The h Bar

At any point $x$ on the graph $x$ is just the distance along the angle axis from the origin, so it is an angle.

user228700

Hang on, what is it that you're explaining?

I feel a diagram coming on ...

user228700

NO!

user228700

All I'm asking is what any of this has to do with alternating current. Well, OK, not quite, since I know that it's a periodic function and all, but well, OK, what's $\omega$?

user228700

12:05 PM

Oh, u're drawing a diagram, aren't u? .__.

$\omega$ is just $2\pi f$, where $f$ is the frequency

user228700

And $\phi$ sort of represents where we started..?

Yes. When $t=0$ the current is $I_m\sin\phi$

Actually I'm not sure we need a diagram now ...

user228700

@JohnRennie :-P What made u rethink that?

You seem to understand what's going on.

We call $\phi$ the phase.

user228700

12:07 PM

@JohnRennie Well, u just didn't believe me at first :-P

user228700

@JohnRennie Oh, so not $(\omega t +\phi)$?

@Kaumudi.H If the phase is zero the equation is just $I = I_m\sin(\omega t)$

@BernardoMeurer How did your exam go?

user228700

@JohnRennie Huh. This is the first time my textbook has properly messed up even terminology.

user228700

Alright, that's all...for now :-P Thanks very much! :-)

12:10 PM

By saying the phase is $\omega t + \phi$ ?

user228700

Yeah..?

The domain for $\sin$ is an angle.

user228700

Yeah...

And $\omega t + \phi$ is an angle, that depends on time.

user228700

Right...

12:12 PM

However the $\phi$ bit it time independent, and it's usual to call this time independent bit the phase.

user228700

Right, wokay.

Phase (waves)

Phase is the position of a point in time (an instant) on a waveform cycle. A complete cycle is defined as the interval required for the waveform to return to its arbitrary initial value. The graphic to the right shows how one cycle constitutes 360° of phase. The graphic also shows how phase is sometimes expressed in radians, where one radian of phase equals approximately 57.3°. Phase can also be an expression of relative displacement between two corresponding features (for example, peaks or zero crossings) of two waveforms having the same frequency. In sinusoidal functions or in waves "phase" has...

user228700

Oh, so Wiki says it's $(\omega t+\phi)$?

Actually I see Wikipedia defines phase in two ways, one of which matches the definition I've just given you.

> Phase can also be an expression of relative displacement

The other is indeed the angle $\omega t + \phi$

user228700

relative displacement? Wait, which one is that? I'd think that that's just $\omega t$, isn't it?

12:15 PM

Suppose you have two waves $\sin(\omega t + \phi)$ and $\sin(\omega t)$

I would always call $\phi$ the initial phase, at least in Spanish.

user228700

@JohnRennie OK...

They are the same curve but displaced along the $x$ axis by an angle $\phi$

user228700

> "Phase can also be an expression of relative displacement between two corresponding features (for example, peaks or zero crossings) of two waveforms having the same frequency"

That's what displacement means in this context.

user228700

12:16 PM

Ah, okay, so that's definitely just $\phi$, then.

Yes.

user228700

Alrighty, that's about it. Thank you :-)

But as AFT says maybe I should refer to that as initial phase

Whatever

user228700

@JohnRennie :-P Only I am capable of caring about these things...well, almost.

@AccidentalFourierTransform It also has a special name called epoch :)

12:18 PM

Epoch?

I've never heard that used to describe a phase difference

I saw it in a Russian book

epoch sounds like a geological term =)

Epoch (reference date)

In the fields of chronology and periodization, an epoch is an instant in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured. Time measurement units are counted from the epoch so that the date and time of events can be specified unambiguously. Events taking place before the epoch can be dated by counting negatively from the epoch, though in pragmatic periodization practice, epochs are defined for the past, and another epoch is used to start the next era, therefore serving as the ending of the older preceding era. The whole purpose...

I can't find it

on the net though

user228700

> "A particular period of time in history or a person's life."

user228700

^ This is what I thought epoch means.

12:19 PM

Well, it was a very old and dusty book

@Kaumudi.H one day you'll get a short answer to a question :-)

maybe archaic terminology

:D

Just a fun fact :)

from another epoch ;-)

user228700

@JohnRennie One day :-P

@JohnRennie @AccidentalFourierTransform see in.answers.yahoo.com/question/index?qid=20110327105337AAZ9GJ7

Atleast someone on the internet used it :P

12:21 PM

lol

TIL I guess

Someone on the Internet said it, so it must be correct :-)

Two people on the internet said it :P

(Including me :D)

user228700

OK, I'm not quite done yet.

Q: Wave displacement with phase difference 180

In more general usage a "period" is a property of an oscillation (others are ampliture, timbre (relative sizes of superposition weights in a Fourier expansion) and epoch or phase). The usage you show is not precise and the question needs tightening up. My guess is that it would likely refer to the full period - that's how I would read it - but if you interpreted as the half period (peak to trough), then you could not be faulted as clearly to use "oscillation" in this way is not precise. — WetSavannaAnimal aka Rod Vance Apr 3 '15 at 0:12

2

The variation with distance x along a wave of its displacement d at a particular time. A second wave has the same frequency and speed as the wave shown in Fig. 2.1 but has double the intensity. The phase difference between the two waves is 180°. I need to sketch the second wave on the graph, ...

also here ^

user228700

Earlier, I had asked about finding the average value of a function. Honestly, I do understand what's happening; we're finding the area under the graph and then dividing by the length of the base or whatever...but I'm still a little confused as to why this gives us the average height of all those infinitesimal rectangles.

12:24 PM

so yeah, youre not alone :D

Hurray! The term isn't extinct yet :D

Haha

user228700

Hang on, so we're finding the area by integrating...and then dividing by the base just leaves us with...the sum of all the heights, right? :-|

@Kaumudi.H Suppose you have some function $f(x)$ defined over a range $x_1$ to $x_2$.

@Kaumudi.H well, how do you define the average of something to begin with?

say, whats the average of $\{1,2,3\}$?

user228700

Erm, now to whom should I respond? :-|

12:27 PM

Ah, actually AFT's approach is probably better than the one I was going to take ...

@AccidentalFourierTransform My ass still hurts

4

@BernardoMeurer you got shafted then? :-)

user228700

@JohnRennie OK, no, hang on, does this: "Hang on, so we're finding the area by integrating...and then dividing by the base just leaves us with...the sum of all the heights, right? :-| " make any sense at all?

@JohnRennie Yeah, I got hardcore shafted by my analysis prof

Ive been there too

12:28 PM

Speaking as a room mod I'm not sure we should be starring a comment my ass still hurts ...

the calculus exam was the one worst of my undergrad studies

@JohnRennie What? I fell down after the exam

Visitors to the room will see that at the top of the star board and wonder what on Earth they've stumbled into :-)

@JohnRennie Fell on my ass, so it hurts

user228700

Uh, anybody..?

12:29 PM

@Kaumudi.H Um, why?

@Kaumudi.H as AFT was getting at, it's a matter of how you define the average

@AccidentalFourierTransform I will fail this class unless I can become a proof god meme

I don't understand why you think that at all

user228700

@BalarkaSen Well, the area is just base times height and then we divide by the base and we've also added all the areas so...

@Kaumudi.H there are lots of different types of average. The definition you've been given is the mean.

user228700

12:31 PM

OK..?

@Kaumudi.H Dividing by the base leaves you with the height

Not sum of stuff

user228700

@BalarkaSen Sure, but we've added all the areas, no?

If you have area under some curvy thing then you're still left with a height.

That's the average of all the heights

@Kaumudi.H Suppose your graph was of velocity. Then the area under the velocity:time graph is ... ?

user228700

WAIT!

12:32 PM

:: everyone freezes ::

3

user228700

OK, @JohnR: That's displacement and @Balarka: How is it the average of all the heights?

Sir Cumference

@Kaumudi.H 'Fraid not

@Kaumudi.H yes, the area under the $v:t$ graph is the total distance travelled. And the total distance travelled divided by the time taken is ... ?

user228700

@JohnRennie Distance? That's just speed then...Oh, but wait. How did we get here? :-|

@Kaumudi.H Suppose $(\int_a^b f(t) dt)/(b - a) = h$. Then $\int_a^b f(t) dt = h(b - a)$.

So area under the curve $y = f(x)$ over $[a, b]$ is area of the rectangle with base $[a, b]$ and height $h$.

12:34 PM

Suppose $0=1$. Then $\int v(t)\mathrm dt=F\cdot\eta$

It's as if you're "normalizing" the various heights $f(t)$ for $t \in [a, b]$, preserving the area.

user228700

Gimme a minute...

If you think about a discrete set of heights, that's precisely what the average is.

user228700

@AccidentalFourierTransform Dude, why? I'm almost crying.

@Kaumudi.H This is a concrete example of why the process described calculates the mean of the function.

12:35 PM

@Kaumudi.H OK, here's a concrete example.

user228700

WAIT WAIT WAIT, gimme a minute!!

20 hours ago, by John Rennie

I think your answer is on the order of Assume 0 = 1. Then 13 is not prime. Violations of the conservation of momentum are inconsistent with general relativity, so you can prove anything if you assume them. — Peter Shor yesterday

I was going to give you an example to show why that's the correct notion of average but ok, I'll chicken out

user228700

@BalarkaSen Just gimme a minute, I beg you.

@Kaumudi.H let us kniow when you want us to start talking again.

In the mean time, should I put an offer in on this?

ebay.co.uk/itm/DELL-INSPIRON-5720-CORE-i3-17-3-LAPTOP-/…

user228700

12:40 PM

We could start talking now but I'm afraid I'm just...stuck.

It would be really easy to fix.

@Kaumudi.H if i may interject, i think i can introduce something not at all rigorous that might illustrate.

I was going to give you some concrete and rigorous, but ok

user228700

@JohnRennie It's been...two months, no? That's actually pretty impressive (for you).

It's a bit scruffy, but it seems to be all working.

The description says the keyboard isn't working, but I have a spare keyboard that will fit.

user228700

12:41 PM

> "“BOOTING UP, NO HDD BUT HDD CADDY IN, I PUT IN AN HDD AND TRIED TO BOOT FROM THE DVD DRIVE NOT BOOTING LOOK LIKE DVD DRIVE FAULTY (UEFI BOOT DISABLED), KEYBOARD IS FAULTY AS WELLCHARGER NOT INCLUDED, HAS SCRATCHES PLEASE CHECK ALL THE PICTURES FOR CONDITIONS”

user228700

No kidding, keyboard is definitely faulty.

Caps lock stuck down :-)

user228700

@heather OK..?

user228700

Oh no, @Balarka left .__.

when you are finding the area under a curve you are choosing a standard width, let's call it $w$ for all the rectangles. Each rectangle also has a height, $h_1$ for the first, $h_2$ for the second, $h_n$ for the nth. So really, we're doing $w(h_1)+w(h_2)+...+w(h_n)$, right? and we get the area.

but we're dividing out the total width, to get one number.

so we're left with heights, yes?

12:43 PM

no i only use Lebesgue

the average of those heights.

(I know, terribly un-rigorous, but maybe that helps a bit?)

@Kaumudi.H sorry, I was typing it out =)

user228700

"We're dividing out the total width". I think that's the most important point to understand with regard to getting the average of the heights and all, but I still haven't...gotten it.

@Kaumudi.H Draw a sine

try "filling" it's area with rectangles

they must all have the same width

that's a Riemann integral basically

user228700

I know what the integral is...I just don't understand what magic happens when we divide by the width of the interval or whatever.

Is it worth going back to the example of velocity?

user228700

12:48 PM

@heather :-) Thanks...I'm just...yeah, I don't get the dividing thing yet.

ok, listen to me for a sec

user228700

:?

let $E(t)$ be the energy of a certain particle

measured in Joules

I'm not sure that everyone talking at once is helping ...

user228700

12:49 PM

Wow, never before have so many people tried to help me all at once.

after 10 seconds, the mean energy is $$\frac{1}{10\ \mathrm s}\int_0^{10\ \mathrm s} E(t)\mathrm dt$$

user228700

@JohnRennie That is correct.

@JohnRennie If we all flood her with random information it will work, I am certain

@BernardoMeurer :-)

It will work if driving her insane is the aim :-)

if you didn't divide by $10\ \mathrm s$, then you'd get something with units of Joules times seconds, $\mathrm {J\cdot s}$

but the mean energy should have units of $\mathrm J$, so it should make intuitive sense that you have to divide by something with units of seconds, right?

12:51 PM

Anyway I have to go shortly, so that's one less voice

user228700

@AccidentalFourierTransform Sure, yeah, that makes sense but it's not what I'm looking, for, sort of. I mean, look, I understand that it makes sense, OK? I just don't understand what happens to the area when we divide with the base. It's obvious--length times breadth=area so dividing by base should give me height but all I'm saying is, haven't we summed up all the small areas?

user228700

@JohnRennie :-| OK...

user228700

Sigh, I'm not even sure if I've done a good job of explaining what I know and what I don't. If I had done a better job, it wouldn't have gotten so chaotic.

@Kaumudi.H can I quickly try a different approach?

user228700

Sure. Anything to get me out of here, please!

12:54 PM

Suppose we take your function $f(x)$.

user228700

OK.

We define the average as the constant function $g$ that satisifies $$\int_a^b g dx = \int_a^b f(x) dx $$ does that make sense?

user228700

What? No. What are u doing?

The value of $f$ depends on $x$ so the value of $f$ changes for values of $x$ in between $a$ and $b$

The average value of $f$ between $a$ and $b$ is just a constant. Yes?

user228700

Oh, are u trying to tell me how the area of the function is just given by the average height obtained times the width of the base?

12:57 PM

Yes

user228700

@JohnRennie Don't u mean $g$?

^ maybe this could help?

@Kaumudi.H The constant $g$ is the average value of $f$ between $a$ and $b$

user228700

@JohnRennie Oh, sorry, misread. Yeah.

Anyway, does this approach make sense?

user228700

12:59 PM

A little bit...

I'm saying that the area under the curve $g = \text{constant}$ is the same as the area under the curve $f(x)$.

user228700

Yeah, I know! But, I mean, gah, never mind. Go get lunch or whatever it is u were going to do. I'm going to go pull out some of my hair and then have a go at it again...on my own, without all the noise.

OK :-)

user228700

I sound bad. Sorry. Thanks very much, everyone, for trying to help :-)

wait, i had a moment of clarity:

remember how in my earlier terrible explanation i was talking about the w's multipled by the h's? well, remember, you take the lower riemannian sum and the upper one (sorry if that's not the right terminology) and take the average of the two. well, if you're getting rid of the widths by dividing out the whole width, you're left with the average of all the heights, right?

does that make any sense @Kaumudi.H?

user228700

1:06 PM

Wait, hang on, does $\int_a^b dx$ give me the total number of divisions I made b/w $a$ and $b$ ?

uh...there's no $x$ in there.

i don't know what that means =)

user228700

@heather Huh? Where?

@Kaumudi.H $\int^b_a\, dx$

i have to go in a minute, sorry! if you're around after 3:30-ish central time, i'll be around.

user228700

.__. Yeeah, no, no moment of clarity for me yet.

user228700

Excuse me while I go and have existential crisis No. 2 of the day.

1:09 PM

sorry. maybe i'll ask my math teacher, and see if he has a better explanation.

you've already had one!?

user228700

@heather :-) No, that's OK. Thanks so much for trying to explain. I really appreciate it.

user228700

@heather Almost :-P I'm just kidding.

user228700

Anyway, like I said, I probably have to go and figure some stuff (integrals and all) out. Thanks very much :-) @heather: Have a nice day!

1:52 PM

Let width of each rectangular strip be $w$ and heights be $h_1,h_2,h_3,...,h_n$. So total area of all the rectangular strips is $$w(h_1+h_2+h_3+...+h_n)$$. This total area exactly matches with the area under the curve when the width of each strip is taken to be very small i.e. $dx$. That is the area which $\int_a^b f(x) dx$ gives you

Now, when you are dividing by total width what you are actually doing is $$\frac{\int_a^bf(x)dx}{b-a}=\frac{w(h_1+h_2+...+h_n)}{nw}=\frac{h_1+h_2+...+h_n‌}{n}$$=**AVERAGE HEIGHT OF ALL THE RECTANGULAR STRIPS** (i.e. average value of the function in the given interval).

Remember that $b-a=nw$ since the region between $a$ and $b$ is divided into $n$ parts of width $w$.

@Kaumudi.H I think this might make it a bit clearer for you

Einstein the troll

2:05 PM

So I want to compute the power spectral density of the sound of fall of a ring. How do I do so?

Using MATLAB, I recorded the sound of fall, but what is the most accurate representation of the power spectra?

2:44 PM

@Kaumudi.H That gives you the sum of widths of all the tiny rectangular strips i.e. $b-a=nw$ where $n$ is the number of strips and $w$ is the width of each tiny strip.

@Einsteinthetroll This is a very vague question. What type of ring are you talking about ?

Don't be mad once you see that he want it

@AccidentalFourierTransform Was that message aimed at me ?

'Cause if you liked it, then you shoulda put a ring on it

Okay, so you are humming a song

Go on

:)

Q: I want to ask questions about tiny black holes, but want to read some basic knowlage first

Oh, oh, oh, oh, oh, oh

Physics Meta

3:52 PM

0

I would like to have a better understanding of black holes, especially tiny black holes and Hawking radiation. But I'm painfully aware that my understanding of the subject is far too poor to ask good questions about that. My question here is, what should I read to cover the basics? What I woul...

discussion support

I see the masses are assembling for the chat session :-)

Well, it's chat session time!

I think we don't have an actual agenda today, though

this has to be our chattier chat session so far

Anyway, welcome everyone. If you're new here and have some questions or if you have any other topic you want to discuss, feel free to throw it in

I want to ask questions about tiny black holes, but want to read some basic knowlage first

4:04 PM

Be nice

I want my hats back!‌!!

9 hours ago, by DanielSank

In case I miss the chat session, someone please mention the best of 2016 meta post.

Well, anything new in physics lately? I'm afraid I haven't read much outside of stringy stuff lately, so I might've missed some things

Jan 3 at 4:13, by vzn

Scientists detect a quantum crystal of electrons and “watch” it melt / MIT news

in theory salon, Jan 5 at 15:26, by vzn

The Trouble with Quantum Mechanics / Weinberg, NY review books

13 hours ago, by vzn

Super graphene! MIT reveals revolutionary ultralight material that's TEN TIMES stronger than steel / dailymail

How charon help lessen the atmosphere loss of pluto

There are lots of black holes out there ...

4:14 PM

Some ferroelectric stuff that I don't understand but seemed significant

Q: Best-of PSE 2016: description and categories

Daniel asked that we consider the Best of 2016 suggestion:

9

As suggested in another meta post, let's do a Physics Stack Exchange "best of 2016". There's a nice precedent for this in the Puzzles and Code Golf site. Objective Reward and draw attention to some of the best content our community has created this year. Have fun :D Procedure Establish cat...

discussion

First observation of collisional plasmoid during magnetic reconnection. This will further help predict space weather and solar flares

@JohnRennie Is there something to consider about it except making people aware of it?

It's already featured as a "hot meta post" but if it drops from there we might consider featuring it manually

I would guess Daniel was hoping for volunteers to start seeking out candidate questions.

Or possibly a general agreement that it's a good idea and volunteers to take the process forward i.e. assemble the list of categories.

but did we agree that its a good idea?

4:20 PM

Yes in principle, but I don't sense an outpouring of excitment over the idea.

I'm neutral on that point. I don't see it as detrimental or anything, but I'm also not really convinced it's worth the effort

I suspect most of us feel something similar

@JohnRennie lol how often do you sense an outpouring of excitement around here? :P

To be fair there has been some pretty lively chats. Often ending up with flags being raised :-)

@JohnRennie yeah, typically not the scheduled ones though...?

4:24 PM

Now, now, we did have some lively sessions without any flagging

But the sessions have always been wildly fluctuating in their liveliness and number of participants

@ACuriousMind chat room(s) truly are like a "bar"... :|

It's better when there is some outstanding matter to discuss, but inevitably that will be the exception not the rule.

@vzn except that if the conversation is flagging in a bar asking "who wants another drink" is guaranteed to reinvigorate it :-)

@JohnRennie metrolyrics.com/…

> On the other hand, the problems of understanding measurement in the present form of quantum mechanics may be warning us that the theory needs modification. —Weinberg

@vzn Yeah, don't cherry pick that one. It's formulated with the appropriate caution "may be", and is followed by an excellent discussion that there is no experimental evidence whatsoever that quantum mechanics has problems, and even gives specific experiments that show that certain proposed modifications of QM, if they happen, must be ridiculously neglegible. The problems are solely in our minds and with our interpretations.

@ACuriousMind think he is not entirely up on latest experiments & that weak measurement is the wildcard. agreed it does not (apparently) contradict known theory but that is too strict a requirement to rule against "deeper theory".

4:45 PM

Observation of predicted looped trajectories when increasing the near field component of the EM field

@Secret saw that. wild stuff! wonder if its (new) experimental evidence for (something like?) a pilot wave. o_O

It's not really new, it is a known result in QFT, but it is nice to finally being able to observe them

(NB I actually read that paper in full)

I guess a natural question is that what sceanario (besides quantum computing, because the artile cover that well) will we want to enhance such looped trajectories

@vzn Why would you think so? The non-zero observation in question is predicted by the canonical path integral formalism, which the linked article clearly states.

@ACuriousMind its true they say nothing about bohmian trajectories or pilot wave... :| there are other experiments for that :) ... oops! look at ref 10! Mahler, D. H. et al. Experimental nonlocal and surreal Bohmian trajectories. Sci. Adv. 2, e11501466 (2016).

Initially I do have that "wow" feeling because it looks so weird, but reading the article then taught me that it is not a new thing

however, because it is still quite uncommon, it then wonders me what we can use that for

4:54 PM

@vzn lol, please actually read the paper. ref. 10 is used together with a host of other references to support the sentence "As the superposition principle lies at the core of quantum physics, many of its counterintuitive features such as entanglement, non-locality, wave-particle duality, and delayed-choice concepts can be demonstrated or tested using a two-slit system.", and nothing else.

It would be quite bland if all of these quantum results can only be used in quantum computing, not that it is a bad thing because quanutm computing itself is very useful

@ACuriousMind lol, ref 10 is a paper... a very interesting one :)

but ... I would like some variety for applications of more uncommon quanutm phenomeon

@vzn which has only superficially to do with the topic at hand. What is your point?

@ACuriousMind do have a point, still looking for someone to eventually grasp it :)

4:57 PM

Acuriousmind, in your opinion, besides the quantum computing application suggested in the article, when would we want to enhance the occurence of looped trajectories?

@Secret No idea. I do not usually evaluate experimental results for their practical usefulness ;)

5:34 PM

@ACuriousMind: perhaps a silly question, but in string theory is the string tension a constant i.e. a fundamental property. Googling suggests that is it as does Motl's answer here.

5:49 PM

Wow! Lubos Motl even has a Wikipedia page. en.wikipedia.org/wiki/Lubo%C5%A1_Motl

6:03 PM

In the absence of an answer I have risked my PSE reputation on my limited undering of Zwiebach.

6:20 PM

@JohnRennie I think you are correct

6:43 PM

Aw man I missed the chat session again :-(

6:56 PM

One of these days I will get back to being around for them

though it is good to see that they carry on in my absence

@DavidZ me too

I always miss them :(

I'm sure you have a good excuse though

Sleeping late?

I'd count that

:-P

I dunno. I kinda wish I'd make more of these.

There are one or two ideas on which I'd like feedback. The meta is good but a lot of people I barely ever see around here show up to the sessions.

I doubt your reason for missing is less respectable than "slept in".

7:13 PM

I just forgot it was happening. That's definitely less respectable.

Ah

Can you make the intertubes remind you?