Basic Physics III Lecture 4

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Basic Physics III Lecture 4
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Nut (hardware) Hot working Cosmic distance ladder Day Harmonic Local Interconnect Network Lapping Force Particle physics Spring (season) Wire Rope Mask Microwave Roll forming Wavelength Orbital period Crest factor Engine displacement Mast (sailing) Telephone Progressive lens Audio frequency LORAN-C Steel Combined cycle Force Cocktail party effect Kopfstütze Cogeneration Becherwerk Density Fahrgeschwindigkeit Cartridge (firearms) Ammeter Caliber Book design Wind wave Movement (clockwork)
Cosmic distance ladder Bottle Will-o'-the-wisp Bauxitbergbau Visible spectrum Force Particle physics Negativer Widerstand Spring (season) Rope Roll forming String theory Orbital period Nanotechnology Telephone Regentropfen Steel Tool Year Cocktail party effect Drehmasse Interval (mathematics) Direct current Astronomer Fahrgeschwindigkeit Cartridge (firearms) Tram Transfer function Caliber Wind wave Last Movement (clockwork) Flight information region
Theory of relativity Oncotic pressure Barrel Dipol Spring (season) Rope Wavelength Laser Transversalwelle Atmosphere of Earth Crest factor Engine displacement Sedan (automobile) Sound Year Cocktail party effect Power (physics) Source (album) Density Direct current Cartridge (firearms) Fahrgeschwindigkeit Sewing needle Ammeter Food storage Funkgerät Cosmic distance ladder Pulse-amplitude modulation Boat Force Presspassung Wire Shadow Arbeitszylinder Video June Hose coupling Mast (sailing) Air compressor Bulk modulus Kilogram White Microscope Chandrasekhar limit Atmospheric pressure Tram Wind wave Water vapor Model building Atmosphere of Earth Last
Boat Amplitude Crystal structure Negativer Widerstand Presspassung Spring (season) Tin can Oceanic climate Transversalwelle Rail profile Book design Atmosphere of Earth Lumber Sensor Optischer Halbleiterverstärker Year Locher FACTS (newspaper) Interface (chemistry) Tram Moving walkway Transfer function Mint-made errors Caliber Noise figure Water vapor Wind wave
Doorbell Density Semi-finished casting products Tool Fahrgeschwindigkeit Active laser medium Presspassung Material Cable
Funkgerät Cosmic distance ladder Will-o'-the-wisp Grey Bomb Geokorona Amplitude Desertion Mitsubishi A6M Zero Bird vocalization Separation process Roll forming Orbital period Mast (sailing) Audio frequency Pulse shaping Tool Intensity (physics) Sensor Optischer Halbleiterverstärker DVD player Year Presspassung Cocktail party effect Power (physics) Answering machine Source (album) Kopfstütze Seeschiff Density Direct current Pulp (paper) Fahrgeschwindigkeit Moving walkway Caliber Wind wave Power supply Ground (electricity)
Cosmic distance ladder Tiefdruckgebiet Harmonic Vehicle Amplitude Force Minute Couch Horn antenna Bird vocalization Wavelength Spare part Orbital period Anvil Hose coupling Engine displacement Linear motor Lumber Audio frequency Typesetting Textile Pulse shaping Initiator <Steuerungstechnik> Bus Magnetic core Optischer Halbleiterverstärker Kilogram Cord (unit) Cocktail party effect Pair production Wavelength Density Moon Fahrgeschwindigkeit Cartridge (firearms) Ammeter Caliber Silo Wind wave Miner Last
Typesetting Audio frequency Mat Hot working Magnetic core Amplitude Schwimmbadreaktor Cord (unit) Energy level Mitsubishi A6M Zero Measurement Phase (matter) Angle of attack Moon Phase angle Fahrgeschwindigkeit Cartridge (firearms) Ammeter Miner Gradient Wind wave Engine displacement
So I Today we will be starting the 2nd chapter in the book about Wave motion and the picture showing
Actually from what tsunami 1 of the more dangerous A kinds of emotions
So last time I assure you that if you take a steel wire and supplies some tension then that it is Top of translating waves and you can actually see that In She also showed this little a demonstration program that illustrates how this Labor movement progress and it's very important for ways to distinguish between the emotions of the EU each piece of role just which just goes up and down and not left or their left to the left and right just goes up and down but the combination of our off all that bad up-and-down movement on each of the pieces of roles actually creates a movement of the entire thing which is then called the ways seems to be moving to the right If I moved malls Honda and was of particular point Then this little on top him actually shows you how bad the displacement at that point as a function of time so when it's greeted means it's deflected OpenWindows red means it's deflected down and you can see that each in the case of this place that each of These pieces of rope actually undergoes A simple harmonic motion a sort of try and move the mouse bundled list the ways You see the Displacement has remains roughly constant so coming back To Libya to experiment of about 2 days ago The yeah As A rate velocities Different from the velocity of course and can characterized the and just like we did for simple harmonic motion by their various prominent us we did Define amounted to which is the maximum deviation from the rest position can define the wavelength purchase the distance phone Pressed Crest often profit dropped And as it happens to you gonna be waived troubles 1 distance of land in the time that it takes for each of the pieces of rope Complete 1 Period of simple harmonic motion Trouble out by 1 lap and the time period of tea and therefore we can measure the speed The which the crests trouble with Velocity is simply the frequency times wavelength off wave at the and divided by the period since the frequencies in inverse of the period those will formulas are equivalent IV A driving force behind the movement of the wave is actually the attention and the wire so as to parameters that determine this speed of the way 1 missed this tension and the other I Sort of work hairdresser masts and the problems with the in Britain and in this case it's not a mosque the mask from us density so are all marched programs for each Meters of rope and just like had the angular frequencies career being related to the ratio The spring constant divided by master so in this case the velocity of The waves Square is a ratio of the tension for divided by D My density That is a very similar booking form so the next thing we might ask ourselves is
Can be actually derived this formula from my from long and Turns out to be not so hot we simply assumed that His 2nd drop If we we ignore the force and At a certain time period called Little here then the product of those still must be the changes moment when out form of crime and law And from this little graph concede that the ratio between detention for between the Force among the and perpendicular to the world is similar to the um Grace off of This Distance here Which is proportional to the velocity of the and there is this Portions of richest proportional to the runoff velocity of a piece of rope And I to know that Those forces are now have the same ratio as a ghost will distances we can then calculated what is These are accelerating for In the transverse direction and simply knowingly kid you must for this Problem which is simply a distance Tee times master For that gives us the Mosul that piece of rope and Every arrived with this equation is this ratio of boastful gossip and this The master and this is the year velocities Together Those tools are the changes memento momentum equals Last time velocity and in this equation have heavily prime on both sides here so that cancels out and also the T councils on when sold for tension force them to get their attention force divided Marston that gives us Not so that is how 1 can understand phone so I I showed you a transfer rate last time with a steel I will try to show you now longitudinally which is a little bit harder demonstrated so he I have my long sprained suspended by these areas
Pieces of string and now I will try and excited traveling spring Can sort of see it traveling back and forth Little changed ascensional So in this The movement of their piece of spring is in the same direction as the movement of the way they're still different movements because obviously an area Ultimately the spring doesn't move it each each bottle just oscillate spectrum for try this again this time with a little bit more attention and sort of a wave traveling Saying that What In this case the emotional of the wave is in the same direction as each piece of spring for each use of Spring moves back and forth in this direction and the wave troubles as a whole in the wild for the transfer was where you are It was that These emotional each piece of World perpendicular to most of the way so added
Those are at different heights Waiver summerize it again so I would try and Will this spring like this and you see that awaits trouble perpendicular To be era's most of each piece of spring well in this case It goes in the same direction and soaring And this case You can sort of see a distortion or bring Is this year compression and expansion of them both Cases We have a formula like this where the velocity is given The attention although we mustn't for longitudinal a way it tends to be something like Some elastic modulus divided by the density of some old model Depending on what exact know it's so if I go back to minor simulation program again kindly provided by a task is still running you can simply at 112 a lonely putting away where for ease of representation at the displacement is is still indicated by On this acts as well But the little barrels Tells tell you how each Piece of rope On Turkey's offspring in this case is moving So typical example off Between the laser passed away For example a solemn and what does sound ended on speak of for example in this case a produces It is volumes of Compressed And rarified enough so that sort of indicated But Stopping shadow of regional like show regions On the slide in so they add They alternate in those volumes of Compression then that will want the left The right and the wavelengths is given in this As distance Between successive compression for example the compression corresponds to the crest of the wave or not We have the pressure as a function of the distance that this would be a normal air pressure The compressed air and purified Here so this is the crest of the trough the would Yes shown on the previous life last 2 square can be calculated from a bulk modulus divided so let me now goes a little example so let's assume we have an 80 meter long time at 2 . 1 will diameter of couple wire that stretched Between 2 poles and the bird lands exactly in the middle of the wife and When it lands it will send a small falls Most The left and the right And the about those pulses reflect them at the polls and Arrived back The boats per patient 0 . 7 5 seconds After land and the question is how much tension is the wife of what is the tension force In the wife And so on so this this questioned the use this relations that The ratio between pension for Last density equals lost square or the potential costs We must spend 2 times lot square And now we need to learn actually look up of 2 numbers we need the air density off of cop Watson's didn't just given that it's a copper wire so that It is shown here And The air from that we can calculate the total masts So we have an 18 meter long while we have this density factor and then we have a high times these radios square and given the diameter But while its 2 . 1 million ml and powerful At 1 . 0 5 times tent Modestly meters radius of what could do that then we arrive at the total masts of of the wine from the total Marcel The line and the length of the we can Get the linear density of The White Simply dividing those numberless gives us 0 1 0 3 0 8 kilograms of weekend that we also calculate quite easily the velocity in that The distance between burden This is 40 meters in both cases the left and right from pulse but it needs to come back so the total distance that each pulse troubles Is actually 18 meters and divide that by the . 7 5 seconds that it takes for the whole store arrived back at the location of the and from that we get these uh the speed of the way and now all we have to do with this We have to square this number and Multiplied by the linear density of of the White House and tension force 350 art OK so that this issue
So the question was how do I arrived It is Formula for the total not so we ever so we have a wire which is sort of Look that are under a microscope would looks like a saloon and that's as cylinder has radios and length In all cases the length 18 needles and the radius it 1 half of We have a diameter And the diameters Given the problem as 2 . 1 million of its 2 . 1 divided By 2 times 10 to the minus 3 meters off 1 . 0 5 Times 10 to the minus 3 meters and the volume of birth of a cylinder of fears the length times 5 times a radius square And the demand back and the master of the the water is the density of cobbled times this So a source other words I need to multiply the length of the year hired radius square of the wider multiplied by the density of copper and then I get the total Marcel why they're actually other waves and just longitudinal and transverse
It's more complicated systems for example of the race may encounter The ocean have features of Both transfers and which will always be actual water molecules they will so-called that So not a simple an up-and-down emotional forward and backward motion sensors for the transfer of which would ever Very deep under the surface of the water hole Tends to be a more among which would always because there is no room for the water molecules will support a can of compressed and of course a year California will Wilbert aware that their earthquakes Produce what airwaves Most Canberra destructive and then beat near-death actually produces both Transverse waves and lumber told Norway's so have most figure for example at the opposite end of the year These wasteful travel sometimes even for the quarter of that reflected The fact the various interfaces into the complex structure And then I arrived On occasion here and there There's usually a time delay between told boats But quickly for the next thing I wanted to talk about this The energy that transport and obviously anybody who has ever tried surfing was that Quite a bit of energy contained in waves and the question is how much so I know what I'm going to use this as from the previous chapter of the air energy off oscillation
The simple harmonic motion so from that You might remember that B The energy the total energy was given us 1 The spring constant times The amplitudes Guerrero of the way and this doesn't change as a as a functional Time will solve all our constant time or we can act since we know know that plumber desk Korea equal scaled and we can also error replaced the Kate Omega script and on desk rail lost Paola can and difficult
Cables on guts and so we can replace the spring constant
The last time on the square and now we know how we apply that tool will wait Because we can now defined shots in a piece of volume in a medium of density role very similar that they did with the Wyatt so we we consider us But a slab of material so it has some some Area And some fitness Bell And the thickness that we assume is a velocity of a velocity times some small time difference with called T so since as before
There's a two-year mast volume We can then get the master the density times bought and sold at this is the density times we surface area
Times the thickness of assumes the fitness was The velocity times higher than that baguette Several times Best Times NYTimes and became well defined the average power of the way and powers Energy time And All we have to do is a job in this formula for the last This equation him And divided all the time And to arrive at one-half role A bombing us career basically times So this is about a bunch of Constance Times the surface area and you can actually form the ratio of the average call surface Area and that ratio is called the intensity of the intensity is pulp firm surface Area and it is 1 half A role will Only Austria and the toe or if you prefer Using frequency omega equals tool High Times frequencies Just gray areas For Christ's Korea Times Frequencies clear that or one-half Goes away Kansas The 1 factor of 2 from the form and to get this formula he And these are the really important thing to remember from this Following that the intensity is proportional to the U.S. and the food of the square and that means that Twice as high and that the That means 4 times Intent and if should enjoy certain that's maybe something you wanna remember so what happens if assume spherical ways Meaning that you have some from way sitting in the center and Graves called in all directions in space and dozens all that surface Area of awful office field is for 5 times the radius of the Graham And if we assume that the average Howell remains constant that means that the intensity uh there should be proportional to 1 over the radio script The service area grows With a radius of the sphere of an intensity should follow off right in most of the race and so the seer that we are considering his that this has radius between the source and everyone all the intensity and Come back from this proportionality that intensity goes like 1 of the greatest player 1 the distance clear between them you and And that means that prices closed means 4 times as intense and that's also important to remember when approaching a powerful source Wake of wanna protect itself they're going twice as far means that you suffer only quotas much and can sort of we can compare the intensity pulled points with distances are long and told this just Illustrate Proportionality point so the intensity ratio I at The distance tool or what I had the distance all want to be ratio Both distances Square The advert tool as a metaphor Those distances are long behaves differently however since we already know that These intensity goes like the will square and that That must mean there We attempted to load A distance 2 over the average of distance or 1 must be Equal to the ratio of 1 or 2 And that is because a intensity is is proportional to the applicants career which is But it's also proportional won over the years and therefore Bamford told Should behave like 1 worried so I let me make an example of how about the intensity of earthquakes and have and those of the graves troubles with you so let's assume 1 earthquake and it makes a P wave and also the earth and is detected 100 kilometers from the source and that Pointed this Detective with an intensity of 4 about 1 times tend to lose 6 walks from square and the question is what is the intensity of the wave when is detected 400 kilometres from the source and the answer we assume that there are 3 ways this aspherical the distance Our want equals 100 kilometers and the distance about tool equals 400 kilometers and Therefore the distance of 1 or what It's just a quarter That means This distance Graeme Swann mobile 60 and Take Chris This racial our sorry for the square if I take this ratio Square it and multiply the intensity of attention the 6 lots of leaders square and we get 6 and a quarter times Bad the for what score And By late and the amplitude would be one-quarter of since behaves like so let me describe how how 1 can represent Ladies in general and mathematically and so the way what you have initially at some time we Role for example with Arab role that we consider the beginning We had some complicated pulse ship be any arbitrary pulse ship which called a D 0 Chu and for example Made it so that Maximum did a deviation from the rest of the world is that x equals 0 so that's what That's what we have given the pulse shape at time t You and that Then of course be a simple assigned function And anything else The Nollar travels known in the time period some other location and the other location will be X equals BT this maximum variation from Zero travel troubled was sitting or Mexico's
So how do we is how do we describe that 1st of all I remember that we already know the velocity phase velocity of fast pressed who equals ever Times lounge at the frequency And lumber with that are redefined the displacement for each Position x at any time teen comedy a functional X T and if we have this pulse His initial Pulse at time because that means that deal of excellence equals is your ex And ban you can convince yourself that A D of ex ante that's do These X minus V T that describes the pulse of troubling to the right meaning that If closes euro and it's obviously true and These pulses trouble to the right distance of 18 for example the maximum The maximum will be sitting at the E T and T minus 0 so the maximum trouble that was Chief So I similarly if you replace the minus sign with a plus sign we that pulse instead of moving to the right is moving less so as to make this a little bit easier to understand next Talking about signed ordeal but use plunder case of silos ways this Pulse shape assigned functions and they've already characterized The way some Osorio ways With this wavelength prime sole heir we now define another prominent on 2 overland across the society function as a period of Toe part And troop Iowa lumber is kind of like what we had to hire over the time period for the simple harmonic motion and call that promise that Kate Matters is often referred to as the wave number so that means that These euro assigned 8 times X plus mangled time Just like had for the simple harmonic then since we have this will not easy or equals a signed K experts find their weekend then I'll find an expression of What happened Any other time the field and use of vehicles Times Labrador And We can say as equals or mingle with 2 time at times because all my across higher at the weekend they that only with And that means that we have all my goal alarmed over to Cairo on case also gives us the wave velocity And using that We can then calculated Buddhist 8 times X plus or minus T which is what we need to describe these waivers of functional space and time and when we do all that we arrived at K X plus-minus got so instead of hiring and the formula he just there Kate Ex all you have to do is we have to add a term last Miners on team or not words for the for pulse of traveling to the left or right and we get better deal excellent T is the amplitude time signed KX plus-minus on their team bus so let me give you an example of what not to do that we will conclude today so that let's assume that we have a long horizontal stretched quote and That oscillate But A single harmonic motions The frequency of wanted to get her and Thereby creating a wave of traveling alone and the left hand and also That accord that oscillate Enacted told of 2 points extending the court desire is under tension of 140 and has a linear Marston city of about 0 . 1 2 Kilograms At type equals euro at the end of the court has a couple of displacement of 1 . 6 centimeters and it is falling and the problem is determined the wavelength of the waste produced and equation for the problems were so I try answer those questions We 1st stalled the phase velocity of the phase velocity again can be calculated by this formula of this Guerrero of racial tension force divided by linear must density and A real given that these attention forces 140 militants and the linear must density is 0 . 1 2 pilgrims from meter And theorized that a wave velocity of 34 . 2 meters was set and next to use these creation that uh the velocity equals the frequency times greater length We sold that for the wavelength so that gives us the velocity over the frequency on 34 . 2 meters per 2nd Divided By 450 And That gives us 13 . 7 centimeters or 0 . 1 3 7 so now that we have the wavelength has a 13 . 7 centimeters for the equation or for the traveling wave We want the wave numbers as well 2 Take the ratio True Members This wavelength if we do that we arrive at a great number of 46 . 0 From Neto That once you have These are these wave number will you can use the Braves velocity and this wave number to get back give us the frequency of the way It was in dire need we coast
Omar del OK so that means that Palmer got equals can leak case and that gives us our 1571 are preceptorship for the U.
For the angular frequency and they've already been given the amplitude for the way it was 2 . 6 sent Seoul and as usual the hardest part of and this problem is determining the phase of ways This Please angle that we need to find out so in this case what we know That At times your position equals we know that we have By simply plugging it into the equation and the pool time signed KX miners on that finds this is outer toward this is Uh KEX miners on tea which is just Zero And that must be as given by the property in the problem of 1 . 6 sent in from other works 2 . 6 cm times assigned functions must equal 1 . 6 and then we can now Use a calculator and type in the interests of the sine function for this ratio and we arrive at . 6 6 3 gradients can and just like for this simple harmonic motion we have to be careful That The inverse sine function is not Not unique and we need to actually That test level this a solution is correct and Kabul that EU leaders look at the velocity So for the velocity every derived this with respect to time and Assigned becomes a cosine and the miners And we go Miners on guy a cosine an 18 miners on their which is 0 and this 1 is smaller than 0 and that's good Because given that we can let the court Has set up what displacement but it is falling meaning that the velocity is negative and that means That This Angle fine is the correct so we can then some O'Reilly speak with a An equation for the wave as a function of both X and T misses the amplitude 0 . 0 2 6 meters this is the wave number 4 to 6 . 0 per meter this 1 is the frequency 1571 for 2nd and finally that this 1 phase angle of . 6 6 to read So that was all for today


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