Mechanical Waves

[Music] [Applause] [Music] [Music] [Applause] [Music] [Applause] [Music] n [Music] [Applause] [Music] which way is this wave moving here's something moving across the screen or only up and down then what is moving across the screen here twoo dots are moving up and down why isn't the effect the same there must be something special about the way these dots move to produce a wave which itself seems to move in this program we shall be asking a lot of questions and here are two important questions about waves I want you to keep them in mind and see if you can discover the answer to them during the program first in a wave does anything move along and how can dots moving in straight lines produce a wave when you see a large question mark like this appear on the screen it means the question is particularly important and we shall repeat it at the end of the program for you to take down but why we should be studying waves at all is probably the first question you want to ask I'm sure you've heard of sound waves and radio waves and perhaps even of light waves the fact is that waves are a very important part of our daily lives indeed the fact that I'm able to talk to you now depends on two different kinds of weight but first let's look at some wave motions which we can see clearly these have great practical importance for example in the design and testing of ships an exact model is made and is placed in a large tank of water to observe Its Behavior often using slow motion film this large vibrator at the end of the tank generates waves of the kind that the real ship will meet at sea the models can be attached to a traveling Gantry which runs down the length of the tank the reactions of a model to real conditions can be carefully recorded using a mass of instruments on the Gantry but in the school laboratory it's easier to start with a single wave we can do this very well on a slinky spring I expect many of you have seen one it consists of a coil of sprung Steel and of course all the turns are connected together if I give this end a sudden flick we can see a single wave travel down the slinky a single disturbance like this is called a pulse so this is a pulse wave clearly the pulse travels quickly from one end to the other but what happens to each individual coil here it is in slow motion notice the reflected wave here's another apparatus where we have even more control over the waves it consists of trolleys connected together with springs in the slinky we have coils all joined together and in this apparatus we have tooles joined together if I move the first trolley across the Springs pull the second trolley across to one side as well but it doesn't move at once because it always takes a little while to get anything moving when it does move the next Springs pull the third trolley across and so on down the line and I can move the first trolley back now watch a complete pulse wave and Its Reflection and again in the speed with which a wave travels along this apparatus depends on how the apparatus is made in fact depends on the medium through which the wave travels and we can sometimes find out quite a lot about the medium by knowing how fast the wave travels how do you think I could alter this apparatus so that the wave went at a different speed well one thing I could do would be to put weights on each toley do you think that would make the wave go faster or slower have a guess have you decided yet well here's another line of toilet just like the first only each one has a heavy lead block on it watch well the wave goes more slowly it seems just for comparison I'll send a pulse down the second line of ters at the same time as I send one down the first you ready yes it's slower on the trollers with lead blocks more weight less speed perhaps some of you thought of having more Springs what difference do you think that would make well here we've got a third line of Tres and these are all connected up with twice as many Springs as the first line watch it looks as if the wave is going faster now just so you can compare it with the original line again I'll send the pulse wave down both together you ready yes well with this extra Force the wave goes faster more Force more speed to some of eyes here's the pulse at normal speed more weights on the trolley make the wave slower and more force between the trolleys makes the wave go faster now here's a problem for you I should like you to consider after the broadcast hurry could make a wave on this machine travel faster or slower by altering the machine in some ways notice how it's constructed the dots are at the end of cross arms and these are all fasten into a central wire which gets twisted back and forth the important thing is that once again like the slinky and the Tes all the parts are connected together our machine is rather elaborate but you you can easily make a simple one for yourselves by taking a rubber band gluing drinking straws to it and fastening drawing pins in the ends so I want you to think of two ways of making a pulse wave go faster and two ways of making a pulse wave go slower remember the T experiment and how this apparatus is made when thinking about your answer I'll remind you about these questions again at the end of the program so that you can drop them down then we've been talking a good deal about the speed of waves so how fast do you suppose the waves go on our machine to find out what two measurements do you need yes time and distance the machine is 2 m long from here to here and we shall measure the time it takes a wave to travel from end to end by using this electric clock an electrical contact at one end starts the clock the small hand goes around once a second and the large hand moves on oneis Vision every second and the second contact at this end stops the clock right we reset it ready there it took nearly 2 seconds 2 m in 2 seconds so the wave must be traveling about 1 m a second and I can't change that Speed without altering the machine in some way natural water waves are rather more complicated than those on our wave machine but those from the bow of a boat are fairly regular and smooth do you think their speed is always the same notice that the roar boat moves up and down like the dots on our wave machine most important you probably noticed that water waves are usually continuous to get continuous waves on our machine we should need to keep the end moving up and down like this a motor is more convenient so we'll attach one to the Machine by this bar and set it going to produce vibrations this is how we produced the pattern that you saw at the beginning of the program the pattern shows a continuous wave you may think we've changed the speed which the waves move along the machine now but we haven't what have we changed then yes the rate at which the end is vibrating in the frequency of the vibration we now have about one complete vibration per second and a complete vibration is called a cycle the frequency is one cycle per second and if we speed the motor up we can increase the frequency say to three cycles per second now I told you that the speed of the wave along the machine didn't change I wonder if you believed me and I told you too that the frequency had changed but something else has changed too do you know what we watch try to choose one particular wave and follow it along the machine and now it's going at a higher frequency is the wave traveling any faster or slower it looks about the same to me well how do we explain this here's a diagram of the two waves moving side by side let's halt them and look at the lower wave this you probably know we call the wavelength the distance from a point on one wave to the corresponding point on the next wave let's say it's 10 cm now what's the wave in progress and notice how many crests pass this point in 1 second let's suppose that it's 3 in 1 second this then is the frequency can we now calculate the speed of the wave if each wave is 10 cm long and in 1 second three waves have passed then the wave has traveled 10 * 3 or 30 cm in 1 second in fact the speed is the wavelength times the frequency how does this fit with our knowledge that the other wave travels at the same speed notice that the frequency is a third of what it was one cycle per second for every three of the lower wave but the wavelength is three times what it was 30 cm instead of 10 cm but we get the same speed 30 cm per second when we multiply the two together this then is an interesting connection between speed wavelength and frequency we Tred to confirm this result on an actual moving wave on our machine and to to do so we use this slow motion film in a moment you're going to see in this film The Machine start from rest and after 1 second we're going to freeze the film and look at the picture we've got remember the small hand on this clock goes around once in a second ready watch the small hand on the clock as well as the wave there it went round once we're seeing what happened in 1 second here is that last picture now first wavelength one wave is about 50 cm long that's half a meter and and now at frequency in 1 second we have one two cycles so the frequency is 2 cycles per second here is the information wavelength half a meter frequency 2 cycles per second can you calculate the speed yes 1 m/ second here it is in the picture 1 m in 1 second that agrees with the speed we measured earlier on the wave machine so we get the same speed 1 m/ second both for a continuous wave and for a pulse wave this then gives us a general formula connecting speed wavelength and frequency if you don't know the symbols for these three quantities you should find them out for yourself remember that this formula applies to any sort of wave we should be concerned with much faster ones vibrations too fast to see with a naked eye and so you can't tell if there's a wave pattern or not this is the case with this vibrating string one simple way of seeing what is happening is to use a stroboscope here is what the vibrating string looks like through a stroboscope another wave pattern so we shouldn't be defeated by faster waves but now for this week's question I'll remind you what they are so that you can write them down first when a wave travels does anything move along and connected with that how can dots moving in straight lines produce a wave second on the wave machine I want you to think of two ways of making the wave go faster and two ways of making them go slower well that's all for today just now and earlier in the program I asked you if anything moved along with the wave and I haven't been very helpful in answering that question but if you were sending continuous waves on this machine I think you'd find that you needed a certain amount of energy to do it what happens to this energy well look at the other end of the machine you've got here a small ratchet device and this is making a wave go up this weight is raised by the ratchet now can you answer that question