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https://youtu.be/noULaukM8SE?t=315
I don't understand the claim that we can't have a smooth transition
between a circular wave with three nodes to a circular wave with four
nodes.
https://www.desmos.com/calculator/uxq23q3nmb
On 26/07/2025 21:13, sobriquet wrote:
https://youtu.be/noULaukM8SE?t=315
I don't understand the claim that we can't have a smooth transition
between a circular wave with three nodes to a circular wave with four
nodes.
https://www.desmos.com/calculator/uxq23q3nmb
I haven't watched the video, anyway that is not the kind of
transform that is relevant.-a Rather:
Consider a real sine wave: changing the frequency needs changing
just one continuous (real) parameter.-a But fix periodic boundaries,
i.e. restrict to the interval -say- [0, T] with point T identified
with 0, and only consider the waves that are *periodic* over that
interval: now, to satisfy periodicity, the frequency cannot anymore
be varied continuously...
-Julio
Op 26/07/2025 om 22:53 schreef Julio Di Egidio:
On 26/07/2025 21:13, sobriquet wrote:
https://youtu.be/noULaukM8SE?t=315
I don't understand the claim that we can't have a smooth transition
between a circular wave with three nodes to a circular wave with four
nodes.
https://www.desmos.com/calculator/uxq23q3nmb
I haven't watched the video, anyway that is not the kind of
transform that is relevant.-a Rather:
Consider a real sine wave: changing the frequency needs changing
just one continuous (real) parameter.-a But fix periodic boundaries,
i.e. restrict to the interval -say- [0, T] with point T identified
with 0, and only consider the waves that are *periodic* over that
interval: now, to satisfy periodicity, the frequency cannot anymore
be varied continuously...
-Julio
Ah, I see.. thanks!
A physics question asked, and a physics question answered.-a On
sci.physics of all places.
Brings feelings of nostalgia.
sobriquet wrote:
Op 26/07/2025 om 22:53 schreef Julio Di Egidio:
On 26/07/2025 21:13, sobriquet wrote:
https://youtu.be/noULaukM8SE?t=315
I don't understand the claim that we can't have a smooth transition
between a circular wave with three nodes to a circular wave with
four nodes.
https://www.desmos.com/calculator/uxq23q3nmb
I haven't watched the video, anyway that is not the kind of
transform that is relevant.-a Rather:
Consider a real sine wave: changing the frequency needs changing
just one continuous (real) parameter.-a But fix periodic boundaries,
i.e. restrict to the interval -say- [0, T] with point T identified
with 0, and only consider the waves that are *periodic* over that
interval: now, to satisfy periodicity, the frequency cannot anymore
be varied continuously...
Ah, I see.. thanks!
A physics question asked, and a physics question answered.
Then, for a mathematics that does that, my guess is to
"normalize" the sum, otherwise the self-interference of
the periodic waves would simply diverge.-a So I end up
with something like this:
```
for 0 <= x < T,
-a F(x) = lim_{n->oo} [ Sum_{i=0}^n f(x + n*T) / (n+1) ]
```
On 28/07/2025 13:44, Julio Di Egidio wrote:
Then, for a mathematics that does that, my guess is to
"normalize" the sum, otherwise the self-interference of
the periodic waves would simply diverge.-a So I end up
with something like this:
```
for 0 <= x < T,
-a-a F(x) = lim_{n->oo} [ Sum_{i=0}^n f(x + n*T) / (n+1) ]
```
Sorry, should of course read ... f(x + i*T) / (i+1) ...
On 27/07/2025 23:10, William Hyde wrote:
sobriquet wrote:
Op 26/07/2025 om 22:53 schreef Julio Di Egidio:
On 26/07/2025 21:13, sobriquet wrote:
https://youtu.be/noULaukM8SE?t=315
I don't understand the claim that we can't have a smooth transition >>>>> between a circular wave with three nodes to a circular wave with
four nodes.
https://www.desmos.com/calculator/uxq23q3nmb
I haven't watched the video, anyway that is not the kind of
transform that is relevant.-a Rather:
Consider a real sine wave: changing the frequency needs changing
just one continuous (real) parameter.-a But fix periodic boundaries,
i.e. restrict to the interval -say- [0, T] with point T identified
with 0, and only consider the waves that are *periodic* over that
interval: now, to satisfy periodicity, the frequency cannot anymore
be varied continuously...
Ah, I see.. thanks!
A physics question asked, and a physics question answered.
We should then explain why and how only the periodic ones.
Here is my guesses, as I have never seen that made explicit:
The physics as far as I can guess it:
- The wave upon wrapping around interferes with itself;
- The interference is constructive if and only if the wave
is exactly periodic.
Then, for a mathematics that does that, my guess is to
"normalize" the sum, otherwise the self-interference of
the periodic waves would simply diverge.-a So I end up
with something like this:
```
for 0 <= x < T,
-a F(x) = lim_{n->oo} [ Sum_{i=0}^n f(x + n*T) / (n+1) ]
```
where, F(x) tends to f(x) for the periodic functions, and
F(x) tends to 0 otherwise.-a ---a But I'd have to double-check
and prove it...
Anyway, is that it?-a Otherwise why/how only the periodic ones?
-Julio
If we look at the way a string vibrates, for instance on a guitar,
we can imagine that same wave motion on a circle instead of a straight
line.
On 29/07/2025 04:46, sobriquet wrote:
If we look at the way a string vibrates, for instance on a guitar,
we can imagine that same wave motion on a circle instead of a straight
line.
No, that's a different setup where the curve is fixed at
the boundaries and not periodic, and gives standing waves.
There is indeed a lot of mathematics on various possible
"boundary conditions", but you were asking for a *physics*
setup and explanation underling *wave quantisation*...
-Julio
Op 29/07/2025 om 10:34 schreef Julio Di Egidio:
On 29/07/2025 04:46, sobriquet wrote:
If we look at the way a string vibrates, for instance on a guitar,
we can imagine that same wave motion on a circle instead of a
straight line.
No, that's a different setup where the curve is fixed at
the boundaries and not periodic, and gives standing waves.
There is indeed a lot of mathematics on various possible
"boundary conditions", but you were asking for a *physics*
setup and explanation underling *wave quantisation*...
But if we look at electron orbitals, surely these are not static
shapes over time?
https://i.imgur.com/ovN6xme.png
Are they just rotating or are they also fluctuating in size/amplitude?
Would an electron absorbing or emitting a photon just be like a
variation of the same shape or going from one shape to a different shape?
