Simple Waves (1959)

almost every day you see examples of this kind of behavior in flapping flags and whipping clothes lines but I'll bet you hardly ever seen it happen this slow before in the classroom and in the laboratory you have been studying the properties of pulses and waves in this film I want to show you in more detail some of the wave properties that are pictured and discussed in the text I hope that by seeing actually how waves behave in various situations you will be able to understand them better this steel spring is very similar to the slinky that you have used in the laboratory I can launch a pulse on it simply by giving my wrist a quick flip any pulse I generate has certain properties it has a side and the shape and a speed along the spring perhaps you can see these features better in slow motion note that at any point on the spring the medium is at rest both before the wave arrives and after the wave has passed by down at the other end of the table where the spring is rigidly fastened the pulse is reflected back toward my hand note also that after a few such Reflections the wave dies out this dying out is due mainly to the friction which the tabletop exerts against the crosswise motion of the coils of the spring now there are a number of fundamental properties possessed by waves of all kinds which it is important for us to know about and to understand and I've devised a number of simple experiments here which should lead us to some fairly definite conclusions about these fundamentals now just what is it that we wish to know well first does the speed of a wave depend upon the nature of the medium it is traveling in or to put it in other words will waves travel in different media with different speeds second will a wave travel with a constant speed in a uniform medium and third How does the speed of a wave or pulse depend upon its size or upon its shape now let's concentrate our attention on the first of these three questions does the speed of a wave depend on the properties of the medium it is traveling in here I have three different things a small diameter brass spring the slinky that I have used in previous experiments and a long piece of heavy wall rubber tube each of these three things can be used as a medium for the propagation of waves this cross piece will enable me to launch pulses on all three of these things at the same time the pulses travel with different speeds don't they here let me launch a few more while you watch them in slow motion let's watch that again you see this experiment answers our question doesn't it the speed of a pulse depends on the nature of the medium it is traveling in now let's think about our second question in a uniform medium is the speed of a wave constant say will you take care of these for me please what I want to do now is to study the motion of a pulse along this brass Spring by taking six flash photographs of a single pulse as it travels along doing this will give me a picture showing the six instantaneous positions of the pulse at 5 equally spaced intervals of time all as a multiple exposure you see on the same picture in this picture I shall be able to determine the six positions of the pulse by interpolating between the lines on the tabletop these marks are 50 cm apart the spring itself is made of brass wire of uniform diameter the spring has a constant number of turns per centimeter and in the experiment it will be held hel under uniform tension so that it can be considered to be a uniform medium now let's have a look at the apparatus I'm going to use to fire off the flash bulbs this is a rotating switch turned by an old phonograph motor which will close an electric circuit to the six flash bulbs one after the other at intervals of 12th of a second now we don't want any of those flash bulbs to go off before the pulse is launched on its way so I have included in that battery circuit a master switch a mouse trap which will be set off by the pulse Itself by the pull of this white thread when the pulse has reached this position on the table all right now that everything seems ready I'll darken the room and my assistant will open the camera shutter and I'll start the pulse on its way all right ready 5 4 3 2 1 zero here is an enlargement of that flash picture we took a little while ago Let's uh look at it and analyze it for what information we can extract from it in it you can clearly see the positions the pulse occupied at each of the six flashes 1 2 3 4 5 six oh and here also is evidence that the pulse was dying out as it traveled along look the size of the pulse at this end of the table is noticeably smaller than it was up here when the first flash went off all right granted the dying out now what about the speed I could go to some trouble to analyze this picture and carefully determine where say the middle of the pole was at each flash however I don't think doing this will be necessary for I believe you can see with half an eye that the pulse positions are equally spaced and that in each 12th second interval the pulse Advanced about 50 cm there is no evidence in this picture for either speeding up or slowing down and we may therefore conclude that at least within the limits of our simple observation the pulse traveled with substantially constant speed the size of the pulse was dying out to be sure but its speed remained constant now so far we have demonstrated that waves travel with different speeds in different media and that a wave travels with constant speed in a uniform medium with these facts established we should be able to predict that equal waves in equal media should travel with equal speeds let's see if this is really true here are two slinkies as identical as it is possible to make them both pulled out to the same tension I'm going to launch identical pulses on these two slinkies and you watch what happens to them they travel side by side didn't let me do it again now let's watch that all over again in slow motion now I'm going to make you think a little suppose I reach out and gather in a few turns of the right hand Slinky so as to stretch the remainder tighter than it was before is there any reason to believe that the speed of a pulse will be any different under this new condition if the same Slinky is it after all I have stretched it tighter and changed its condition well will a pulse travel faster or slower or with the same speed as before this test will give us the answer watch now now let's watch that all over again in slow motion well there's no doubt about it the pulse traveled faster on the tighter Slinky now let's watch that again evidently then the speed of a wave depends not only on the medium it is traveling in but also on the condition of that Medium as well for example here when I tightened up this Slinky I changed its condition by increasing its tension and it's hardly surprising that by doing so I change the speed of a pulse along it now I'm going to ask my assistant to get rid of these slinkies for me and bring me that rubber tube that I was playing with before this is the same piece of thick walled rubber tube that you saw in an earlier experiment perhaps you noticed that it has a black stripe painted down one side now this time instead of giving my wrist a quick flip so as to generate a transverse pulse traveling down this tube so I'm going to give the end of it a quick twist generating a wave of twist which travels down and which I hope you will be able to follow by observing the behavior of the black stripe watch this well that pulse traveled awfully fast didn't it and I question how much of it you could really see in any detail so I suggest that we have a look at a different kind of twist wave apparatus this Rod behaves very much like the rubber tube we were just looking at in order that you may follow the progress of a pulse along its length I have soldered a number of cross arms between its two ends these cross arms make the pulse travel more slowly this thing down here is simply a tin can full of water with a little piston pumping up and down in it that piston is attached to the end crossarm so as to prevent that cross arm from overshooting when a pulse comes along now if I twist one end of this Rod by simply displacing the cross arm in my hand that pulse of twist travels down the length of the rod and displaces this cross arm in turn the speed of a pulse on this Steel Rod of course is very fast and it may have seemed to you just now that the action was almost instantaneous however I'm going to repeat these pulses at periodic intervals and if you watch carefully you will be able to note that there is a time lag between the displacement of the Cross arm in my hand and the resulting displacement of the Cross arm at the other end this time lag is precisely the time it takes for a wave to travel the length of this Rod now let's have a look at still another wave machine this one is very much like the one I was just playing with except as you see it has a larger number of cross arms spaced at equal intervals between it two ends the central Rod that is the backbone of this beautiful structure is resting in bearings which permit it to twist freely remember now it's this Central Rod that is behaving like the rubber tube in the last shot the speed of a pulse along this Rod is very fast because steel is much stiffer than Rubber and in order to slow the pulse down these cross arms have been added it will be difficult for you to see the progress of the pulse along the central arm and therefore it'll be necessary for you to observe the progressive displacement of the ends of these cross arms as the pulse itself travels along the central Rod now I'm going to produce a Twist of the central Rod by giving this cross arm an up and down motion now watch isn't that simply fascinating You observe that the pulse traveled the entire length of the machine was reflected at the far end came back again and was reflected at this end and repeated back and forth many times of course it eventually dies out and you've seen examples of this dying out before in the case for instance of the slinky on the tabletop this machine has a lot less friction however than the slinky and it's not surprising therefore that the pulse lasted a great deal longer before it eventually died away now I wonder if you wouldn't like to see this thing happening again in slow motion and the next thing that you see will be another pulse which I will start traveling along the machine at about half the normal speed here it goes this is a very handy piece of of apparatus for studying the behavior of waves let's use it therefore to answer our third question does the speed of a wave depend on its size or its shape thank you on this apparatus a wave travels slow enough so that I can get a reliable determination of its speed simply by measuring with this stop clock how long it takes the wave to make a round trip down and back let's try it here goes start stop that took 40 seconds let me do it again just to get confirmation here we go in slow motion start stop that took 3.9 seconds about the same as before now let's study the behavior of a pulse which is noticeably smaller than the two I just launched here we go start STP that took 4.0 seconds and I'll do this one again too just to make sure ready in slow motion start stop that took 3.9 seconds about the same as before well this is interesting in apparently the size of a wave has little effect on the speed with which it travels now let's study a wave of different shape so far the pulses we have been using have been little short pulses uh maybe five or 6 in long let's Now launch a pulse which is half the length of the entire machine and see how that travels here we go start stop that took 3.8 seconds substantially the same as before let's do this one again too just to be sure this time in slow motion start start 4.0 same as all the others well now this is an interesting development isn't it here we have a wave medium on which waves of all kinds regardless of size and shape seem to travel with substantially the same speed nature abounds with this kind of wave behavior for example when you're listening to a band playing on a football field between halves the sound waves of various sizes and shapes which correspond to the different pitches and loudness of the music you're listening to all reach your ear with the same relative timing as when they left the instruments down on the field now let's examine a few other aspects of wave Behavior [Music] here is a second wave propagation machine it is similar to that one except that the cross arms are only about half as long it is therefore physically a different medium and we will would expect the speeds of waves to be different in the two this difference I can show you quite grammatically if I mount the second machine over the first and with the aid of this little wire connector launch pulses on both media simultaneously in slow motion watch now well there's no doubt about that the pulse travels a lot faster in the medium with shorter cross Arms This observation is quite in keeping with what we have already learned in other experiments waves travel in different media with different speeds now let me show you something else here I have placed the second machine end to end with the first machine and I am now going to clamp their Central rods rigidly together this little clip will do it now what do you think will happen to a pulse as it travels along the first machine and crosses the boundary into the second it should slow down shouldn't it in any medium a wave travels with a speed which is characteristic of that Medium therefore as a wave comes along and Crosses this boundary we expect that it will change its speed now let's see if it really does watch carefully there did you see that did you see that as the wave crossed the boundary into the second medium it did indeed change speed I'll bet you'd like to see that again in slow motion watch now isn't that simply beautiful but wait a minute have we seen everything there is to see did you notice that as the wave crossed the boundary it was not only partly transmitted into the second machine but it was also partly reflected back again onto the first machine I'm going to repeat this experiment again in slow motion while you watch carefully for the reflected pulse watch now evidently then when a wave crosses a boundary between two dissimilar media it is partly reflected and partly transmitted now have you ever seen behavior of this kind before I'm sure you have you know that when a beam of light passes from air into glass or water it is partly transmitted and partly reflected at the surface in this respect at least light behaves much as waves behave on our mechanical models and the farther you go in your studies of physics the more similarities of this kind you will find between the behaviors of all sorts of wave now let's review the things that we have been studying the speed of a wave depends on the properties of the material in which it travels in different materials the speed of a wave will in general be different even in the same material changing the conditions will cause a change of speed and thus the same material may become a different medium in a uniform medium the speed of a wave is constant this we showed by demonstrating that a wave on a uniform medium traveled equal distances in equal intervals of time while transverse and longitudinal waves are common place waves of twist also occur in many cases the speed of a wave is is independent of its size or shape when a wave encounters a boundary between two different materials it is partly transmitted across the boundary into the second and partly reflected back into the first we are going to need to know a great deal more about wave Behavior as we progress in this course and later on we shall spend a good deal of time in such studies in other films