How This Equation Describes All Waves Around Us (+ the Most Boring Solution) - Parth G Wave Equation

[@ParthGChannel]

Hi friends, thank you all for watching! If you'd like to see more videos discussing physics equations, check out my "Equations Explained" playlist here: kzbin.info/aero/PLOlz9q28K2e5j4UHkeBXhrtga_qC5ZCzf And as always, let me know what other topics I should cover in future videos!

[@freewill4912]

Please make a video on logic gates

[@the_nuwarrior]

you can solve it in a few lines using fourier transform

[@ayansayan8229]

Or by separation of variables.. but it would be tedious

[@stevenjones8575]

This is so awesome. I just recently came across your channel, and it has quickly become one of my favorite education channels. You seem to just nail the kinds of questions I have been wondering about myself. Do you think you could do more videos on how exactly equations like these are used? Like, the Hydrogen atom solution to the Schrödinger equation. What does it mean that it's a solution? What values did someone plug into where, and what popped out? When a mathematician or physicist sits down at work in the morning with the with Shrödinger equation written in front of him, what does he do with it?

[@Honk987]

Also interesting to mention is that u(x,t)=f(x+c t) +g(x-c t) solves the equation for any function f and g.

[@arushibali7784]

Parth, you have amazing communication skill and one can easily connect with you in minutes. Also, you teach us the entire concept so simply that it seems quite easy. Thanks for this video and hope you'll keep making videos on physics ❤❤ Our education system needs teachers like you ❤❤ Lots of love to you and your videos ❤❤

[@altuber99_athlete]

Perhaps a follow-up video for the future would be the telegrapher’s equations. The latter also describe waves, in a different manner. For example, they are used in electrical engineering for modeling transmission lines (whether they’re radio frequency or power transmission lines).

[@adiaphoros6842]

But because any function can be approximated by linear combination (more specifically a weighted infinite sum) of sines and cosines using Fourier series, then all functions are valid solutions to “the” wave equation.

[@MDKalach]

An amazing introduction, you rock, thank you! =)

[@DuckStorms]

How does the wave equation apply for compression waves? Are u and x equal in that case? Examples are a spring mass system and a slinky being compressed and expanded. And of course sound. Also it might help people intuitively understand the wave equation if you derive it for a simple system from first principles like a spring-mass system where acceleration (second derivative with respect to time) is directly proportional to the square of displacement of a point from its neighboring points on the spring. (In a trivial spring-mass system the mass and the origin are much “heavier” than the spring making only 2 relevant points.)

[@dapotatoguy7019]

In that case you can convert the compressive waves to transverse, magnitude of compression can be amplitude, frequency is still frequency, wavelength is distance between two compressions or rarefactions, and distance travels depends on medium.

[@TheGeoffable]

Loving these vids, great way to get a rough grasp on it without the hours required to be totally rigorous :)

[@Errenium]

u = A + Bx + Ct + Dxt is my favorite solution, because everyone who has studied this in any detail always has to take a detour to explain why they are ignoring it.

[@santimonto26]

Isn't this just kinda the extension of the trivial solution when both second partial derivatives are 0?

[@Errenium]

@@santimonto26 yep!

[@gowrissshanker9109]

Parth🌟🌟🌟what is the difference between detection and measurement....in quantum mechanics? Why detection does not collapse wave function but MEASUREMENT DOES ?? THANK YOU 🌟

[@alphalunamare]

Any detection implies an interaction just by definition. Whether it's a measurement or not is irrelevant to the system. So to my mind, any detection actually does collapse the wave function, it is just that you haven't recorded any empirical data in that moment other than it happened but then that is a measurement in itself.. This is my problem with the simplistic 'multiverse' idea that the Universe cleaves at every measurement, if it does then it will cleave at every hit on a Geiger counter etc. It is just pure whimsy to write popular books on such a subject whereby people think monkeys are shattering the Universe by trying to type Shakespeare.

[@alphalunamare]

Actually Hamlet catches it quite well: To Be or Not To Be ... A Universe from Nothing :-)

[@dapotatoguy7019]

I presume detection is simply being aware of the system through arbitrary means while measurement is a type of detection which is applied to the system. causing collapse.

[@eulersfollower7140]

Please make a similar video on The Heat Equation(Fourier)

[@physicskool598]

Pls make a video on eigen values and eigen vectors used in shrödinger's 2 equations . Since I don't understand it . I only studied it in matrices but in quantum it's seems complex.

[@MrBroseph19]

One of your best!

[@jlpsinde]

Great as always, love from Portugal :)

[@SciHeartJourney]

Thank you for thre videos!

[@forgor7180]

I have a question, how do you study for PDE's, like any recommendations on books or internet sources that might help?

[@DeadToTheWorld92]

Highly recommend the channel 3blue1brown here on KZbin. He does amazing math videos and has a series on DE's.

[@alexandertownsend3291]

Yeah look up partial differential equations book pdf. You should be able to find some results.

[@omarelatyqy4129]

The textbook "PDEs: an introduction" by Walter A. Strauss is a good ressource if you want to self-study pdes with no intensive prior knowledge required. I highly recommend it.

[@georgecop9538]

0:54 the correlation between the second derivatives of acceleration (u) via the speed of light

[@jamesblank2024]

What if we added waves moving forwards and backwards in time? We would have a standing wave in time dimension.

[@sivasakthisaravanan4850]

Please post a video on Klein Gordon wave equation.

[@skipii1234]

You show there the Schrödinger equation as an example, but that's wrong. It is not a wave equation because there is only time derivative in the first order. Schrödinger equation can actually be looked at as a heat equation (with imaginary constant, of course).

[@DrDeuteron]

True. A complex diffusion constant allows propagating wave solutions, but they are dispersive, so a traveling wave packet diffuses (in space) as it propagates.

[@ParthGChannel]

This depends on your definition of a "wave equation". If your definition is that a wave equation is always a second order PDE (which we only do because the common wave equation is a second order PDE), then you're right. However, if a wave equation is any equation that describes a wave, then the Schrodinger equation is also an example since it describes the time evolution of wave functions!

[@josemello649]

Thanks...

[@darshanpatel8995]

Hey Bro plz make a video on DARK MATTER OR some astronomical phenomenon Plzzz parth... Any way U r best... ❤️❤️

[@Stephanpar23]

Question: Is the U with respect to the derivative an aspect of the potential energy value given the eigenstate? I think I understand it now in the time-dependent Schrodinger model since the kinetic value is always the same based on derivative of the wave function.

[@pedrosso0]

6:32 fourier series? 👀

[@rh4282]

Next video will be calculus.

[@pedrosso0]

I don't understand, how can a wave go the other way? sin(x) goes both ways

[@sasukeshinden9333]

Gooddd

[@depressedguy9467]

Solve using monge method

[@platano5805]

We always think of the universe as unimaginably large... but maybe we're just unimaginably small... #ShowerThoughts #HortonHearsAWho

[@joeeeee8738]

And e^cx ?

[@tonyn.5592]

it's 2nd derivative with respect to t is 0 whereas it's 2nd derivative with respect to x is c^2e^cx, so both sides cannot be equal.

[@usamakeerio1141]

First one

[@jwangosho]

First to like.

[@hetoan2]

If u = 0 is an allowed solution, but the vacuum energy is non-zero, then is 0 = 0 a patch? Does nothing not exist? Godel's incompleteness theorem assumes zero is in the language, but perhaps nothingness is just a transitory equilibrium state. We don't need to throw out the wave equation, but rather understand that we need full knowledge to achieve a 100% accurate prediction. This is the core of the Heisenberg uncertainty principle.

[@aakashdeepsrivastava169]

jai shree ram

[@savvythagoat]

I’m firsttttt

[@Aryan_dotexe]

Noice

[@japneetsingh8091]

Are u of indian origin?

[@srajanverma9064]

Of course he is !

[@savvythagoat]

Hii

[@hOREP245]

@@HiiamChaitanya Linux users are so annoying lmao

[@aarushkumar168]

First

[@jewett425]

Why people watch him. He never replies to any question. He is not a physicist.........

[@siddharthjain2127]

Calculus is boaring part of mathematics 😜😜😜

[@misterlau5246]

Lol mate u=0