For more information, please see full course syllabus of High School Physics

For more information, please see full course syllabus of High School Physics

### Intro to Waves

- There are three main categories of waves:
*Mechanical*Waves: These travel through a material medium.*Electromagnetic*Waves: EM waves do not require a material medium to exist.*Matter*or*Quantum Mechanical*Waves: These describe the motion of elemental particles (electrons, protons, etc.) on the atomic level. We won't investigate them in this course.

- We also classify waves based on how they move:
*Transverse*Waves: The particles of the wave move__perpendicular__to the motion of the wave.*Longitudinal*Waves: The particles of the wave move parallel to the motion of the wave. This is done through compression and rarefaction (expansion), i.e., the wave is transmitted by pressure changes.

- We describe a wave with the following characteristics:
*Amplitude*(A): How tall the wave is at its maximum height.*Wavelength*(λ): The distance between "repeating" points on the wave, such as top-to-top.*Wave speed*(v): How fast the wave is moving.*Period*(T): The time it takes to go through a full oscillation.*Frequency*(f): The number of oscillations that occur per second. [The unit for this is the hertz (Hz) where 1 Hz = [1/1s]. Thus, f = [1/T] and T = [1/f].]

- Because speed, frequency, and wavelength are all related, v = λf .
- We can find the height (or pressure differential if it's a longitudinal wave) with the following equation:
y(x,t) = Asin(kx − ωt). - x is the horizontal location we are considering.
- t is the time we are looking at the wave.
- k is the
*angular wave number*and is connected to the wavelength:k = 2π λ. - ω is the
*angular frequency*and is connected to the period (which is connected to the frequency):ω = 2π T⇔ ω = 2π·f.

### Intro to Waves

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Pulse 1:00
- Introduction to Pulse
- Wave 1:59
- Wave Overview
- Wave Types 3:16
- Mechanical Waves
- Electromagnetic Waves
- Matter or Quantum Mechanical Waves
- Transverse Waves
- Longitudinal Waves
- Wave Characteristics 7:24
- Amplitude and Wavelength
- Wave Speed (v)
- Period (T)
- Frequency (f)
- v = λf
- Wave Equation 16:15
- Wave Equation
- Angular Wave Number
- Angular Frequency
- Example 1: CPU Frequency 24:35
- Example 2: Speed of Light, Wavelength, and Frequency 26:11
- Example 3: Spacing of Grooves 28:35
- Example 4: Wave Diagram 31:21

### High School Physics Online Course

### Transcription: Intro to Waves

*Welcome back to Educator.com Today we’re going to be talking about an introduction to waves.*0000

*We’re going to finally get an understanding of how waves work and they have an incredibly large presence in our daily lives.*0005

*Waves are way for one object or location to have energy transferred to another object or location.*0011

*That seems like a really large definition and it is. It’s not the only way for energy to be transferred but it a motion of energy from location to location.*0018

*It also has a lot of other effects and we’ll be investigating some of those.*0028

*There are many different kinds of waves and you’re constantly around them.*0032

*Some basic examples that you’re being currently being exposed to: sound and light.*0036

*Also any vibrating strings, waves in water, and the list goes way on.*0041

*There’s all sorts of other things, seismic waves in the ground, vibration along a steel pipe.*0046

*There’s quantum motion in waves, though we won’t be getting into that.*0052

*Waves make up a fundamental part of the universe and nature around us.*0055

*To begin with, let’s imagine the idea of a pulse. Imagine you’ve tied one end of a string to a wall, so it’s tied over here and you pull the string taunt.*0061

*Then you whip it, really suddenly, once. You whip it hard, what’s going to happen?*0072

*Well you’re going to create a pulse of energy that’s going to be sent down the string.*0077

*As the energy might be here, we’ll have a sort of raised up area and then as time goes on, not long time probably, it’s going to move to here and then it’ll move to here then it’ll move to here until eventually it hits the wall.*0081

*So that pulse of energy will be sent down the string and it’ll keep moving down the string towards the wall.*0095

*We whip it once and we move the energy, the energy that we put into our whip gets transmitted down the string.*0099

*Some of it goes into heat and other things, we won’t actually be investigating the energy, we will just be investigating the motion of waves.*0105

*There is definitely a change of energy from a location to another location.*0111

*You transmit that motion down the line into the wall.*0119

*Do the same situation but this time you start whipping the string up and down regularly, creating multiple pulses at even time intervals.*0122

*Some of these pulses are pointing up and some of these pulses are pointing down. What’s going to happen then? You’re creating a wave.*0128

*Instead we’ve got one pulse here and one pulse here but they form together to make a continuous wave shape. The whole thing makes a wave.*0133

*Once again, as time moves on, the things going to slide over and the whole thing will move farther along the line and get closer to the wall.*0141

*As time goes on, the thing shifts forward an amount. It has a constant velocity moving towards wherever it’s moving towards.*0150

*We’ve created a wave, there is a number of characteristics about the wave. Some of these drawings aren’t quite perfect but the important things is that waves have regularity.*0159

*It’s the fact that we can always trust it to get to the same height or pressure differential as we’ll talk about much later in sound.*0168

*We can always trust it to get to the same levels every amount that it goes.*0173

*Once it goes through one oscillation, one period of itself, it manages to repeat all the same effects.*0178

*So looking at one snapshot, the right chunk snapshot, it can look just like another chunk snapshot, can look just like another chunk snapshot.*0184

*That’s when the important ideas of waves, the fact that we’ve got regularity, something we can trust is going to be regular coming down the line.*0191

*There are three main categories of waves.*0199

*Mechanical waves are the waves that you probably have the most familiarity with at this point.*0202

*These are the waves that travel through any sort of material medium.*0206

*Common examples, the most common one that we’re all used too, sound waves.*0209

*Every time you hear something, if you hear a big bass drum get kicked at a concert and you feel those vibrations in your chest, in your body, that’s actually another form of sound waves.*0212

*They are just a very low frequency, so they’re able to vibrate your entire body.*0223

*Another type would be water waves. Waves on the top of waters is another form of waves.*0228

*Seismic waves, waves in the motion of the Earth. Things that cause earthquakes, these are all different forms of waves and different propagations of energy.*0234

*Electrometric waves, EM waves, don’t require material medium to exist.*0244

*We’re also exposed to these constantly, but you might have less of an intuitive understanding of them.*0248

*Examples of this is radio waves, the visible light that you’re currently seeing from the screen, X-rays.*0254

*Anything that has, that is, is light, is a part of the electrometric spectrum, but we’ll talk about that more.*0258

*That’s a little bit difficult to understand, because light has a whole bunch of special properties that really affect the nature of the universe in incredibly strong ways.*0267

*That’s going to be its on special section. We’ll very lightly touch the surface of that.*0277

*But for now, we can just think of it as light.*0281

*Finally, matter or quantum mechanical waves. These are waves that describe the motion of elemental particles, like the electron, the proton, or even smaller, the quark or the photon on the atomic level.*0284

*They’re very important to modern physics. They have a whole big impact and what we understand now and where our research is going currently.*0296

*We’re not going to be investigating them in this course. They behave a little bit differently than the classical waves we’re going to be studying.*0302

*They’re going to be more challenging to understand, so that’s something we’re going to save a future course.*0307

*Alright, in addition to the previous categories, the mechanical waves, EM waves, and mater waves.*0313

*We won’t be talking about mater waves. Mechanical waves are the ones we most understand.*0320

*They’re the ones that have motion medium. EM waves, they sort of come with their own medium.*0325

*In addition to the previous categories, we can also classify waves based on how they move.*0329

*Transverse waves. The particles of the waves move perpendicular to the motion of the waves.*0334

*If we got something that would normally be a flat line like the surface of the sea.*0339

*Then we’ve got a wave, an undulating curve on top of it that causes the surface of that sea to move up and down depending on the location of the wave.*0344

*That’s going to be a transverse wave. It’s happening transverse to the motion, it’s happening perpendicular to the motion of the wave.*0353

*Examples include a vibrating string, EM waves, any waves in water; not any waves, sorry you can also have sound waves in water.*0361

*Waves that we’re used to seeing in water. There is a huge varieties of things like this.*0369

*If you were to knock on a pipe, you’d also once again…if you were to shake a pipe, you’d get waves. If you were to knock on a pipe, you’d get sound waves.*0375

*We’ll talk about this more later.*0384

*Longitude in the waves. The particles of the wave move parallel to the motion of the waves.*0387

*So this a little bit harder to see and we’ll get the chance to get a better visual understand of this once we get to sound.*0390

*The particles of the wave move parallel to the motion of the wave. This done through compression and rarefaction, expansion.*0395

*So if we got two particles like this and remember they’re charged particles so they don’t like getting to close to each other normally.*0401

*The wave is going to be transmitted by pressure changes. If one particle pushes towards the other one for a moment, a brief moment, they’ll be together and push back away from one another.*0407

*That pressure wave will wind up getting transmitted all the way through.*0418

*A pressure front and once they push away from each other, we’ll have a rarefaction of area and they’ll wind up getting pushed back together again by the next pressure front coming through.*0423

*Pressure changes will transmit the information, will transmit the energy. The motion is being caused by pressure changes.*0431

*Most common examples is sound. But it also exists in certain kinds of seismic waves.*0439

*Alright, let’s investigate the wave more deeply. Here’s an okay drawing of how a wave looks.*0446

*This is a general sinusoidal wave and we can treat most waves as sinusoidal.*0451

*Meaning it comes from sin, as in the sin function that looks like just like this when you graph it out.*0456

*First off, amplitude. How tall the wave is at its maximum height.*0464

*In this case, the amplitude would show up right here. We’d get A there.*0469

*Somewhere else we’d see it here, we’d see it also right here. Anytime we see the maximum height.*0472

*What about down here? Well down here, it’s also going to be a height of A.*0477

*Instead if we were to look at it from an absolute point of view it’s going to show up at –A, although the length will be A.*0482

*Amplitude is the absolute value of you location from the medium location.*0489

*Its how far up or down you go, but it’s always going to wind up being a positive number.*0495

*How tall the wave is at its maximum height is amplitude. A.*0499

*Wave length, the distance between repeating points on the wave, such as top to top.*0504

*Remember, one of the important qualities of the wave is that it repeats itself after a certain amount of time.*0508

*If we go from here to here, notice that this entire area here looks just like this entire area here.*0513

*Just like this entire area to the front of it and this entire area to the front of it looks the same.*0523

*And if fact, if we were to go all the way through, we’d wind up getting all the same information.*0528

*It’s going to look like the exact same thing from the wave length point of view.*0532

*When you get a one wave length, the distance that it takes to do an oscillation in the wave, you’re going to see repeating points.*0537

*Everything will wind up repeating. If we go from top to top, we’ll have a wave length.*0545

*The guy that we use to call out wave length is lambda. Lambda is another Greek letter, he gets thrown around now in waves, he becomes very important.*0553

*He’s pronounced lambda and spelled in case you’re curious, lambda. Lambda. Lambda is the guy.*0561

*What some other repeating points on this? What about from here to here?*0569

*Well that isn’t going to wind up being lambda because notice how this section right here is doing something different than this section right here.*0573

*If we wanted to say, look from this point, we’d have to go all the way to here because know we’ve got just to the right of it.*0582

*It’s going up a bit and just to the right of it over here it’s going up a bit.*0588

*So from here to here would also be another example of lambda.*0592

*We could do to this from anything as long as we wound up being at the same height and we went through the right amount to wind up having it experience the same affects inside the wave.*0597

*We’re able to get one wave length. The important part about a wave length is that after you go that distance everything repeats in the wave.*0607

*More characteristics. Waves speed, how fast the wave is moving.*0615

*Remember this whole thing is moving forward at some speed. We’ve got some velocity that it’s got.*0619

*After one second it will be that many meters farther ahead.*0625

*For velocities and meters per second, we take that and one second later it will be that much velocity meters ahead.*0630

*Remember the wave is moving along. And as this moves forward we’re going to wind up seeing more of it coming out of it.*0638

*There is always more wave that’s going to be put in. Either it’s too the left outside of where we’re looking or it gets whipped into place by the motion of whatever is creating the wave.*0645

*The wave continues out on either side, and the whole thing moves forward.*0656

*Period. The period is the time it takes to go through a full oscillation.*0664

*Remember if we got some speed V, that this whole thing has, we’re going to be able to get from here to here and we’ll have a repartition.*0668

*Now one way is we could change the location we’re looking, but we could also fix the location that we’re looking here.*0678

*We’d be able to see that T later. We start here, say we start here, but T later because of the velocity will wind up showing up there.*0684

*If you notice, the velocity times the period is always going to wind up equaling the wave length.*0698

*Because the amount of time that it takes, if the velocity goes this way and T later is how long it takes to go through a single oscillation, the period is how long it takes from wave peak to get to another wave peak.*0708

*Or one point on the wave to get to its corresponding twin point on the wave.*0721

*That’s going to wind up having to be the wave length right? That’s what the definition of the wave length is.*0727

*We can think of it as a movement, the time that we’ve allowed it to move, and has given us a repetition, a period.*0732

*Or we could think of it as how far different we’ve seen in the distance that we’re looking in the wave, has given us a repetition on the wave.*0740

*So we’ve got the velocity times the time that it takes for the period is going to equal that wave length because they’ve got to be equivalent.*0747

*Frequency, the number of oscillation’s that occur per second.*0754

*Say we’ve got some period. T is equal to the period right? So in here…it’s gets from here to here if we’re looking from some single place.*0759

*If we fix our gaze here, so fix our gaze on this blue line, this blue dash line and we look up, we’re going to see this point here.*0775

*T time later will see the red dot above us. T time later the red dot will have moved to where the blue dot is.*0783

*If that’s the case, we can ask, alright so, it takes T many seconds and T could a larger number, greater than one or T can be a small number that’s well less than one.*0791

*We could ask, if it takes us T many seconds to get a repetition in the wave, how many repetitions are we going to get every second?*0805

*How many oscillations are we going to have per second? How many wave peaks are we going to have per second?*0814

*Well if that’s the case we’re going to need something that measures per second and that’s where the hertz comes in.*0820

*That’s one hertz equals one per second. One over one second. So that means the frequency is equal to one second divided by the period.*0825

*The period, so if we have something is the period of T=0.2 seconds then that means the frequency is going to be 5 because in one second we managed to have 0.2 seconds occur five times.*0836

*Frequency is the inverse of the period. And the period is equal to the inverse of the frequency.*0854

*Anytime we want one for the other, we just flip it and we’re able to get the answer.*0859

*One divided by the other and we take reciprocal and we’ll get it.*0863

*That’s because the fact we’re looking for long it takes to get from one like point on the wave to another point.*0866

*How long it takes for a single oscillation to occur is going to also be if we divide one second by how long it takes we’ll get the number of times we get an oscillation.*0873

*If we have the number of times oscillation happens in a second and we divide one second by those numbers of oscillations, we’ll get how long it takes each oscillation to occur.*0882

*Finally because speed, frequency, and wave length are all deeply related, we’re going to have the fact that velocity is equal to lambda times frequency.*0892

*Which is equivalent to velocity times time equals lambda. Remember we know that velocity that we’re moving, times the time it takes to from peak to peak has to be equal to lambda.*0900

*We’ve got the same thing going on here since V=λf. Well if we divide by F on both sides, we get v/f=λ. Which 1/f=t, so we get vt=λ.*0914

*So these are equivalent expressions. Why is V=λf make sense? Well if we’ve got lambda distance here, this is lambda…distance.*0926

*And we know that time, in one second we’re going to see the frequency occur. So if we see ten oscillations in one second, then how much distance have we covered?*0939

*We’ve covered ten oscillations to each oscillation as one wave length, then ten times the wave length.*0949

*So the frequency, the number of oscillations we occur, that occur in one second, we have in one second, times how long each one of those oscillations is, is going to be the velocity since we can just divide by one second.*0955

*Velocity is equal to lambda, the distance, times frequency, which comes in one of our seconds. So we’ve got meters per second.*0967

*Great. Wave equation, finally we can talk about if want to know the height of a point on a wave.*0975

*We’ll need to know two inputs. The horizontal location x and the time we’re looking at the wave.*0982

*Here’s just a quick sketch of a wave. If we got some wave like this, we could either look at this location x or maybe we want to look at this location x.*0987

*We’re going to get totally different results for that. However, what happens if then we also say, one of them is T=1?*0999

*What happens when we look at T=2? Well then the entire wave is going to have slid over some amount.*1006

*We’re going to have the same wave, but it’s going to have slid over and we’re going to get totally different answers for each one of those x’s.*1013

*That means, the time that we’re looking and also the location on the wave that we’re looking matters.*1021

*We’ve got a two variable function, we’ve got an equation that’s going to be based off of two variables that give us that dependent variable, that why, what output value.*1027

*Notice that one other thing about this, if we only care about the point where the wave originates, the very beginning point, x=0, we can simplify this because we can just knock out that x term.*1037

*We can make it simple at A times sin of omega T. Now, at this point you’re probably wondering what k and omega is, that’s a great question, we’re about to answer it.*1046

*Our equation is Y of x,t equals a, amplitude, times sin of kx minus omega t and quantity.*1056

*So before we can use our equation we’re going to define what k and omega mean.*1065

*K is the angler wave number and it causes our function to give the same value for every wave length lambda.*1070

*Now remember, in case you don’t remember some of the stuff from trig, every time sin of 2π times any number, n.*1075

*Where n equals -2, -1, 0, 1, 2… on either side. Any integer number.*1085

*Sin of 2π repeats, the whole thing repeats, no matter what we’ve got added to that inside of it, we’re going to wind up getting the same answer.*1096

*Because what we’ve done, whenever we do 2π, we’ve lapped the circle. And we’ve winding up starting here and we lap the circle, then we’re still going to get the same answer.*1103

*If we lap the circle in the other direction twice it doesn’t matter, we’re going to the same answer as long as we land at the same point.*1113

*As long as we change by things of 2π we’re going to have the same thing show up.*1119

*Which makes a lot of sense because on our wave, as long as we change by some wave length distance, we’re going to have all the same stuff show up.*1124

*If we change by one wave length and we’re using sin, we’re going see inside of it, a factor of 2π show up.*1132

*So for every wave length we change, we show up by 2π, that’s why we get k here.*1140

*Because if k is equal to 2π/λ and then we move over by 2λ amount, well the lambdas cancel out and we get 4π, which is equal to 2π times some n.*1146

*So we’re going to see the exact same thing as if we hadn’t shifted over, which is exactly what makes sense.*1159

*When we shift over by some wave length amount, it shouldn’t have an effect on what we would have seen otherwise.*1164

*Shifting over by a wave length is no different from the point of view of what value we’re going to see for the height or the pressure differentials that we’ll talk about later in sound.*1168

*Same basic ideas going for omega. Omega is the angler frequency and it causes our function to give the same value for every period time. So every period, big T.*1178

*Omega, not sure if I said, I don’t think I said, this guy right here, is once again another Greek letter and its pronounced omega. O M E G A.*1187

*You’re probably seen his bigger brother at some point. Capital Omega is that guy but this is lowercase omega.*1201

*Back to the thing at hand. Omega is the angler frequency and it cause our function to give the same value for every period.*1209

*Remember once again, every time we pass one period of time, as long as we’re looking at the same location, we should experience no difference right?*1216

*Every time you go through one period you’ve gone through one entire oscillation, so the wave just looks the same to you from that point of view.*1224

*As long as you wait 1T to look, everything is going to be the same.*1230

*So if we plug in omega for 2π over T. And then we hit it with some time that is factor of a period, 3t. Those t’s cancel out and we get something that is just going to get canceled out by sin.*1234

*We’re going to care about the other information inside of there. So as long as we wind up shifting some amount by a period, it’s not going to have an effect.*1246

*Let’s look at a slightly more complex example. We’re not going to see the time be just a factor of the period.*1256

*What if we look at t=1 and t=1+t? So if we look at that then we can say, let’s make it easy on ourselves, we’ll look at just generally…we’ll look at the same location x.*1260

*X is going to be fixed, otherwise we wouldn’t wind up seeing the periodic nature of the oscillations reoccur.*1276

*So our two values is going to be, our function is going to be y=a(sin)kx. And what’s k? We’ve got as 2π/λx - ω2π/. x t. The time.*1282

*If plug in t=1, we’ll plug in t=1 over here so t=1, we’re going to get y is equal to a(sin)2π/λ whatever x we’d chosen minus 2π/tx1, so there we are. That’s what we’re going to wind up seeing.*1305

*What happens when we plug in 1 plus one more period of time? Well we’re going to hope that we’re going to see the exact same value.*1328

*We’ll plug that one over here, we’ve got y=a times sin of 2πλ times x minus, now what…times one plus t, we’ll get 2π over t plus just 2π right?*1334

*So if that’s the case then we’ve got y=a sin 2π λ x - 2π/t - 2π.*1358

*This part right here winds up being the exact same as this part right here.*1371

*The only part that’s different is this here, but remember since we’re dealing with sin, since we’ve moved just one more 2π, we’re some location.*1379

*Then we just spin it around and boom we wind up being at the exact same location because we’ve moved by -2π.*1389

*So this location here, this stuff all here, is our real location. So if wind up shifting things by one whole period, even if we start at some time that isn’t a whole thing of a period, the way we’ve got this set up.*1396

*Since we’re using sin, a regular periodic function, we’ve got the fact we’re able to make those oscillations occur in our mathematics, our algebra, is able to support our visual oscillations.*1409

*We move a period temporally in algebra, we wind up moving that same full length time, so we see the exact thing.*1422

*The exact same would happen if we used k, if we used…if we moved x around and this sort of thing, but this is just to illustrate that the math here is really working and why it is.*1430

*We’ve got to make sure that 2π over t is able to handle a motion of a period as causing no effect to the values we’ll get out. Same thing with the motions of a wave length.*1439

*That’s why that 2π comes in, is because sins, sins natural period is 2π right? Its period before it repeats is 2π.*1448

*So we have to have a way to have those two periods, the period of the wave we’re working with and the period of the natural function we’re working with to be able to communicate with each other and that’s what this is all about.*1456

*Then finally, if we have 2π/t since over t is the same thing as times frequency, we get omega is also equal to 2π times the frequency, as simple as that.*1465

*Finally we’re ready to work on some examples. If we have a CPU on some device that has a frequency of 1 gigahertz, then we’ve got a frequency equals 1 gigahertz.*1476

*How many hertz is that? Well it goes, kila, mega, giga. So 10^3, 10^6, 10^9.*1487

*So 1 gigahertz becomes 1x10^9 hertz.*1494

*What’s the time that it would take to complete a single cycle? So if we want to know what the period is, then we remember the fact that frequency equals 1 over t.*1501

*T equals 1 over f. If want to know the period, t equals 1 over 1 gigahertz. 1x10^9.*1512

*Which becomes 10^-9, which is the same thing as mila, micro, nano. So we get one nanosecond is how long it takes.*1523

*There are 10^9 nanoseconds in a single second, which makes sense because 10^9, there has to be 10^9 nanoseconds because each of those cycles has to be complete for it to be able a whole frequency of 10^9 cycles completing.*1524

*So CPU, we’ve got the same, it’s not directly a wave in the same way, but we’ve got the fact that it’s having repetitive things happen.*1539

*Its going through cycles, it’s cycling through data. We’re able to talk about it in terms of frequency and in terms of periods just like we do with waves.*1566

*If the speed of light is velocity 3x10^8 meters per second, mighty fast. And you receive a wave with a wave length of 500 nanometers. Very small wave length. What is its frequency?*1573

*Speed of light is v=3x10^8 meters per second and you receive a wave with a wave length of 500 nanometers. We already know what v is, v is here.*1588

*So 500 nanometers is the wave length, right? The wave length equals 500 nanometers, which is the same thing as nana, 10^-9, 500x10^-9 meters.*1598

*If we want to know what its frequency is, we remember that velocity is equal to the frequency times lambda.*1611

*The frequency times lambda has to give us the velocity because that’s how much distance has been covered.*1620

*Wave length is a chuck of distance and frequency is how many times you have those chunks distance in one second to we cover. Frequency times wave length.*1625

*We cover fxλ and that gives us our v.*1634

*v=fxλ, so v/λ=f, so if we want to know what f is. F is going to be equal to 3x10^8/500x10^-9.*1637

*We plug that into a calculator and we get 6x10^14 hertz. That’s a giant frequency compared to the stuff that we’re used to seeing in sound.*1655

*For light though that’s pretty reasonable and you’re probably seeing a color pretty close to that.*1666

*6x10^14 hertz is a receivable for the human eye, it’s something in the visual spectrum and I think, don’t hold me to this, it’s probably pretty close to either yellow, green, or blue, somewhere in that sort of range.*1671

*Probably a little bit closer to the blue, green or blue. Anyway, that’s something that your eye is actually really able to see and so as opposed to seeing a numerical frequency data when we look at something.*1687

*We don’t say “Oh, that frequency is that”. We see a color. We’ve got these other ways of interpreting the information that the universe is sending to us.*1697

*It is a real thing, we are getting real information here just like when we go to some height, we’re really at a height but we can measure that height and periodically we’re able to measure the frequency we see in periodically.*1704

*If you’re driving a car going 30 meters per second and the car beings to run over a rumble strip, rumble strips are these evenly spaced grooves used to alert drivers, so little down grooves in the road like this.*1716

*So when a tire rolls over it, the tire falls in the up and down motion, winds up jostling the driver and they notice something, or they’re accidentally swerving off to the side, they notice that they’re swerving off to the side or if they’re coming up on some toll, they notice that they’re coming up to some toll.*1733

*It’s just something to alert drivers. If the strip vibrates your car at 98 hertz, what’s the spacing of the grooves?*1747

*First off, I’d like to point out that this isn’t technically a wave. Just like in #1 we weren’t technically working with a wave, but we can still apply many of the concepts.*1754

*In this case, the wave speed, we know the velocity of the car is equal to 30 meters per second.*1762

*While the wave might not be moving, the way it’s experiencing the wave is moving. In another way we could consider the tire is still, and the wave is the thing moving.*1771

*From your point of view you can’t really tell who’s moving when you’re inside of the car, although we look at our scenery and we can easily tell.*1783

*But you know, we can’t be sure who’s the thing that’s moving. It’s possible the road is the thing moving. So you can take it as the wave moving underneath you.*1789

*Once again, we’re not getting full repartition quite the same, maybe. But we’re not necessarily thinking it purely in terms of wave lengths, but that isn’t the issue.*1796

*We can expand a lot of these ideas to more things.*1806

*So we’re running over some rumble strips and it’s moving by us at 30 meters per second, either because the cars moving, or because it’s moving relative to us.*1810

*If the strip vibrates your car or bounces you up and down 98 hertz or 98 times per second, what the spacing of the grooves got to be?*1818

*It’s the exact same thing, if it manages to bump us up and down 98 times in a second and the wave length is the spacing of the strips. The spacing of the grooves is going to be the wave length.*1827

*How far they spread apart, then the 30 meters per second that we experience has got to be that number of times that the wave length times how many times they show up in a second.*1838

*Velocity is equal to the frequency times lambda. So we plug in our numbers and if we want to know what lambda, is we’re going to have the velocity divided by the frequency.*1849

*We plug in our numbers 30 meters per second divided by a frequency of 98 hertz and we get 0.306 meters.*1860

*There we are, the spacing of those grooves is about a third of a meter which makes a lot of sense if you’ve ever looked at them on the street.*1872

*Example four. Use the following diagram to give an equation describing the wave in the diagram.*1882

*Now to begin with, lets point out, we just want to remember y equals a, the amplitude, times sin, the function that allows us to have periodicity, allows us to have oscillations occur algebraically.*1887

*kx - ω x t. So x, the location we are in the wave. T the time that we’re looking at the wave. Omega is the factor that allows us to handle the fact that periods cause repetitions.*1901

*K is the fact that allows us to handle that wave lengths cause repetitions. To begin with, we know that the period is equal to 0.02 seconds.*1915

*We know that amplitude is equal 0.5 meters. Okay, great. What is this here?*1927

*Well that is not equal to the wave length. Remember, if we look just to the right of this point, and look just to the right of this point. We should see the exact same thing.*1935

*We don’t see the exact same thing, it’s going down over. If we go over here though, we will see it.*1944

*And because its sin wave, it’s evenly spaced out throughout, we know that 3.5 meters isn’t going to be the wave length, but it’s going to be half the wave length because it’s in one of the dips.*1950

*So the wave length over 2, so that means that our wave length is equal to 7 meters.*1961

*That’s all the data that we wind up needing. Now we want to solve for what k has to be.*1968

*K is equal to 2π/λ, so k is equal to 2π/7. Omega is equal 2π over the period.*1972

*By the way, k, we’re throwing around k a lot. I never mentioned this but k is not the same k as when we’re dealing with springs. It’s a different k, we’re using it to mean a totally different thing at this point.*1985

*The k that we’re using in this stuff is different than the k we used before. Just like how little t and big t don’t necessarily mean the same thing. We can even wind up using the same letter for different things, and we have know contextually what we’re talking about.*1999

*Sorry, I made that assumption, but that’s actually a really important thing. You don’t want to get confused and think that springs and waves necessarily have to do with each other every time. It’s not that same spring constant we were talking about before.*2011

*Totally different use of k. Anyway back to the problem. Omega is equal to 2π divided by the period.*2024

*If we know the period is, 2π/0.02 seconds and that will wind up giving us 100π.*2030

*Simple as this at this point, we just plug in all of our numbers. Y is equal to that amplitude, 0.5 meters times sin, of the numbers 2π/7x-ω100π times the time that we’re looking.*2039

*That right here is our answer. Simple as that. So we just want to be able to analyze the diagram.*2065

*One of the most important things to pay attention to the fact that wave length has to be not just some distance where you get the same point, but some distance where you get a point that means the exact same thing.*2071

*That if you look just a little bit further on and a little bit further behind you’re going to see a full repetition.*2083

*It’s not just the same point, because the same point occurs at any horizontal thing, except for the very tops and bottoms.*2089

*These pairs of points are not enough to determine a wave length. What you need is to reach is to reach a little bit farther and look here.*2097

*The very top to top because tops themselves only occur once every wave length.*2104

*Whereas middles occur twice. Same with bottoms, you can go from the bottom to the bottom and the top to the top.*2111

*That’s normally the easiest thing to measure, but if you’re measuring from the middle to the middle, this isn’t enough.*2117

*You need to also go to here. Okay, great. I hope you enjoyed that, I hope that made sense, waves are a whole bunch of big ideas, but we’re going to…*2123

2 answers

Last reply by: Peter Ke

Thu Apr 28, 2016 12:50 PM

Post by Peter Ke on March 21, 2016

At 22:50, how you get 2pi/lambda(x) - 2pi/T - 2pi.

Specifically I don't understand where you get the 2pi at the end from.

Please explain..

2 answers

Last reply by: Anna Ha

Sun May 31, 2015 8:29 PM

Post by Anna Ha on May 31, 2015

Hi Professor Selhorst-Jones,

Thank you for your wonderful videos! They have been very helpful :)

I was just wondering do transverse and longitudinal waves require a medium?

I also wanted to check that: mechanical waves require a medium and can be transverse and longitudinal waves. And electromagnetic waves do not require a medium and are only transverse waves. Right?

Thank you!

1 answer

Last reply by: Professor Selhorst-Jones

Mon Sep 9, 2013 11:28 AM

Post by HARRISON IGWE on September 9, 2013

hi professor I've been finding difficulties in solving this problem .

The equation Y=55m(3x-4t),where Y is mm,X is in m,T is in seconds represent a wave motion . Determine (i)frequency (ii)period (iii)speed of wave?

2 answers

Last reply by: Goutam Das

Tue Jun 11, 2013 3:23 AM

Post by Goutam Das on June 7, 2013

Hi professor, as far as I know,

All waves need a medium to propagate.

The medium of sound is a fluid, and fluids have no shear strength, therefor they can only be longitudinal (pressure) waves.

Electromagnetic waves are transverse (shear) waves, so their medium (ether) has to be solid. The formula for the speed of a transverse wave in a solid is

c = âˆš(G/Ï), where G is the shear modulus (stiffness) and Ï is the inertial density of the medium. If we knew the density of the ether, we could calculate its shear modulus from the known speed of light, and vice versa. Evidently, the ether is ultra denseâ€”perhaps a googol times denser than a neutron star. That's inertial density; the ether probably has no gravity of its own, as (I believe) it is also the medium of gravity, and all the other forces. What do you think professor?