# Basic Physics III Lecture 5

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No we will continue our discussion off A wave phenomenon and the 1st thing I'd like to talk about it A reflection of waves solidarity observation is that waves had an obstacle for the end of the medium all bond between media van our reflection of the yield curve which means that these waves reverses
At this this formula because we right just like this For putting BKX And the fine and parenthesis and that Basically just looks like a fixed Angle in this simple harmonic motion so we have basically simple harmonic motion With Some constant in here which is the base of the simple harmonic and northern what the velocity it's That's the symbol So assigned becomes a cosigner Andy A picture of when extra fact outside All we can added termed the acceleration Doing will time derivatives Drive this again and another Oh my God appears And the Becomes now a minus sign and we can then express the fact of The only way A case where time Wave velocity square So we ever get The sliver of Samaranch Just forget them as The article Velocity expression 8 times on KX bus bombing that he find drop 0 and X because now I am again considering any point since I can repeat this exercise for every such world it holds actually fall Point and symbolically right this is partial Derivative of the function was that time And begin ordered that Those for the meaning of this symbol a simple eating the same as the Uvalda Roberto but be that Where At 1 moment we only consider 1 particular position acts Exs Constant probably performed the time and zoom only the 2nd partial but time derivative are particle acceleration which has an air AT Omega square the miners Sun-Times signed KX on the phone And if you pick Away That goes in the opposite direction this 1 troubles actually From left to pick 1 the troubles right then To get very similar expressions only be a Iong ago on that term changes sign you get an extra side so of course we could do a lawyer A similar trip looking instead of At that time to look at The position from now need to focus on 1 instant in time and that confidence and And look At a pulse frozen in time for example the here and if it takes me a derivative of the talks with respect to lead Position than that This something like the smoke on March the pulse slopes forms on a positive slope of the negative somewhere over there would have to put on and The 2nd derivative the changeover And that is something like how much does the role And so I feel for example it doesn't have banded all year bands of it'll be formed from this direction that Up appear at the top it bends a lot because it goes from up to and this Curvature is important because it is actually defining how much for force Uh acts in the transverse direction on the part of transfers direction along with the sole either curvature you'll have more for us for example he would have a lot of curvature we have these Tension force going this way At this point in this way at that point and We combine those forces we get a lot of large Dong pointing transfer or if they have no curvature like healed Those 2 forces are cancel each other out There is no France was forced at all and if they have just a little bit of curvature here with the courage of The opens the other way and therefore the resulting forests pointing up but is smaller than at risk So in general and be the curvature is portion of the force or another words The transfer of course It a potential force times So we can then and a similar expressions for an open the forest For the year and velocity and that Acceleration of gold particles only that this time we to look at X rather than he gave ever similar looking expressions and again We make this funny symbol that We have a partial derivative with respect space and what it means is that while performing the Derivative a only look at 1 instant in time and There was some Osorio leaves at least goes to Formula 1 for time and the 1 of the space look for a similar adjusted different prefab solar before we had an armored square And now we have a case case square And These strong new ideas again for the right traveling so we can put this together with With A Newton's law which tells us that The last time acceleration equals force in this case must density times world Particles transfer Acceleration equals the transfer of force which is the tension force times the curvature and formally me right righted like this which is year the wave equation and this equation is valid actually for signed since they know all that This will last Which is the ratio of these tension force are divided by Masters 2 Yeah Can be also plays in the case of some sort of by the ratio of armor got the the angular frequency all the way and so this wave equation is fulfilled son Osorio and as it turns out It is fulfilled by any general calls U. And generally so what it should remember from from this Discussion he expression for the particle velocity and acceleration and the fact that We wave equation is nothing else But Newton's 2nd law that must density times particle acceleration for become tool and other characteristics But a Waves that all such immigration and that is the principal Superposition we can ask ourselves what happens if you have multiple waves that passed with the same regional space At the same time and that is called the principle of superposition what it means Is that became Simply add a bit deflections each of which awaits just like a are normal additional Displacement is a strictly true only for Libya medium and linear media there are those that result in a waiver creations like the 1 just what it basically means is that Wave speed is independent On things like the amplitude in such a case the sum of all wave functions of several wave functions Always away function also have formed the combined weight since buyers and the additional separate and in particular a multiple of functions also of between make this a bit more concrete by looking at the 3rd Demonstration program let's assume that we have told pulses that A trouble from a very to pollsters that trouble from the left and from the right of the green screen
Against each other It at church If you are The still see the components as the Bruins red But now they actually marriage and a former bigger pulse in the center and since then drifting apart after that They have penetrated childless If nothing has happened and that is another feature of linearly that waves are superimposed after that a more wrong occupy the same space they not changed So as not interest in case and that is what happens if 1 hole Pulse goes up and the other 1 goes down Look at that so rules The pool pulsed stays the same but the red pulse is now I actually Umberto what happens in that case on reviewed what happens in that Case They stop to cancel each other when they're just at the right position than they actually are Cancel each other out completely And this is called a destructive interference the other cases called constructive constructive interference leads to lots of calls destructive interference No pulse of all stories up chances Let's not look That at actual sign was so always And 1st sequences of Them going in the same age End What you are seeing where he is on the way Because the red Hiding under the green is actually sum of the text If now introduce a phase difference between those those wastes the blue and red mud can actually see both of them and they are still sort of Constructive interference because some of those most was bigger than you know 1 of them but as I'm increasing the phase Difference Between them And they have positive result in post Publicist get smaller and smaller until they can Other won't completely So this is Joe we'll have to wait and see but the resultant Almost The stress Let's go go back to that Point and we have a particular superposition which is called interference and Sort of several cases for me that have are cases where the police's and Hansel and we get a destructive and all are now where they cause vying to get constructive Also if We Phases Between them and any other Alberta among between expect Our cancelation perfect edition that we get possibly destructive and also After repulsive Nor on occupy the same space me I'm and continued their troubled just for what this
Superposition principle That makes possible
This we can actually make up that kind of Wave forms A sine wave although time For example if I had 1 sign that looks like that in the 2nd round that like that and the 3rd 1 that looks like that and they all add Together then we get a weird shaped pulses look like that it's almost like a sort All are different kind of these they can combine to make something that looks A similar to square all 1 can and look at it the other way and start the script calls Asked Oneself what kind of sign on a solid deal with the required to make up for that I have another program this kind of idea this is called full-year analysis of for
Just showed 1 instant so we have an old gear and have promote here and there 10 times now and the middle and a pencil Imagine way of continuing the best course not and not that as physical no but banned the distance from here to here would be the wavelength lambda and therefore the distance from him here just half of weight so in general the distance from from 1 note for note
The next known is one-half of The waves and the distance from an old twin and time is a quota of forward and since the yeah Ends fixed therefore that tool Knowles so a fundamental wavelength was given by the length equals Exactly 1 half of the late or the Lambda won the 1st fundamental wavelength must be equal Twice the length so that if you now will go to a higher order mode auto and all but told them that we pick up on additional node in the middle of summer we have a tool and time no and 1 over the middle and 1 Beginning in 1 order and so in this case LONDON tool is equal to the length of Mao the wavelength fits exactly Inside the little boundaries inside the length The World Solar member toll equals length and All we can also say that equal to twice the length Divided by tool so it's kind of like me fundamental wavelength divided by the number 2 We can then moved to the next hole but we have to know In the middle 2 at the end so for of together and the Yantai notes in between and get That wavelength Two-thirds But The length and Therefore we have land The equals at twice the length divided by sweet orange general The wavelength The end oldest twice the length of the world divided by some number and invert this But That'll get if he was seen as a creation a frequency Times uh Lambert equals velocity than we can get the frequencies associated with those wavelengths and we find that the old homes are integral multiples Of fundamental frequency and the fundamental frequencies Given by the varsity always twice
Animal trapping
Patch antenna
Funksender
Lint (software)
Scouting
Interstellar medium
Multiplexed Analogue Components
Source (album)
Magnet
Particle
Rope
Wavelength
Stardust (novel)
Binoculars
Plane (tool)
Book cover
Tool
Astronaut
Atmosphere of Earth
Crest factor
Electron energy loss spectroscopy
Linear motor
Phased array
Source (album)
Weapon
Wavelength
Gedeckter Güterwagen
Direct current
Weight
Phase (matter)
Cartridge (firearms)
Fahrgeschwindigkeit
Electronic media
Plane (tool)
Noise figure
Crest factor
Microwave
Linear motor
Hot working
Transmission line
Optical amplifier
Measurement
Particle physics
Audio frequency
Suitcase
Reflexionskoeffizient
Angle of attack
Fahrgeschwindigkeit
Buoy tender
Game
Refraction
Band gap
Microwave
Spare part
June
Extra-vehicular activity
Mass
Rain
Mast (sailing)
Ramjet
Pool-type reactor
Winter
Hue
Diffraction
Funksender
Refraction
Angle of attack
Audio frequency
Weather front
Sizing
Reconnaissance
Potenzialausgleich
Interstellar medium
Rope
Low-pressure area
Moving walkway
Reflexion <Physik>
Remotely operated underwater vehicle
Band gap
Workshop
Demultiplexer
Interstellar medium
Multiplizität
Hall effect
Particle
Gedeckter Güterwagen
Bird vocalization
Dynamische Lichtstreuung
Separation process
Rigging
Roll forming
Automatic Block Signaling
Tool
Solar energy
Electronic media
Atmosphere of Earth
Magnetic moment
Linear motor
Vehicle armour
Anti-lock braking system
Engineering fit
Pair production
FACTS (newspaper)
Wavelength
Density
Weight
Direct current
Phase (matter)
Lace
Cartridge (firearms)
Fahrgeschwindigkeit
Swimming (sport)
Frequenzumrichter
Electronic media
Gas turbine
Throttle
Jig (tool)
Stream bed
Particle accelerator
PIN diode
Screen printing
Microwave
Linear motor
Divergence
Optical amplifier
Year
Force
Particle physics
Microphone
Thor
AC power plugs and sockets
Band gap
Microwave
Spare part
Regentropfen
Harmonic
Particle displacement
Force
Particle
March (territory)
Transversalwelle
Light-emitting diode
Angle of attack
Audio frequency
Gemstone
Rope
Transfer function
Caliber
Membrane potential
Miner
Car bomb
Last
Magnetic moment
Tanning
Ruler
Interference (wave propagation)
Fur clothing
Pool-type reactor
Stress (mechanics)
Electronic component
Particle physics
Bird vocalization
Black hole
Wavelength
Separation process
Interference (wave propagation)
Interference (wave propagation)
Microwave
Hour
Astronomer
Cartridge (firearms)
Deck (ship)
Astronaut
Electronic media
Microwave
Linear motor
Weapon
Noise (electronics)
Kilogram
Order and disorder (physics)
Assault rifle
Pattern (sewing)
Turning
Wavelength
Dashboard
Tool
Videotape
Tone (linguistics)
Tin can
Transverse mode
Excited state
Wavelength
LORAN
Phase (matter)
Cartridge (firearms)
Electronic media
Mode of transport
Microwave
Resonance (chemistry)
Interference (wave propagation)
Transmission line
Audio frequency
Towing
Reflexionskoeffizient
Map
Interference (wave propagation)
Potentiometer
Microwave
Alcohol proof
Measuring instrument
String theory
Musical ensemble
Spare part
Mode of transport
Molding (process)
Mail (armour)
Lunar node
Fundamental frequency
Typesetting
Ballpoint pen
Electronic component
Cockpit
Resonance
Cellular manufacturing
Cogeneration
Audio frequency
Ship
Interference (wave propagation)
Potenzialausgleich
Ground effect vehicle
Low-pressure area
Reflexion <Physik>
Gamma ray
Movement (clockwork)
Order and disorder (physics)
Summer (George Winston album)
Particle physics
Multiplizität
Wavelength
Automobile
Tool
Solar energy
Crystal twinning
Lunar node
Fundamental frequency
Pair production
Transverse mode
Pencil
Lambda baryon
Black hole
Wavelength
Audio frequency
Weight
Cartridge (firearms)
Fahrgeschwindigkeit
Automobile
Mode of transport
Fundamental frequency
Lunar node
Microwave

 Title Basic Physics III Lecture 5 Title of Series Basic Physics III Part Number 5 Number of Parts 26 Author Smy, Michael License CC Attribution - ShareAlike 3.0 Unported:You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license. DOI 10.5446/12941 Publisher University of California Irvine (UCI) Release Date 2013 Language English

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