Problem Solving Strategies

Anonymous

12:16 PM

@Yashas I am surprised that so many Chemistry questions in JEE Advanced 2016 came directly from NCERT...wow...does that happen always? Almost all the inorganic and physical came directly from NCERT

Yashas

nope

coincidence

only the inorganic part

Anonymous

Even organic can be 50 percent answered with just ncert

Anonymous

I don't see any tough physical chemistry problems

Anonymous

the electrochemistry question is damn easy

Anonymous

I guess I should focus more on NCERT from now on

Madhuchhanda Mandal

12:19 PM

Anyway, Madhuchanda's claim that light intensity can have negative sign is bullshit

I never claimed thay

*that

Yashas

@MadhuchhandaMandal Click on the arrow at the left of the message > right click on permalink > paste it in the chat

Madhuchhanda Mandal

I mentioned a term instantaneous before intensity. Please pay attention to that

Yashas

The chat will format it automatically to appear like this:

51 secs ago, by Madhuchhanda Mandal

Anyway, Madhuchanda's claim that light intensity can have negative sign is bullshit

Madhuchhanda Mandal

Oh.. I am a newbie

Yashas

I think we should leave that topic there.

Madhuchhanda Mandal

12:21 PM

Which topic?

Anonymous

@MadhuchhandaMandal Okay, so you claim that instantaneous energy can be negative?

Madhuchhanda Mandal

Never

Anonymous

"Instantaneous intensity does have sign and its a time dependent quantity."

Madhuchhanda Mandal

I said thay

*that

Anonymous

"does have a sign" implies that it can have negative sign..

Anonymous

12:25 PM

Otherwise that sentence is pointless...

Madhuchhanda Mandal

******* Does not

Anonymous

"When two instantaneous intensity (which are out of phase) superimposes then the net instantaneous intensity is given by vector addition"

Madhuchhanda Mandal

Absolutely

Anonymous

When two "intensities" superimpose?

Madhuchhanda Mandal

I still stand by it

Anonymous

12:26 PM

That is plain wrong.

Madhuchhanda Mandal

Of course

Not wrong

Anonymous

"Intensities superimpose" makes no sense.

Anonymous

Waves superimpose.

Anonymous

Not intensities

Anonymous

That wording is wrong

Anonymous

12:27 PM

Net intensity depends on resultant

Anonymous

amplitude

Madhuchhanda Mandal

Intensity and waves can be used interchabely dude

Anonymous

@MadhuchhandaMandal No.

Anonymous

Show me a source.

Anonymous

Or a link.

Anonymous

12:28 PM

Or a book which uses intensity and waves interchangeably.

Madhuchhanda Mandal

"Let's define Instantaneous Intensity" that's the very source

Anonymous

@MadhuchhandaMandal If you are defining your own semantics....then I've got nothing to say.

Anonymous

It's like saying let mango=light and mangoes interfering...

Madhuchhanda Mandal

Yeah... I understood there lies the problem... Lack of common means of communication.

Anonymous

what nonsense.

Madhuchhanda Mandal

12:30 PM

Leave it

That's the only solution

I tried to explain it this way : One energy is trying to push it up whereas the other energy pulls it down. Hence the scalar summation of energy don't stand trur

*true

Yashas

It does.

hmm, it depends on your definition of pulls and push

energy cannot push or pull

Anonymous

wth, what does energy push it up even mean...

Anonymous

i'll go mad now..

Madhuchhanda Mandal

Waves displacement can

Yashas

if you meant light beam coming from two directions and focusing on ice, then the magnitude of powers add up numerically

Madhuchhanda Mandal

12:36 PM

Two waves interfering carrying energy and traversing the same medium at same time.

(We can consider string hence forth because the same logic of displacement will hold for E and B)

Now displacement due to one wave and hence (the energy propagating ) need to scalarly added up due to displacement of the other wave

Do you think that energy due to two waves are propagating through the string?

"If you meant light beam coming from two directions and focusing on ice, then the magnitude of powers add up numerically" : That's what I am doubting.

Because once they are superposing , power don't have any significant meaning

Anonymous

1:08 PM

@MadhuchhandaMandal You can't really consider a string. A string allows energy loss into the medium, while light waves can't be said to lose energy into medium.

Madhuchhanda Mandal

Ideality

I mean you can always compare it

In ideal case

Anonymous

Even in ideal case you can't compare them like that

Anonymous

In string the material can lose energy as heat

Madhuchhanda Mandal

Why?

"Ideal"

Anonymous

@MadhuchhandaMandal What do you mean by "ideal"?

Madhuchhanda Mandal

1:12 PM

In ideal case it does not

Anonymous

WHAT DO YOU MEAN BY IDEAL??

Anonymous

EVEN IN IDEAL CASES IT CAN LOSE ENERGY AS HEAT

Anonymous

UPON DESTRUCTIVE INTERFERENCE

Madhuchhanda Mandal

Only wave transverse waves propagating through string

Anonymous

THE ENERGY IS LOST TO STRING MATERIAL AS HEAT

Anonymous

1:13 PM

There is always a way to lose heat

Anonymous

In strings

Anonymous

In light the explanation is completely different

Anonymous

In light energy isn't lost like that

Madhuchhanda Mandal

But why I don't know cant we compare it

In ideal case why do you think energy is going to lost I dont understand

Anonymous

@MadhuchhandaMandal Where else can the energy go?

Anonymous

1:16 PM

Suppose two waves on a string interfere destructively

Anonymous

Where does the energy go?

Madhuchhanda Mandal

Oh!!!!!!

Where does the energy go ? Nowhere

Its in the string

Anonymous

No.

Anonymous

In the case of two sound waves interfering destructively, the temperature of the medium will go up and energy is conserved because it turns into incoherent kinetic energy of the molecules of the medium.

Madhuchhanda Mandal

Sure of that?

Anonymous

1:21 PM

yes

Madhuchhanda Mandal

Article?

Anonymous

4

A: What happens to the energy when waves perfectly cancel each other?

I had prepared this answer for a question that was made duplicate, so here it comes, because I found an instructive MIT video. (the second link) This answer is for electromagnetic waves mainly Have a look at this video to get an intuition how interference appears photon by photon in a two slit ...

Anonymous

33

A: What happens to the energy when waves perfectly cancel each other?

Waves always travel. Even standing waves can always be interpreted as two traveling waves that are moving in opposite directions (more on that below). Keeping the idea that waves must travel in mind, here's what happens whenever you figure out a way to build a region in which the energy of such ...

Madhuchhanda Mandal

See the word "Perfectly".

And be honest , did you understand much of the answer you higjlighted?

As in the photon probability.. Stuffs?

I never understood them

Anonymous

@MadhuchhandaMandal I saw. So what?

Anonymous

1:28 PM

@MadhuchhandaMandal I did. Lets talk facts rather than accusing one another.

Anonymous

What did you not understand?

Madhuchhanda Mandal

I had prepared this answer for a question that was made duplicate, so here it comes, because I found an instructive MIT video. (the second link) This answer is for electromagnetic waves mainly

Have a look at this video to get an intuition how interference appears photon by photon in a two slit experiment.

It comes because the probability distribution for the photons, as accumulated on the screen, has destructive and and constructive patterns, ruled by the underlying quantum mechanical solution of "photon + two slits".

That much I did not understand

Did you understand that part?

Anonymous

"I had prepared this answer for a question that was made duplicate, so here it comes, because I found an instructive MIT video. (the second link) This answer is for electromagnetic waves mainly "

Anonymous

You didn't understand?

Osheen Sachdev

Hey, why would NOCl not have a shorter bond length as compared to NO

Anonymous

1:32 PM

"Have a look at this video to get an intuition how interference appears photon by photon in a two slit experiment. "

Osheen Sachdev

sorry to distract you guys

Madhuchhanda Mandal

From the next para

I did not

It comes because.

...

Did you?

Osheen Sachdev

does NO get delta+ or Cl in NOCl?

Anonymous

It comes because the probability distribution for the photons, as accumulated on the screen, has destructive and and constructive patterns, ruled by the underlying quantum mechanical solution of "photon + two slits".

Anonymous

Understood?

Anonymous

1:34 PM

or not

Osheen Sachdev

please just a small doubt guys, stop ignoring

Madhuchhanda Mandal

No

Anonymous

@MadhuchhandaMandal Which part?

Madhuchhanda Mandal

Quantum mechanical solution

Anonymous

Double-slit experiment

The modern double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena. A simpler form of the double-slit experiment was performed originally by Thomas Young in 1801 (well before quantum mechanics). He believed it demonstrated that the wave theory of light was correct, and his experiment is sometimes referred to as Young's experiment or Young's slits. The experiment belongs to a general class of "double path" experiments, in...

Madhuchhanda Mandal

1:37 PM

Did you understand?

Anonymous

I did. You don't need to understand the maths behind it.

Anonymous

It is just wave mechanics.

Anonymous

Leave that part and move to the next line.

Madhuchhanda Mandal

Do you understand the maths behind it?

Or what its referring to?

Anonymous

@MadhuchhandaMandal The maths it is refering to is widely available in qm books. I don't remember it now. And you don't need to know the math.

Anonymous

1:40 PM

It considers photons as wave functions and adds them.

Madhuchhanda Mandal

Ok

Then?

Anonymous

Then what?

Madhuchhanda Mandal

What do they mean by perfect?

Anonymous

@MadhuchhandaMandal Where is it?

Madhuchhanda Mandal

The very title

Anonymous

1:42 PM

Perfectly means completely..

Anonymous

(destructive interference)

Madhuchhanda Mandal

In our discussion we had constructive as well as destructive interference. None of them alone

Anonymous

@MadhuchhandaMandal How does that change the fact that energy is lost to medium in string waves ?

Anonymous

And in strings the waves are out of phase by certain fixed angle

Anonymous

It is not like light

Madhuchhanda Mandal

1:50 PM

Does that not? How do you then explain increase of energy at constructive interference points?

Anonymous

@MadhuchhandaMandal Redistribution..

Madhuchhanda Mandal

Yes

Not los

*lose

Anonymous

The extra energy is lost to medium after redistribution

Madhuchhanda Mandal

*loss

Anonymous

There is energy loss as well as redistribution.

Anonymous

1:51 PM

Do the maths.

Madhuchhanda Mandal

I did not find extra energy!!!

Anonymous

@MadhuchhandaMandal Where did you look for it?

Madhuchhanda Mandal

Wave equation

On interference

Anonymous

Show me your math

Anonymous

Which shows that there won't be excess energy

Madhuchhanda Mandal

1:53 PM

1/2 (Io Cos^2(phi/2) )

Anonymous

@MadhuchhandaMandal That is not the intensity for string waves...

Madhuchhanda Mandal

Well I think it is.. Wait let me calculate

Oh Wait... On Interfering it's not remaining wave at all !!!

Anonymous

3:10 PM

@Yashas How do you find the coordinates of circumcenter of a tetrahedron given its vertices' position vectors

Yashas

the centroid is sum/4

circumcenter

hmm

I forgot

Anonymous

I have a couple of doubts related to vectors

Yashas

I need to open my book

I forgot the formula

I don't know the derivation for it

@blue ?

Anonymous

When they say OA,OB, OC , OD vectors are coplanar do they mean A,B,C,D are coplanar or they mean OA, OB,OC, OD vectors themselves are coplanar?

Anonymous

$O$ is the origin

Yashas

3:13 PM

the vector themselves

it does not matter if O is origin or not

if AB, CD and EF are coplanar then those three vectors are coplanar

if the points A B C D were coplanar, they would have told AB, BC, CD are coplanar

Anonymous

@Yashas And not the points? Are you sure? In some books they mean that A,B,C D are coplanar

Yashas

The book is wrong.

OA, OB, OC being planar implies those vectors are planar

it is so wrong to say that the points A B C are coplanar

I don't believe you

that a book says that

Anonymous

My etoos study material

Anonymous

I need to check it again

Yashas

:|

Anonymous

3:16 PM

Ok I'll check at night

Anonymous

I was reading it yesterday

Yashas

I am pretty sure about this

I have solved around 500 vector & 3D Geo problems

Anonymous

Well I do agree with you

Yashas

I never came across the situation which you are describing

so I am not read to believe it

Anonymous

I just wanted to make sure

Anonymous

3:25 PM

@Yashas Ah I checked, so what they did is ((A-B)*(B-C)).(C-D)=0 to check coplanarity....they wrote OA, OB , OC OD and hence the notation confused me.

Madhuchhanda Mandal

3:57 PM

@blue you are right. Interference in a String is no way comparable to light. Cause the phase difference is not constant between the interfering waves

Anonymous

@MadhuchhandaMandal Yes, you got it !

Madhuchhanda Mandal

It varies with kx

I never thought at it

By the way, you cannot define Intensity for a standing wave

Cause standing wave is not propagating wave at all I think

Anonymous

4:18 PM

@MadhuchhandaMandal Why does a wave need to propagate to have power/intensity?

Anonymous

The particles in the string will have K.E

Anonymous

As well as P.E

Anonymous

It will be a SHM motion

Madhuchhanda Mandal

4:50 PM

Because intensity is defined as amount of energy crossing through unit area in unit time

Anonymous

5:05 PM

@MadhuchhandaMandal So you mean sound doesn't have intensity as it is a standing wave in organ pipes?

Anonymous

Rethink.

Madhuchhanda Mandal

It depends what do you mean by intensity. If you are not confusing intensity with power

Anonymous

Ever used the formua for calculating decibels?

Anonymous

10log(I/Io)

Madhuchhanda Mandal

Never used for organ pipes

Anonymous

5:08 PM

Sound is a standing wave in organ pipes

Madhuchhanda Mandal

Never used inside Organ pipes

Anonymous

That doesn't mean you won't hear any sound in an organ pipe

Anonymous

@MadhuchhandaMandal Oh really?

Anonymous

What makes you think so?

Madhuchhanda Mandal

Hopefully not

Because if you place your ear inside the pipe, does the Wave persist?

What happens if you place your ear inside the pipe? Do we know what will happen?

Anonymous

5:16 PM

Yes, you will still hear a sound due to vibration of the particles about their mean position

Madhuchhanda Mandal

God knows standing wave still persists or nor

*not

No you will hear nothing. Because your ear will act as the base of the Pip's l

*pipe and there will be always displacement node there

Anonymous

@MadhuchhandaMandal wut

Anonymous

base of pipe?

Madhuchhanda Mandal

Organ pipe

If you place your ear inside it will act as the base

And hence there will be node

Anonymous

eh...consider a large organ pipe

Madhuchhanda Mandal

5:23 PM

Wait... No standing wave will be formed.

Why will standing wave form?

I don't understand why will standing wave form if when you place your ear inside a organ pipe

Does your ear reflect waves ??

Ok a JEE question... Enough discussion of no use

Consider an excited hydrogen atom in state n moving with a velocity v(v<c). It emits a photon in the direction of its motion and changes its state to lower state m. Find the frequency of emitted radiation in terms of frequency f0 emitted if the atom were at rest.

Isn't the answer coming f0(1+v/2c) ??

Anonymous

5:40 PM

I'll try tomorrow...

Madhuchhanda Mandal

Ok

Anonymous

BTW...standing waves do have intensity given by energy density*velocity

Anonymous

Think about it

Madhuchhanda Mandal

Velocity.. I derived for standing waves

Anonymous

Right

Madhuchhanda Mandal

5:41 PM

It coming as : v cot x cos x

Anonymous

eh?

Madhuchhanda Mandal

Hence non constant velocity

Anonymous

instantaneous velocity...

Anonymous

time energy density

Anonymous

gives instantaneous intensity...

Madhuchhanda Mandal

5:43 PM

Velocity is not constant. So?

How can we define it to be a propagating wave?

Anonymous

@MadhuchhandaMandal We don't define it to be a propagating wave

Madhuchhanda Mandal

Then you cannot define intensity

Anonymous

You can.

Anonymous

I just now asked in hbar

Anonymous

They said yes as I expected.

Madhuchhanda Mandal

5:45 PM

I don't understand how

Anonymous

Don't forget that the particles are still vibrating in their place

Anonymous

The average intensity is 0

Anonymous

in The h Bar, 10 mins ago, by ACuriousMind

Indeed, the time average of the intensity will be zero

Madhuchhanda Mandal

I said that.. We should not confuse intensity with power

I dont understand how

Anonymous

in The h Bar, 9 mins ago, by ACuriousMind

@blue Energy density times velocity

Anonymous

5:46 PM

in The h Bar, 10 mins ago, by ACuriousMind

But inbetween two nodes, there is an oscillatory flow of energy

Madhuchhanda Mandal

How do you get that velocity term?

Ask that

Anonymous

velocity is instantaneous velocity

Anonymous

which you get by differentiating the wave eqn

Madhuchhanda Mandal

d/dt(y) [partial] ?

Anonymous

yeah

Madhuchhanda Mandal

5:49 PM

No man it cannot happen..... Otherwise whole of my derivations will go wrong

Do you know Quantum Mechanics?

Anonymous

it has happened :-)

Anonymous

@MadhuchhandaMandal Well, nobody on the planet understands it fully

Anonymous

;)

Anonymous

I have collected a few pebbles from the sea

Madhuchhanda Mandal

Ok. Good

Although I am clueless as to why Intensity must be d/dt(y)[partial]*energy density

It must be energy density*velocity of wave

Not velocity of particle

And for standing wave , that velocity is undefined

Anonymous

5:53 PM

velocity of wave is 0...

Anonymous

for standing waves

Madhuchhanda Mandal

Undefined. Not 0

Anonymous

how the hell can velocity be undefined -_-

Madhuchhanda Mandal

Because its not propagating wave

And it can be considered to be propagating wave with velocity as v cot(kx) cot(wt) which has altogether no meaning

Hence undefined.

Not 0

Anonymous

@MadhuchhandaMandal what type of eqn is that

Anonymous

5:56 PM

and secondly it is just 0

Madhuchhanda Mandal

I don't think so.

Well try that question

Enough melting of brain happened...

And anyway, I never tried to attack you neither physically nor personally nor mentally. And I am really sorry if I did.

Its my bad. I can not talk hypocritically.

Do you recognize the equation : ro * v/2 ((d/dt(y)) ^2 + (v d/dx(y))^2 ) for intensity?

Put v=0, you will get intensity to be 0

But I think intensity will be undefined... Or wait put v= v cot(kx) cot(wt) . you get some form of intensity

Well although that will be like a series of local propagating being glued one by one

Anonymous

@MadhuchhandaMandal No, I don't. Where did you get that?

Anonymous

Doesn't seem correct.

Madhuchhanda Mandal

I derived that

Anonymous

Also the velocity seems wrong... 2Asin(wt)cos(kx)....did you differentiate that?

Madhuchhanda Mandal

6:11 PM

It is correct. Put any propagating waves. Such as a sin(kx-wt) in that equation. You get instantaneous intensity. Time average that, you get so called "intensity" of wave.

2Asin(wt)cos(kx)....did you differentiate that? Why should I differentiate that?

Well its bedtime

See you tomorrow

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