass - then you are dealing with (mostly) the resonance of the glass itself.
the physical dimensions used in this part of the equation are the length and width and thickness of the flat piece.
also it must be known if you are flicking it on its' wide flat surface or on one of its' edges.

  this is much different than a "wine glass" resonance. as I just explained above.
take 3 different size wine glasses, from the same set.
same glass material, etc.
put them on your table, and flick each one.

Now, you can hear how their physical dimensions change the frequency.

I have to go wash my hands now,. I think I got some poopie on them..
can someone please throw his dirty diaper away for me...

[MileHigh]

your inability to comprehend overwhelms me.....

the resonance of the glass itself, is a function of BOTH the resonance of the cavity formed by the SHAPE and DIMENSIONS of the WINE GLASS and the materials constant caused by the change in frequency through the glass itself.

if you flick a flat piece of glass - then you are dealing with (mostly) the resonance of the glass itself.
the physical dimensions used in this part of the equation are the length and width and thickness of the flat piece.
also it must be known if you are flicking it on its' wide flat surface or on one of its' edges.

  this is much different than a "wine glass" resonance. as I just explained above.
take 3 different size wine glasses, from the same set.
same glass material, etc.
put them on your table, and flick each one.

Now, you can hear how their physical dimensions change the frequency.

I have to go wash my hands now,. I think I got some poopie on them..
can someone please throw his dirty diaper away for me...

You dare talk about comprehension issues.  Total fail.  You were asked to give a simple answer and the mass of the resonating glass is much much larger than the air in the cavity and around the glass so it can be ignored.  The resonant frequency of the wine glass has essentially nothing to do with the air in the cavity of the glass.  Plus I asked for a simple explanation.  You are supposed to be explaining what resonance in a wine glass is, not having a technical wanking session to impress a bunch of unknown posters.

Your previous long posting is an incoherent technical word salad.  So I am firmly putting you in the poseur category.  You clearly can't express something simple in simple terms.  For all I know you did a Google frenzy.

consider the difference between the speed of sound in air, vs the speed of sound in a vacuum.

Speed of sound in a vacuum?  You must have tripped over your keyboard in a chaotic Google frenzy.

Take your colourful metaphors and wipe your face with them.