The Wave Equation for BEGINNERS | Physics Equations Made Easy

Ever wondered what the Classical Wave Equation is all about? Well now you can find out!
Hey everyone, I'm back with another video. This time, I'm breaking down the Classical Wave Equation for you, because I really enjoy making these videos where I explain what a physics equation is trying to tell us.
The Classical Wave Equation describes the behaviour of waves (duh) as they move through space and time. In this video we discuss one particular solution of the wave equation in detail - sinusoidal waves. Remember though, that there are other solutions to the wave equation, such as spherical waves. However, sinusoidal waves make the wave equation the easiest to explain in my opinion.
We will first learn about differentiation, which is a very important sub-section of calculus. We will learn about this because the Wave Equation is known as a differential equation. Well technically, the equation being discussed in this video is a one-dimensional second-order linear partial differential equation. It might seem like I'm just throwing jargon at you, but in this video I will describe exactly what each bit of that description means. And the best part is, you don't need to be studying physics or mathematics at university to understand it! If I've made this video correctly, then you should be able to understand it if you've studied mathematics or physics up to high school level.
We will learn about differentiation in this video because differentiation is heavily featured in the wave equation. We take an equation that describes the wave we happen to be studying, and differentiate it with respect to both time and position. We do this until we can test if our wave obeys the rules set down by the wave equation (of sorts). If it does, then our wave is said to "obey" the wave equation.
The wave equation describes lots of classical waves, such as light waves, sound waves, mechanical waves, etc. However, there are many other kinds of wave equation - the Schrodinger Equation being a good example. The Classical Wave Equation discussed in this video only deals with the subset of waves known about long before the advent of Special Relativity or Quantum Mechanics.
With all of that being said, if you have any questions, please do let me know in the comments section down below. I will try to answer as many as possible.
If you enjoyed this video, please do leave a thumbs up and subscribe for more fun physics content. Hit that bell button if you want to be notified every time I upload. Follow me on Instagram @parthvlogs to see what I get up to on a more day-to-day basis.

[@ParthGChannel]

Hi friends, thanks so much for watching! If you'd like to see more about the wave equation, including a discussion about the solutions of this equation, check out my video here: kzbin.info/www/bejne/rmPFdWWHnbSrmpI And as always, let me know what other topics to cover in future videos!

[@AmitKumar-oq6qu]

This video ended very quickly , would have been great if it were a bit longer. All I want to say is that , this was very good.. ❤❤

[@naman4067]

Nice video paji

[@kaviya4062]

Sir could you please teach me what is potential difference high potential low potential our books have only definition I literally understand something form that

[@MarceloUmeda]

Parth, for the sake of education, I hope you take teaching for a career, or the world will be losing an amazingly gifted educator.

[@sjlegends]

Nah, we cannot really do this same kind of explanation to a group of individuals, where the interest level of individuals is a distributed function. I think youtube is a very good platform.

[@therandomvidguy5141]

or not cuz he will be something much better for his own sake. Don't tell him what to do, let him lead his own life.

[@abysslinde.zssprime6896]

@@therandomvidguy5141 lol chill out, he wouldnt decide what he would do with his life through a youtube comment The comment was meant to be a compliment

[@joeboxter3635]

Yes, he is a gifted educator. But I ask that he organize the order of his play-lists.

[@Someone-lf7iz]

@@sjlegends I completely disagree. Most of the students I'm in class with are extremely motivated, and instructors who can actually break material down are heavily sought after. One of the problems with universities is some of the most brilliant people can't always teach. It's a problem in many engineering classes, especially the more advanced ones.

[@epromee]

8:22 "Let's differentiate YOU with respect" Thanks for the respect, but I prefer to stay integrated :)

[@bebarshossny5148]

yeah same man i'd actually like my laplace transform taken

[@ivanmarianek35]

You could make a video about Navier-Stokes equations.

[@leonardoalanis220]

You just remembered me that I just handed in a homework in which I had to prove that the Navier Stokes equation for linear elasticity in 3D follows a classical wave equation.

[@guitarttimman]

I'd post a video of it, but I'm too afraid that my head might explode. :)

[@JousefM]

I did a full derivation on the NSE if you would like to have a look.

[@engineering_by_samir]

Hello Ivan, I have a video about the Navier Stokes Equations and how I can simplify them and Solve them. But this video is in german. Here is the link for my Video of N S Equations kzbin.info/www/bejne/p3TXXq1qoa-Vg6c Please let me know if you liked this video :-)

[@prashantjadhav9872]

We also use the same in fluid mechanics.

[@anwesha9580]

Couldn't imagine of such a simplified explanation of seemingly complex wave equation! Really grateful for this...never stop making videos!! They're so helpful!

[@emilylancaster8993]

spitefully growing out your hair and beard to annoy youtube commenters is a MOOD

[@imanabu5862]

I just love you man, I love what you do and I love how you make me love my major after I was traumatized by it in my freshman year ! I can't even express how thankful I am for all those youtube educators out here, they , and you Parth deserve all the credits❤️❤️🙏

[@alfredwilliamson9763]

It’s so helpful having someone who actually explains it all without assuming you already understand A level and university level Maths and Physics.

[@kumar7359]

Thanks Partha. I graduated in Electrical Engineering 35 years ago. Never worked in that field at all. I am right now so happy to revisit all that I studied long ago. Wish you the very best.

[@raghdaelraaie9335]

I just wanna say, Thank you so much for making those "the" wave equation videos 👏 because I really hated how our curriculum is so dull and abstract, but you made things so clear and sensible, especially with visual and analysis 👍

[@Kni90270]

Dear Parth, I should say you are the best person who clearly explains the basics of physics. I have a Phd and now I am recapping some basics from your fabulous videos :) best luck. You deserve more likes and subs.

[@yuvrajmurali8012]

Upnext : One Dimension Heat flow equation..... please!!

[@ParthGChannel]

Great idea, I'll add it to my list! Thanks

[@executorarktanis2323]

yeah please

[@cristianpaulnitulescu9715]

@@ParthGChannel please I beg you could you add einstein field equation on your list too

[@guitarttimman]

What is the first law of thermo-dynamics. LEARN THAT AND YOU CAN SOLVE ANY PROBLEM! (not really! I just typed that because it looks cool.) :-|

[@thewhizkid3937]

some thermodynanics would do.

[@abhishekprasad6350]

If anyone really want to learn what exactly differentiation is the you should what the calculus series of 3Blue 1Brown

[@ParthGChannel]

Agree!

[@SonuKumar-fm3jn]

Ok I am moving towards than.

[@informationparadox387]

Yeahhhh....Thats just Awesommmeeeeeee!!!!!!!😍

[@rajaradi802]

@@ParthGChannel Agree!

[@markbell339]

@@ParthGChannel Thanks for using the same car example to teach. Lots of people see it and you helped those people bridge the gap I think

[@JulianJawadAhmad]

You are truly a great explainer. There are very few people who can make basic things understandable so easily.

[@markbell339]

You helped me understand another reason for the standardized use of specific simplified scenarios - in this case using the position and speed of a car to teach derivatives. What a wonderful way to help people form interdisciplinary connections faster. Thank you for this video.

[@das250250]

Fourier series and transform :-)

[@curvebal]

Yes Fourier series and transforms appear frequently in chemistry and physics text books. Example is FTIR Spectroscopy

[@guitarttimman]

Fourier? Whart a joke. I suppose next you'll be telling me that there is a Fivier or Sixier series and transform! It doesn't exist? :-)

[@thewhizkid3937]

Linear Transformations lol ?

[@michiele3479]

@@guitarttimman It does exist. try to google it before making a reply

[@alirezanabavian771]

I am an electrical and electronics engineer myself and I have seen many professor's and highly talented engineers but hats off to you since your on my top list for the best instructor/professor ever seen..I really enjoy watching your videos..you are such A gifted talented technician ...and I by technician I mean the you have it in your DNA...so plz never stop what you're doing...

[@alirezanabavian771]

Plz omit " the " after "gifted "

[@drunkmadala]

At first I was intimidated by this complex equation; thanks to your explanations. I can't believe how simple this equation is.

[@MateusCavalcanteFonseca]

I see a lot of science videos for at least 10 years. Your explanation was one of the most powerfull, in regard to be understandable, i ever seen.

[@costbart]

I've been stuck with understanding the concept behind the equations, but it's quite intuitive when you think about it. Great video.

[@tejobhiru1092]

THANK YOU SO MUCH...!!!! i really appreciate how you broke down the concepts so the eqn makes 'physical' sense..!

[@watermelons2921]

This is one of the best descriptions of a derivative I've ever seen

[@user-fw9vf2or8f]

Loved it. Helped me restore my basic understandings which had gone all fuzzy.

[@richardhead8264]

_Parth, your cranial foliage is _*_glorious!!_* _And so are your explanations!_

[@Tom-sp3gy]

You are a genius at simplifying physics!!! Thanks a lot for all your great video uploads.

[@akshatnerella5995]

I have been searching for these kind of videos for a long time. I think I found the right one. Kep going

[@MrRickinVirginia]

I am very impressed with your ability to clearly explain the otherwise dense & complex nature of “elementary” physics. Gud on ya.

[@adochshanov]

Pretty clear, thank you very much. With this kind of videos for those who interested we'll make the World a better place to live in.

[@gavinyu6251]

I love you. Never stop making videos like these

[@sbergman123]

Thanks Parth. You are helping me out a lot with your videos. Math concepts are starting to click (And physics as well). I haven't done any decent math in waaaay over two decades and am currently reviewing undergrad precalculus (trig and algebra as needed) so I can sink my teeth back into calculus again. Your vids really deal with technical stuff in a down to earth and unpretentious (is that even a word? Lol), err ... simple manner. Hell, even at 55 it is never too late to learn.

[@calvinnewkirk4232]

Parth, as a non-physics student I have been trying to sit in on some open course ware physics classes. The prof obviously believes the students already understand what you just explained, because he doesn't explain it in his lectures. The students must get it from their books and homework which I do not have. I can't tell you how great it is to find this video. Now, I get what is going on in class. Thanks. Cal

[@alexandrvoronkov7530]

Thank U!!! I"m old pens from SPb ex-scientist microbiology with great pleasure to know a new branch of knowledge that I didn't know when I used to have a job

[@Juliandav0908]

First time I watch a video of yours. Bravo, great explanation. Keep it up.

[@stefan2028]

Thank you soooo much!! This is so helpful! The explainations are utterly great!

[@Someone-lf7iz]

This is the first video I've found that can explain things in a way that makes sense. I would pay you to do videos like this on discretization/finite differences with the linear advection equation, going into the modified wave number, truncation errors, etc. However, that might be a little specific to CFD, but maybe not after seeing this? Seriously though, I've been skimming through videos and content for weeks. This is the only video that made sense.

[@andreylima-geofisica1563]

Best explanation I have seen in a while. I am teaching seismic wave theory, in Portuguese though, but I am going to point your work for others. Thanks.

[@emrek473]

Great video! Loved the explanation, it was very understandable even for a second year high school student. Keep it up, love your videos!

[@ParthGChannel]

Thanks for watching, glad you could understand my ramblings :)

[@matthewcapstick6242]

Started calculus and series and I love it!

[@calvinjackson8110]

Well done. I will look at this again. I learned a lot. Thanks. It will help me teach so much better.

[@TheSIDHARTH007]

bro... You did great work... Appreciate your efforts..!!

[@youkaihenge5892]

Solving the Wave Equation with Fourier Series and Vectorspaces is really a great time! One problem takes like 1hr to do 😃

[@helmutalexanderrubiowilson6835]

As a teacher i must say you are a fantastic teacher. Very clear explanation you should consider to write a book filled with your colored drawings by hand and explanations of every detail... I will buy it for sure

[@lanaalabbasi5315]

Thank you! This video helped me a lot with my studies. Could you explain ladder operators and how they act on the harmonic oscillator?

[@abdelrahmanabdelalim4000]

That was really helpful. Thank you so much!

[@lameiraangelo]

Intuitive explanation... you're the best.

[@mohammadbinmahbub9160]

Thanks to this I have gone down the rabbit hole of PDE study. cool thang!

[@parthmahajan6057]

from one Parth to another, Thank you! i think you just saved me with my exam

[@umachandran1708]

Thank you so much Great explanation, very well protrayed with examples

[@nitengurung2288]

Such a beautiful explanation thank you so much

[@babayaga1698]

You could not explain this more easily...no one can...kudos.

[@cherishnnn237]

The best video ever! You are my life savior. Thanks

[@tobydunbar1153]

Parth, you're an excellent teacher!!! Your explanations are succinct, clear and very well presented!!! Thank you so much!!! I love your hair and beard, too!!!

[@noornedal4574]

in love with this video ... made alotaaaa sense

[@Marketspoons]

Could you explain methods used, to create or generate an equation to solve a problem you may come up against? Great video explanations top class! Thank you

[@whenwhathuh]

First, your videos are awesome! Second, I have an engineering degree and I'm sure there are plenty of other users on here who would like to hear more about the deeper math. So I would like to put in a vote for videos which are "way too advanced" :D

[@armandocastaneda1546]

Wow man I have to give it you this was an absolutely amazing explanation..

[@MartinStaykov]

Veery well explained, gave me a better intuitive understanding for what u is and why both sides of the equation have to be equal.

[@definty]

Hi P, I also love your explaining videos! Could you do a video on how lenses and optical zoom/binoculars work and why we can't/can have an infinite zoom? Thanks.

[@hasan1066]

I love the way you explain ❤

[@zahraaa59676]

this video felt like it was aimed to teach the physics side of waves more than math. And while I was looking for something for math, I loved this video. The explanation now makes me know what in the world I am actually solving, and it was an easy and nice briefing to make me even more ready to jump on the math side. And lets not forget the equation shown in the video with the detailed solution, which was super helpful. Now I basically just need to find examples and practice. fun fact: I watched this video in the middle of my math class because our teacher is quite hard to understand.

[@lored6811]

I was just researching this and didn't come further, thanks!

[@khalafjehadabed6776]

Thanks for your nice and crystal clear explanation

[@ihsanafeefapm9060]

you are too good in this manh.excellent explanation .just feels good

[@anthonyheak3479]

Parth, very well explained. Thanks!

[@taseenbanu3828]

Thank you so much for explaining us very clearly and very easily.Really all your vedios are very very interesting and helpful.

[@Oristes]

This was the best explanation of the wave equation that I could find. And you explained differentiation so clearly. Thank you so much for this. Do you have an explanation for the Schrodinger equation as well?

[@msibai]

Excellent.... simply marvelous

[@tapankumarbasu2901]

Very Good Explanation. D"Alembert's equation for wave propagation nicely explained.

[@Mulkek]

Thanks, and it's so easy & simple!

[@ishanagrawal922]

Such a brilliant teacher !!

[@yuvalashkenazy5778]

Great explanation, thank you!

[@giovannimariotte4993]

Look man i just dont know how to tell this...INCREDIBLE you gain a fan

[@anisahmed4799]

I, Dr Anis Ahmed , Professor in Medical College at Udaipur,Rajasthan,India following you since last 2 years. I fond of physics especially Quantum physics. Please make a video on quantum fields . Your way of explanation is excellent. Keep it up

[@omerabuagla427]

You are doing great things here 🔥🔥

[@omegab4856]

Amazing! Clear, focused and simplified.............Thank you! Just one follow up question, is it ok to have the "d/dt" in the Schrodinger stationary wave equation instead of the curly "d" that is used for partial derivatives? Thank you again.

[@Jehannum2000]

A truly excellent video. One suggestion I have is to copy-paste (or re-do) the section on differentiation into its own video. Subsequent videos involving calculus can reference this, removing the need for repetition.

[@sharat.achary]

So beautifully explained. Keep this going, amazing talent and wonderful educator. 👍 🤝

[@NedStarkZA]

Bro, I've been doing advanced math for a long time and I've always known that the derivative of sinx is cosx but never really interrogated why... now it makes sense!

[@renatolara1545]

This video kinda motivated me to study mathematics during quarantine

[@anitahill8801]

How did it go

[@shaileshverma7176]

Amazing work Parth!! Could you make a video for wave equation taking special relativity into account.

[@josemello649]

Thank you very much for this video.

[@gamerino1096]

bro I have my physics olympiads coming up and as a 9th grader, I found this video amazing as it was easy to understand

[@hasiburrashid1966]

Beautiful video...thank you!! Love from BANGLADESH ❤❤❤

[@ashishkumarvishwakarma4583]

Your explanation about the wave equation is really lucid and easy to understand. I have another topic for you to explain. Would you please explain the physical meaning of Maxwell's equations in both integral and differential form?

[@curtpiazza1688]

Great explanation...thanx!! 😊

[@salmanzafarsatti1346]

Great explanation. Actually I really like your screen explanation setup. Can you explain how you do this thing?

[@nobisphysics7651]

I want you to explain " The Standard model equations or Equations of everything in the Universe ." Otherwise Please explain the concepts Newtonian Physics , Relativity, & Quantum Mechanics in a serial order. If not possible then explain the Einstein's field equations.

[@alexandergarcia6479]

wave physics is the principle of quantum mechanics, you must to understand this first to understand quantum mechanics

[@ParthGChannel]

All great ideas! Thanks for commenting :)

[@nobisphysics7651]

@@alexandergarcia6479 I know but that's too basic. I want him to move forward explaining more concepts(in a series) rather than random equations.

[@thewhizkid3937]

Albert Einstein's field equations when solved, I believe there is like 10 of them, yield or rather give us potential interpretations and outcomes of our universe. It is wise to assume, we live in the multiverse, theoretically speaking and the colliding of universes is possible, but repulsion is also possible, given the laws of attraction.

[@ligasoofilms8033]

Your video is really amazing. I am not exaggerating. ❤️❤️❤️🎉❤️❤️

[@miladnaeimi1514]

Thank you. That was fantastic 👏👍

[@antaresguitar]

Very nice explained, thumbs up!

[@alokesarkar2793]

Excellent! Very easy explanation!

[@bananablood2031]

Beautiful explanation, mate

[@jaydasg6]

Pretty good, loved the simple way it is put up.How about discussing wave harmonics.

[@mevkenzieevorius6902]

Amazing explaination of differentiation

[@neilphilip2320]

Simply excellent!

[@tracytran1676]

Loved this video!!!

[@axelmeramas976]

Thank you for the great explanation , I would appreciate if you can explain Navier-Stokes equations please :)

[@mandresyfalimanana3538]

🌅🌅usefull for those who learns more about physics!!✨✨ thank youuu. This channel coud be an educational dream🌾

[@aamir122a]

Your explanation was very clear, as I understand we are taking the derivative twice, my question is what is the practical application of the wave equation, I mean the end game. My suggestion for all your videos would be to tie abstract concepts with some real-world applications.

[@ilikechopin8112]

Great explanation! 👏👏👏👏👏