To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.
group velocity is parital derivative of angular frequency over wave number, without undurstanding it, i don't think you deeply get it. The video barely shows superposition of waves and it only works in linear case.
You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: czcams.com/users/timedtext_video?v=EIqKG5TiSYs&ref=share You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit buttons for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.
Impeccable timing! I'm working on various numerical schemes for ocean wave propagation for a videogame, and revisiting the very core physical principles at play is usually where the inspiration comes from. Thanks for bringing wave dispersion into focus, it's helping me out in think more clearly about difficult topics like error buildup and numerical dispersion artifacts.
WOW. Just wow. I dont think that this could have been explained more clearly. Thank you sooo much, this has helped tremendously! Keep up the good work and consider me subscribed
As always, you manage to describe these ideas with great clarity and precision. I much prefer your videos over videos of some guy waving his hands while trying to articulate these ideas in a "personal" way.
Well done sir u cleared a lot of my concepts. May u live long. Please now make a video on photo electric effect. Where we could visualize the photons coming with frequency same with the frequency of the valence electrons and then their collisions and see how photons of identical frequency push electrons from a metal surface by colliding with the electrons. And also dont miss to make a visualization of threshold frequency
Thanks. I will add the photo electric effect to my list of topics for future videos. Though, I briefly talk about the photoelectric effect in my video on nuclear physics at czcams.com/video/r40h66qiF5I/video.html
Very elegant explanation of how "wave-like" particles, such as those emitted by the sun during coronal mass ejections, travel at a speed 1000 times slower than the speed of light, yet have eerie, shimmery, wave-like behavior as they interact with the earth's magnetic field. There are few things readily visible in nature that travel at a speed in the middle of the continuum between the Newtonian realm and the relativistic realm, and also roughly in between quantum dual wave-particle realm, and the more strictly particle-like macro paradigm. Explains why auroras are very strange and complex.
Thanks a lot! That is definitely an important video to understand this concept of wave velocity. I know you have millions of videos planned ahead already. But I just want to suggest that maybe you make more videos on solid-state physics, I think this is a huge part of physics that many students have problems with. I hope that in the future I'll see here videos about the Bloch wave, tight and weak binding, Brillouin zone, charge traps, more semiconductor physics and so on. That would be a dream come true! Thanks for what you're doing!
I know I'm commenting on a 2 year old comment but I study chemistry and my professor deduced the Bloch Theorem via Group Theory for us. Afaik it is usually taught different in the physics world and imo it is much simpler and more elegant via group theory. I also would appreciate more videos on solid state physics but I appreciate any video this channel uploads really.
"when we have a wave describing a quantum particle, it is the group velocity that determines the velocity of the particle." This statement could use some further clarification, in particular in regards to the semantics of a particle's velocity. The total superposition is what is used in Born's rule, and this is the case whether we look at the position or momentum basis for the wavefunction. The wavefunction represents a wave of probability (e.g. the probability of a given configuration for a given particle), and in terms of the momentum basis, the group velocity refers to the location of the relevant envelope that covers the regions where the particle's momentum is most likely to be, even though the actual value of the momentum upon measurement may be any value given non-zero probability by the wavefunction.
Exactly why I believe a mining tool can be created from waves...and why wave forms planes are a future general purpose product...literally your channel is what schools need desperately, classes can be augmented to allow for tablets and students can be free to explore, and now be tied to a class room
I really like your awesome animations. Can we please see a standing wave that results from waves of different amplitude and/or different wavelengths going in opposite directions?
This is not exactly what you are asking for, but I have a video on the polarization of electromagnetic waves at czcams.com/video/8YkfEft4p-w/video.html
Subconsciously ..As your back round music suggests an orchestra conductor is essentially the wave keeper. Whaling his hands about the air I guess isn’t purposeless. Seeing this video is when it dawned on me why he probably does this. As I may be wrong knowing nothing about an orchestra per say this video gave me an ahh hah moment. ..so. Different sounds aka groups of instruments must be kept in the same wave pattern to keep the flow moving smoothly. Since the person playing an instrument can only tune in on his particular wave sound. The visual affect of the conductors arms allow every one to know where the are in the wave. Keeping everyone in sync and making sure every one “goes with the flow”
This phenomenon is cited as reason for slower speed of light in glass in a fermilab video. Can light induce secondary EM waves in glass and move at slower group velocity.
Uncle Garfield i was studying for my medical entrance exams. It was then when i came across these videos. I loved them, made me understand the depth of physics. But now since I am already in 3rd year of medicine and my country probably doesn’t work like that so idk if I can do that.
Don't forget that physics includes a lot of mathmatics. Understanding the consequences (these videos) is only a small part of what you must do as a physicist. So before changing your life/study be sure you love math ;) and have some talent in it, cause otherwise wou will regret your decision for the rest of your life.
It is never too late to get into physics. Do what you can, when you can. You may not be able to dedicate your life to it right now, or perhaps ever, but you'll be able to give it a place, and let it grow from there. :)
Thank you Dr. Khutoryansky! Because waves have the capability of carrying information, can complex packages of mathematical information be preserved in a wave form for very great distances? Or will the information degrade over the dispersion lifetime of the wave? How can a transmission into deep stellar space be preserved and transmitted without replicative fade or degradation? Certainly a carrier frequency of the magnitude required to send a package, would also disrupt or destroy the package by the very nature of its amplitude. Thank you Sir! Mr. Fractal
it's very bizarre that the physical waves (sound waves, ocean waves, waves in a string or rope) have any similarity whatsoever with that of quantum waves
It's not bizarre actually. Any wave phenomena can be written in the form of wave equation. It is the same equation, whether it be for electric field in EM waves, or pressure in sound. Dirac and Schrodinger equations for the quantum wavefunctions, are also very similar to the wave equation. It's called "wavefunction" for a reason, right?
No it really is bizarre considering that there is no actual wave. So why would it behave as a wave? Maybe they're is some unknown particle that will help explicate though, like the x17 which may have an interaction with light and electrons at high energy.
My dude, Fourier transform and wave equation are different things. Fourier transform lets you express literally any function as a linear combination of sinusodials. Whereas wave equation is a type of partial differential equation and not every function can be a solution of it. EM waves, sound waves, quantum wavefunctions etc. can be Fourier transformed, yes, but they also obey a certain wave equation. In fact, if you Fourier transform the wave equation, what you get is a Helmholtz equation. We use Helmholtz equations to analyse EM waves in frequency domain.
@@GabrielCazorlaPersson1 just to be clear, particle shows effect of behaving as a wave. Every time you observe there is a particle, not a wave. Believing in actual waves is unscientific. That's the only thing quantum mechanics proves until the source of the wave-like behavior can be found. When it is, it will still be true that waves are composed of particles, and those are what interacts, and you don't have any mathematics before the universe decides what to build with them.
@Marko The particles behave as if they are following waves. But there are no waves. EM waves do not exist. Only electrons and photons. There may be an x17 particle that might help explain their behavior though.
I have many videos on waves. Some of them are listed below: Waves: Light, Sound, and the nature of Reality -- czcams.com/video/Io-HXZTepH4/video.html Diffraction interference patterns with phasor diagrams -- czcams.com/video/NazBRcMDOOo/video.html Polarization of Light -- czcams.com/video/8YkfEft4p-w/video.html Quantum Wave Function Visualization -- czcams.com/video/KKr91v7yLcM/video.html Phase Velocity versus Group Velocity -- czcams.com/video/EIqKG5TiSYs/video.html Art made with wave interference -- czcams.com/video/_7XNu2lUKIA/video.html Sonic Boom -- czcams.com/video/lGlyNl1srAc/video.html Electromagnetic Waves -- czcams.com/video/W1cTpqM9DaU/video.html Beat Frequency -- czcams.com/video/lH6hRdmY0DY/video.html
Yeah, I am sure Fourier had a solution for this. It is not too complicated, you can roughly even start matching waves to the group wave by your eye, starting from the biggest wave you can fit in it, then scrap the rest and fit smaller ones in it, etc.
Yes that algorithm is Fourier transform. You put in a given wavefrom and it gives the amplitude of different component plane waves of each possible wavelengths.
To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available).
--To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable.
--To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video.
--If you believe that the translation in the subtitles can be improved, please send me an email.
I play these videos on the big screen in the waiting room at my dental office so my patients forget all about the terror that awaits them.
That is cool man!
Making the world smarter, one patient at a time.
I practice the Standing Wave form at the Doctor's Office.......I stand up and wave goodbye before the appointment!
Haha
@@RadioReprised that's the best.
I like to wave at people. Even better is when they wave back. I love that.
If you wave at each other at the same speed you cannot move because it is a standing wave.
@@germanvisitor2 I thought a standing wave is when you stop walking to wave so they can see you better.
Me two! And scientifically, that is plausible lol
@@germanvisitor2 maybe if you move your observation point relative to your hands lol
Oh how I wish I could have seen that simple animation of phase vs group when I was an undergraduate!
Undergrad here, can confirm it is very useful!
@@millieh3179 Even more jealous now! Glad that it is helping you though. Good luck with your course Millie.
@@millieh3179 Ditto.
Almost managed to understand this through though process, then i came across this video which cleared further doubts.
Hey neil, you are sooooo correct.
I knew about group velocity... now i understand it. You couldn't explain it better than this! Great job!
Thanks for the compliment.
group velocity is parital derivative of angular frequency over wave number, without undurstanding it, i don't think you deeply get it. The video barely shows superposition of waves and it only works in linear case.
Last 5 seconds explained to me more about "Standing Waves" then entire books!!!
I am glad the last 5 seconds were helpful. Thanks.
You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:
czcams.com/users/timedtext_video?v=EIqKG5TiSYs&ref=share
You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit buttons for both the title and for the subtitles, as they are submitted separately.
Details about adding translations is available at
support.google.com/youtube/answer/6054623?hl=en
Thanks.
Hi, thanks for your videos! Do you need volunteer programmer for your videos?
k a, No. Thanks for the offer, but I make all the animations myself. I am glad you like my videos. Thanks.
I need vietsub 😢😢😢
Does the "group velocity" of component waves explain why light seems to slow down and photons seem to change direction when moving through glass?
@@tom_something Yes. Original EM wave passing through electrons create a second wave. The resulting wave is slower than the original.
Impeccable timing! I'm working on various numerical schemes for ocean wave propagation for a videogame, and revisiting the very core physical principles at play is usually where the inspiration comes from. Thanks for bringing wave dispersion into focus, it's helping me out in think more clearly about difficult topics like error buildup and numerical dispersion artifacts.
The gold standard for explaining and visualizing math & physics since video #1.
Thanks for the compliment.
WOW. Just wow. I dont think that this could have been explained more clearly. Thank you sooo much, this has helped tremendously! Keep up the good work and consider me subscribed
Thanks for the compliments. I am glad my video was helpful and I am glad to have you as a subscriber.
This is a really helpful animation for a hard-to-visualize topic, thanks so much!
Thanks.
As always, you manage to describe these ideas with great clarity and precision. I much prefer your videos over videos of some guy waving his hands while trying to articulate these ideas in a "personal" way.
Thanks.
Well done sir u cleared a lot of my concepts. May u live long. Please now make a video on photo electric effect. Where we could visualize the photons coming with frequency same with the frequency of the valence electrons and then their collisions and see how photons of identical frequency push electrons from a metal surface by colliding with the electrons. And also dont miss to make a visualization of threshold frequency
Thanks. I will add the photo electric effect to my list of topics for future videos. Though, I briefly talk about the photoelectric effect in my video on nuclear physics at czcams.com/video/r40h66qiF5I/video.html
ありがとう
こんな良い動画が見れる事がとても嬉しいです
As usual, better than any other explanation on the whole internet.
Thanks.
OMG ...it is the first time to know that the standing wave is produced with this technique
this gave me a WAVE of inspiration
@Bob Trenwith well, my brain FUNCTION still works
Yes you finally made a new video! I love your stuff so much!
Thanks.
@Bob Trenwith Haha true I had missed those!
Thank you, Eugene and Kira for your amazing work on these videos!
Thanks.
Very elegant explanation of how "wave-like" particles, such as those emitted by the sun during coronal mass ejections, travel at a speed 1000 times slower than the speed of light, yet have eerie, shimmery, wave-like behavior as they interact with the earth's magnetic field. There are few things readily visible in nature that travel at a speed in the middle of the continuum between the Newtonian realm and the relativistic realm, and also roughly in between quantum dual wave-particle realm, and the more strictly particle-like macro paradigm. Explains why auroras are very strange and complex.
Your videos always mesmerizes me. One more great video. Thankyou.
Thanks. Glad you like my videos.
Thanks a lot! That is definitely an important video to understand this concept of wave velocity.
I know you have millions of videos planned ahead already. But I just want to suggest that maybe you make more videos on solid-state physics, I think this is a huge part of physics that many students have problems with. I hope that in the future I'll see here videos about the Bloch wave, tight and weak binding, Brillouin zone, charge traps, more semiconductor physics and so on. That would be a dream come true!
Thanks for what you're doing!
Thanks. Solid state physics is on my list of topics for future videos. I will add all the topics you mentioned to the list too. Thanks.
I know I'm commenting on a 2 year old comment but I study chemistry and my professor deduced the Bloch Theorem via Group Theory for us. Afaik it is usually taught different in the physics world and imo it is much simpler and more elegant via group theory. I also would appreciate more videos on solid state physics but I appreciate any video this channel uploads really.
sir , no words , only standing ovation to u
Thanks. Glad you liked my video.
"when we have a wave describing a quantum particle, it is the group velocity that determines the velocity of the particle."
This statement could use some further clarification, in particular in regards to the semantics of a particle's velocity.
The total superposition is what is used in Born's rule, and this is the case whether we look at the position or momentum basis for the wavefunction. The wavefunction represents a wave of probability (e.g. the probability of a given configuration for a given particle), and in terms of the momentum basis, the group velocity refers to the location of the relevant envelope that covers the regions where the particle's momentum is most likely to be, even though the actual value of the momentum upon measurement may be any value given non-zero probability by the wavefunction.
Please never stop posting please
More videos are on their way. Thanks.
@@EugeneKhutoryansky thats awsome
I always get excited when I see you post a new video! thanks!
Thanks.
Who else has nothing to do with physics but watched these just for fun
Aha! So I'm not the only one. I finished writing my final test two weeks ago, now I keep watching for fun.
I also watch it for fun and knowledge
I am a dentist 😂
@@efeplevneli9063truly
Oo
Exactly why I believe a mining tool can be created from waves...and why wave forms planes are a future general purpose product...literally your channel is what schools need desperately, classes can be augmented to allow for tablets and students can be free to explore, and now be tied to a class room
Thanks.
I never knew that there's a term for the speed of the regular sine waves and the speed of the resultant wave
This channel is eligible for minimum 1MILLON views and subscribers
Thanks for the compliment.
The behavior of waves can be counter-intuitive, your visualizations help to get a better grasp of the subject.
Thanks.
I never understood this in school. Thanks for the good visualizations.
Thanks.
Best CZcams channel ... Love to learn from your videos.
Thanks for the compliment.
So nicely described..now all my doubts get cleared.. feeling lucky to subscribe this channel. Thank you Eugene and Happy New year.
Thanks. Happy New Year.
liked before watching just by looking at thumbnail
edit: too good, just too good.
thank you thank you thank you
Glad you enjoyed my video.
Wow now the imagination comes into existence with the help of these videos
best channel on youtube
Thanks for the compliment.
These animations are just beautiful.
Thanks.
Eugene thank you so much for this video!
This is an eye-opening animation!
Glad you liked my video. Thanks.
thanks eugene :D
You are welcome and thanks.
Great work. I like they way you provide an intuitive understanding of some very complex phenomena.
Thanks for the compliment.
NIICEEE. Been waiting for this! Thank you!
Thanks.
It seems that this would account for the occasional roque wave at sea.
Exactly!
I wish I had this video back in 2009 when I was studying at uni! I would end up being a scientists.
Excellent, as always. Can't wait for more :)
Thanks.
It's like how a "traffic jam" propagates backwards while cars drive forward.
I really like your awesome animations. Can we please see a standing wave that results from waves of different amplitude and/or different wavelengths going in opposite directions?
Very nice explanation. Thank you very much.
Thanks. Glad you liked my explanation.
@@EugeneKhutoryansky can you make a video about TEM, TE and TM wave propagation i guess this waves needs visualiton for better understanding.
This is not exactly what you are asking for, but I have a video on the polarization of electromagnetic waves at czcams.com/video/8YkfEft4p-w/video.html
Thanks, and it's so easy & simple!
Thanks.
I love all your videos they got me through college
I am glad to hear that my videos have been useful. Thanks.
Спасибо Евгений, как всегда отличное видео!
Спасибо.
Extraordinary as usual
Thanks for the compliment.
Very useful for better understanding passive-seismic physics
Thanks.
You're work is fantastic
Thanks for the compliment.
Looking at the comments while the video is playing
You were awesome, you are awesome, you will be awesome... Thanks :)
Thanks for the compliment.
Nice! Go Eugene go! Love these
Thanks.
great video as always! Helps immensely with gaining intuition while studying.
Thanks.
Such a great video. Thank you so much for making this video❤️❤️🔥
Subconsciously ..As your back round music suggests an orchestra conductor is essentially the wave keeper. Whaling his hands about the air I guess isn’t purposeless. Seeing this video is when it dawned on me why he probably does this. As I may be wrong knowing nothing about an orchestra per say this video gave me an ahh hah moment. ..so. Different sounds aka groups of instruments must be kept in the same wave pattern to keep the flow moving smoothly. Since the person playing an instrument can only tune in on his particular wave sound. The visual affect of the conductors arms allow every one to know where the are in the wave. Keeping everyone in sync and making sure every one “goes with the flow”
Another work of art. Thanks!
Thanks.
Good video for understanding before studying waves in physics
Thanks.
Very Very Amazing! God bless your soul.
Thanks. I am glad you liked my video.
This phenomenon is cited as reason for slower speed of light in glass in a fermilab video. Can light induce secondary EM waves in glass and move at slower group velocity.
Love your videos.
seen all
Thanks. I am glad to hear that you have watched all of my videos and that you like them. Thanks.
highly effective educational material. thank you.
Thanks for the compliment.
Can you explain in brief(somewhat intuitively) that why in case of electrons the shorter wavelength waves are faster but opposite in water waves.....?
★★★★★(10/5)
Great! Very nice job! Thanks! You are the better animator!
Thanks.
You made me love physics but now i am studying medicine coz it was too late to get into physics
Uncle Garfield i was studying for my medical entrance exams. It was then when i came across these videos. I loved them, made me understand the depth of physics. But now since I am already in 3rd year of medicine and my country probably doesn’t work like that so idk if I can do that.
Don't forget that physics includes a lot of mathmatics. Understanding the consequences (these videos) is only a small part of what you must do as a physicist. So before changing your life/study be sure you love math ;) and have some talent in it, cause otherwise wou will regret your decision for the rest of your life.
It is never too late to get into physics. Do what you can, when you can. You may not be able to dedicate your life to it right now, or perhaps ever, but you'll be able to give it a place, and let it grow from there. :)
очень интересно и наглядно! большое спасибо!
Thank you Dr. Khutoryansky!
Because waves have the capability of carrying information, can complex packages of mathematical information be preserved in a wave form for very great distances? Or will the information degrade over the dispersion lifetime of the wave? How can a transmission into deep stellar space be preserved and transmitted without replicative fade or degradation? Certainly a carrier frequency of the magnitude required to send a package, would also disrupt or destroy the package by the very nature of its amplitude.
Thank you Sir!
Mr. Fractal
Amazing explanation
Thanks. I am glad you liked my explanation.
Your work is amazing Eugene thank you for doing this. (:
Thanks. Glad you like my videos.
you are the goats
Thanks.
You're early, it's not xmas yet!
I wish there is a site that add waves on different amplitudes and phase velocities to enjoy the resultant wave randomness
Brilliant - absolutely brilliant.
Thanks for the compliment. Glad you liked it.
Thank you for this miracle!!!
Thanks.
So group velocity can be faster then light
it's very bizarre that the physical waves (sound waves, ocean waves, waves in a string or rope) have any similarity whatsoever with that of quantum waves
It's not bizarre actually. Any wave phenomena can be written in the form of wave equation. It is the same equation, whether it be for electric field in EM waves, or pressure in sound. Dirac and Schrodinger equations for the quantum wavefunctions, are also very similar to the wave equation. It's called "wavefunction" for a reason, right?
No it really is bizarre considering that there is no actual wave. So why would it behave as a wave? Maybe they're is some unknown particle that will help explicate though, like the x17 which may have an interaction with light and electrons at high energy.
My dude, Fourier transform and wave equation are different things. Fourier transform lets you express literally any function as a linear combination of sinusodials. Whereas wave equation is a type of partial differential equation and not every function can be a solution of it.
EM waves, sound waves, quantum wavefunctions etc. can be Fourier transformed, yes, but they also obey a certain wave equation.
In fact, if you Fourier transform the wave equation, what you get is a Helmholtz equation. We use Helmholtz equations to analyse EM waves in frequency domain.
@@GabrielCazorlaPersson1 just to be clear, particle shows effect of behaving as a wave. Every time you observe there is a particle, not a wave. Believing in actual waves is unscientific. That's the only thing quantum mechanics proves until the source of the wave-like behavior can be found. When it is, it will still be true that waves are composed of particles, and those are what interacts, and you don't have any mathematics before the universe decides what to build with them.
@Marko The particles behave as if they are following waves. But there are no waves. EM waves do not exist. Only electrons and photons. There may be an x17 particle that might help explain their behavior though.
Amazing! Thank You👍
Thanks. Glad you liked my video.
Thank you, thank you so much!!!
You are welcome and thanks.
Wow.. Just amazing
I am glad you liked my video. Thanks.
Thanks for the video!
Thanks.
please more video of waves… they are very difficult too imagine
I have many videos on waves. Some of them are listed below:
Waves: Light, Sound, and the nature of Reality -- czcams.com/video/Io-HXZTepH4/video.html
Diffraction interference patterns with phasor diagrams -- czcams.com/video/NazBRcMDOOo/video.html
Polarization of Light -- czcams.com/video/8YkfEft4p-w/video.html
Quantum Wave Function Visualization -- czcams.com/video/KKr91v7yLcM/video.html
Phase Velocity versus Group Velocity -- czcams.com/video/EIqKG5TiSYs/video.html
Art made with wave interference -- czcams.com/video/_7XNu2lUKIA/video.html
Sonic Boom -- czcams.com/video/lGlyNl1srAc/video.html
Electromagnetic Waves -- czcams.com/video/W1cTpqM9DaU/video.html
Beat Frequency -- czcams.com/video/lH6hRdmY0DY/video.html
Very useful
Thanks. Glad to hear that.
Great visualization
Thanks.
Thanks, it was helpful 🌹
Glad to hear that. Thanks.
Superb video
Thanks. Glad you liked it.
Nice explanation
Thanks.
Perfect. I can use this.
Thankyou sir.... Again as always your video helped alot to build the concepts... Please make video on space time curvature.
I am glad to hear that my videos are helpful. Thanks.
Just as I was thinking where I can find a video with the most "wave"..
Is there some kind of algorithm or something, that can de-construct the "resulting wave" into its many "component waves"?
Nice question. I'll wait for an answer too
Like Fourier transform?
Watch 3Blue1Brown's videos on Fourier Transform if you want some high quality animation, he does a great job explaining that concept
Yeah, I am sure Fourier had a solution for this. It is not too complicated, you can roughly even start matching waves to the group wave by your eye, starting from the biggest wave you can fit in it, then scrap the rest and fit smaller ones in it, etc.
Yes that algorithm is Fourier transform. You put in a given wavefrom and it gives the amplitude of different component plane waves of each possible wavelengths.
Hi Good evening from India
And good afternoon from France 😜
@Robert Rodgers the earth is therefore not flat? 😂
Good morning from Asheville North Carolina USA
@Robert Rodgers been there hell yea have family in marion
Good afternoon from Egypt
I frequently think about waves
Why is phase velocity greater than the speed of light and yet does not violate any principles ?
We want this we need this. ty
Very nice
Got a new subscriber 😄
Glad to have you as a subscriber.
@@EugeneKhutoryansky yepp 🇮🇳