the topic of this video is electromagnetic energy and specifically waves the learning objectives are on the screen so you can go ahead and pause now to write these down in your notes i'm going to jump right into talking about basic behavior of waves and describing the difference between a traveling wave and a standing wave so to to start let's take a look at a traveling wave on the screen is a a graphical representation of a traveling wave and if if you uh are in any doubt of of identifying a traveling wave all you need to do is pick a point on the wave and follow its motion so let's pick a peak which is the highest point of the wave and follow its motion and you see that it the wave is moving from left to right or traveling in in a particular direction you can pick a different peak such as the trough which is the lowest point also follow its net motion as the wave uh uh is moving by here we see that it is indeed traveling so this is an example of a traveling wave to contrast the traveling wave i have here standing wave so a standing wave uh as opposed to a traveling wave um you can see if you pick a particular point it is not moving like a traveling wave uh uh wood instead the the peak here is just inverting to become a trough and reinverting back to become a peak and so on and so forth and this is actually happening in multiple segments of this particular standing wave one of the key aspects of the standing wave and i'll refer resort back to this at the end of the video is this uh red circle here in between these areas of peak to trough inversions these are called nodes and this is where it's a part of the wave that's not there's no net movement at all despite uh peak to trough inversions occurring on either side of it okay now the electromagnetic nature of light has to do with a traveling wave so let's go back to the traveling wave where uh the wave is is moving we can follow any point on the wave and it is moving through space um light let's see if i can zoom in here if that is beneficial is a traveling wave that is occurring in the uh electromagnetic field and the electromagnetic field is essentially uh perpendicular oscillations in the in electric field and a magnetic field okay so that's why we call this electromagnetic radiation so light can be thought of as a traveling wave okay and um and and there are some fundamental uh aspects of light as a traveling wave that we need to consider okay but when we talk think about light as a wave and particularly as a traveling wave um this is what we're referring to as electromagnetic radiation uh in oscillation a perpendicular oscillation in an electric field and the perpendicular magnetic field so to help us describe waves more generally we can look at this figure that i'm showing on the screen right now and in this figure there are a few uh fundamental aspects of waves that are highlighted for us the first is the wavelength which is you uh we denote the wavelength using the symbol the greek symbol lambda lowercase lambda and that is going to be the distance in meters between two equivalent points in a wave so here we can pick two peaks that are consecutive and the distance between those two consecutive peaks is the wavelength um the another fundamental aspect of a wave is the frequency denoted with the greek letter nu uh which is sort of like a v with a with a um sort of like a v and a u hybrid letter um [Music] and this is going to refer to the number of cycles per second uh of a wave that is how many um for example how many peaks pass through a given point in space in a given amount of time so here we can see that this for this first wave that we're looking at with a relatively large wavelength where we can count up three cycles per second um three cycles per second or one over seconds is going to be also equivalent to hertz that unit one over seconds is also equivalent to hertz okay that's really important to know um if we look at what happens now if we decrease the wavelength of a wave and look at what happens to the frequency over the same distance traveled here in one second is what i'm looking at at up top here so that's sort of bracketed by these dashed lines on either side that's the distance traveled in one second what we see is that we decrease the wavelength but the frequency increased if we decrease the wavelength yet again you can visually see that there are more cycles or more peaks that can pass through this distance traveled in one second for a shorter wavelength higher frequency so there's it seems to be just from a qualitative comparison um of these two variables an inverse relationship when one goes up the other goes down and another another aspect of waves is the amplitude so if you draw an imaginary line that cuts halfway between the peaks and the trops the distance or the the height between the midway imaginary line and the peak or the midway imaginary line and the trough is the amplitude so you can notice here that in the top there's an example of a higher amplitude wave on the bottom a lower amplitude wave but the wavelength that is the peak to peak separation is the same here and the frequency the number of peaks second or cycles per second is the same so amplitude is independent of frequency and wavelength i'm going to go ahead and write down some definitions here for wavelength the wavelength is the distance between two consecutive peaks or troughs in a wave the frequency is the number of wave cycles that pass a specified point in space in a specified amount of time and the amplitude is going to be the magnitude of the waves displacement okay so now what we can do is i mentioned this inverse relationship between wavelength and frequency and so this is actually uh really interesting because if you multiply the two together if you take wavelength and you multiply it by frequency think about the units right where meters um is is the si unit of distance for a wavelength and um frequency is going to be uh hertz or you know reciprocal seconds times one over seconds what we get is a unit value of meters per second which is a speed and it turns out that for electromagnetic radiation not just any waves in general but for electromagnetic radiation the multiplication of the wavelength and the frequency will give actually a fixed speed so if we take for electromagnetic radiation wavelength times frequency we use the the the variable c and this is actually the speed of light and so this is a fundamental constant of the value 2.998 times 10 to the 8th meters per second we could have more significant figures but this 4 sig figs is is going to be good for most purposes okay so why don't we go ahead and apply this uh right away to a practice problem um so here we're going to be determining the frequency and wavelength of radiation so you can pause the video now and work on this problem uh and then uh resume the video once so you can compare your answer to mine so what i'm going to do here is i'm going to start by revisiting the calculation or the the equation that i just wrote so wavelength times frequency is equal to c the speed of light we are given up here um a wavelength and we're given a conversion factor so and we know that the speed of light is a constant so what we need to do is solve for or isolate frequency so frequency is going to be equal to the speed of light c over uh lambda the wavelength so uh one way to do this is to just go ahead and plug in what we have 2.998 times 10 to the 8th meters per second i'm actually going to change my notation quickly so the speed of light is given in meters per second that's the units um you can also write this as meters times uh reciprocal seconds okay so that that is really useful um sometimes for dimensional analysis problems keeping track of what's a numerator unit what's a denominator unit so that's the the speed of light divided by the wavelength of 589 nanometers now personally uh i would convert this nanometer value to meters first before putting this in but i want to show you that you can actually handle this um in in using a dimensional analysis type of approach but keep in mind that the nanometers down here will not cancel out with the meters up on top because they're not the same unit we actually have to uh fix this problem so to cancel nanometers on the bottom over here i'm going to write nanometers up on the top to cancel meters on the numerator to the left i'm going to write meters in the denominator here so the conversion factor we could do a couple different things but i'll stick with 1 meter is equal to actually let's use the conversion factor given to us by um the problem here so we have um one nanometer is equal to one times ten to the negative nine meter let's just use that conversion so now what we can do is let's always check that our units cancel out meters will cancel out with meters over here nanometers cancel out with nanometers over here okay so this is the dimensional analysis part we treat the units as if they are being modified by multiplication and division uh okay so if you do this what you should get is a value of 5.09 times 10 to the 14th per second per second is the only unit left okay so that's that's a frequency so does this answer make sense yes it does all right to wrap up this video i really briefly just want to discuss quantization and the definition is on your screen it is where only discrete values from a more general set of continuous values of some property are observed okay what does that mean so let's take the case of a standing wave these black circles on the left and right are fixed points they are not moving to to jostle the the weight if one of them was moving to jostle the wave then you might get a traveling wave where a peak moves from left to right but since they're both locked there and let's say some other energy source is being used to to um uh move this rope uh to provide a standing wave well what happens is we can only have certain frequencies in this particular case for a standing wave why is that the case well we can see here that in the most simplest wave form there is no node right there is a peak and a trough and it is simply just inverting between those two okay with fixed points on the left and the right so we can say here that the node is zero but if we want to jump up to uh one node now in the next case okay if we want to actually increase the frequency of this standing wave to get it to one node there's only uh we can't pick any frequency that's higher than the than the first waveform we actually have to pick a very discrete frequency to get up to one node okay so for one node two nodes or three nodes these correspond to discrete frequencies to get to these points okay so um let's just say for for all of these actually all of these cases correspond to discrete uh i'll write new for frequency uh for each i'll call it a wave form okay that's just a different type of standing wave that we have so each waveform here corresponds to a discrete frequency that is an example of quantization because in theory you know for traveling waves we can we can have um a huge spectrum of frequencies we can almost have you have as many frequencies as you could possibly think of for electromagnetic radiation um the only thing that will happen with the frequency is that the wavelength will change inversely but for standing waves where the ends are fixed that is the case where only certain frequencies will enable that waveform to exist this is quantization and this is going to be a really key part of understanding the electronic structure of matter