3.2 Waves

Key Takeaways

welcome back to age 20 special relativity in this section we'll talk about waves um you've all seen waves you know what a wave is in principle you might have had an opportunity to serve in a wave just like the one behind me what you want to do here is be more quantitative and more precise in in the definitions and also look at different sorts of waves i find this wikipedia article here quite interesting it starts with saying that in physics a wave is an oscillation accompanied by the transfer of energy that travels through space or mass it continues then talking about the various types of waves and it makes the distinction between mechanical waves which travels through medium or substance and the deformation is of of the substance is reversed by restoring force in contrast there is waves which we have just seen in the previous section um they do not require a medium and that is topic of the next sections as we as they continue the discussion of special relativity here the electromagnetic waves consist of an oscillation of electrical and magnetic fields which are generated through charged particles um electron since they don't require a medium they can travel through the vacuum but an electromagnetic wave can also travel through a medium um like water or anything else you come up with um it doesn't stop there really because you know the concepts of weights are really like everywhere in physics specifically when you start studying quantum mechanics the behavior of particles those are described by waves and you know really exciting recent results are those of the discovery of gravitational waves which are vibrations or movement of the gravitational fields also zones those don't require a medium they travel through vacuum um when we look at waves we can start characterizing them and and one primary sort of characterization is the polarization of a wave meaning whether or not there's the oscillation itself happens in a transverse way with respect to the direction of of movement or in the longitudinal direction of longitudinal to the direction of movement mechanical waves can be transverse and longitudinal polarizer polarized or have transverse and longitudinal components electromagnetic waves in free space are transverse only so here's a picture of a wave sine or cosine um and you know we can start with the characterization the one aspect is the amplitude how big is for example the water wave how big is the maximum strength of the electric or magnetic field that's the amplitude waves propagate and they have a velocity that is a characterization the length of the waves the wavelength is another way of characterizing in physics it's always important to understand the unix units of the objects we discuss here just as a reminder the velocity given in meter per second the frequency of your wave so how often do we find a trough for a wave for example per second the frequency one over second the wavelength in meters we can continue with the characterization and be a little bit more complete we can start from the medium the period the polarization transfers are longitudinal the wavelength frequency velocity or even how much energy is being carried by the wave when we compare waves and look at their properties we have to consider the phase of the waves so where do for example two waves line up the difference in phase between two waves and some of one some waves can interfere um so if you have two waves which interfere and they're out of phase like the one drawn in this picture the resulting wave has amplitude zero this is called destructive interference you can have constructive interference for example when those two waves are aligned there's no phase difference and then the amplitudes simply add at situation can be more complicated we study the speed of a wave there's a number of considerations the first one is that the speed of a wave depends on the medium in which it travels and the study of the speed or the the velocity dependence on the medium is part of what we will discuss whether or not when in the discussion of whether or not there is a medium responsible for carrying electromagnetic waves um the source so you know for electromagnetic waves you have a charged particle does the speed of the source change the speed of the wave the answer is no it changes the wavelength or the frequency but the velocity is not changed and you find this for example in sound waves in the doppler effect when you listen to a police car you hear that the frequency changes depending on whether or not the police car is coming towards you or driving away from you that's called the doppler effect that does not change the velocity of sounds in air that's independent um if you're when your medium is moving that changes the velocity um and so here you have to add the velocities of the meter so for light as a summary light is an electromagnetic wave which is moving in vacuum with speed c and that is independent of the source okay um but you can ask in which frame in which frame is that the velocity of light and what is the medium and that is really the discussion we want to carry on from here at the time when einstein developed special relativity there was still a discussion going on whether or not electromagnetic waves are of the nature of the particle or of the nature of a wave and whether or not that wave moves in a medium which was called ether so we can then you know experimentally determine this we can look at various properties of our waves and ask whether or not this is consistent with the hypothesis that this is a particle this is a wave in ether maybe both maybe neither and we can then fill a table like this one here and now answer the question so this is again an opportunity for you to stop the video and think through this and try to answer the individual questions i do this here for you um one characteristic of light at least when there is no heavy masses involved is that it travels in a straight line that is certainly consistent with this light being a particle but it's also consistent with its being the wave so the answer is both um are correct interference and diffraction pattern that's rather difficult to describe for particle model but waves as we just saw can interfere and there can be diffraction polarization what does it mean for a particle to be polar polarized um but waves can be polarized we have just seen transverse and longitudinal polarization light velocity depend on the velocity of this on the source velocity for particles that doesn't seem to to uh to hold for waves the stars and then the last is you know the speed of light crater and air than in water that's true for for wave for particles you know you might argue this one but i put a no in this table here which means that in our discussion up to this point clearly the hypothesis of a wave for light and ether holes we'll see in the next sections that there's aspects of light where the discussion will not forward like this especially for the ether hypothesis you