AT&T

Does the object in t Possibly take you back to college physics class. Dr. John S It's called the S The mac It was part of a general effort on the part of ATT's Bell Labs to provide novel educational tools for the next generation of scientists. Now it's a staple in physics classes around the world. You can still buy one newly manufactured, though it will set you back hundreds of dollars. Besides being an inventive engineer, Straight from AT&T Arc In the various fields of physics and engineering, are impressed by the similarities w These similarities are due, of course, to the basic fact that waves of all kinds behave fundamentally a These two rib- With them I can show you many of the various wave properties w The waves w Attached to the central wire are these cross arms w The entire structure is supported in a set of bearings w T It has cross arms w You'll see later on why I have these two mac First I want to show you the two different ways in w Observe that right now that is, t If I start a wave at t But now let me terminate t I'll clamp the reflection is still total as it was before, but the wave is inverted upon reflection. In a mechanical wave system then there are two ways in w Right side up, if the reflecting end of the medi Now if nature has any consistency and we And these other drawings here show that indeed it does. Take the case of an electrical transmission line for example. And similarly in the case of waves traveling down an acoustic tube, there are two different reflection possibilities, depending on whether the end of the tube is closed by a rigid termination or by the acoustic analog of a free end. Note that in the mechanical situation a clamp is a constraint preventing the displacement of the end of the wave medi The electrical analog of t And the acoustic analog is a rigid closure at the end of an acoustic tube, preventing the longitudinal vibration of the air. In all of these cases, the reflected waves come back upside down. And in all of these other cases, conversely, which are analogous to the case of the free end of a reflecting wave medi You see nature really is consistent. Well now let's have a look at some of the other t One of the most important topics in the general development of wave behavior is the principle of superposition. When two waves traveling in opposite directions on the same medi The instantaneous amplitude of the resultant wave is the algebraic s T When one of the two waves is positive and the other one is negative. Observe that in this case, at the instant of exact coincidence, there is a momentary cancellation of the amplitude, and the medi Now let's have a look at the superposition behavior of continuous trains of periodic waves. With t Alright, in slow motion now, here come the waves. After reflection, the waves travel back up the mac The pattern that you see on the various portions of the medi Observe that in this pattern, there are places where the medi These dead spots, or nodes, are exactly half a wavelength apart. Now I'm sure that you've all seen behavior of t For example, a vibrating string. Always vibrates naturally in one or more segments, separated by such nodes. Now let me show you somet Suppose I simply move t Under these conditions, the new waves w The system thereupon becomes resonant, and the amplitude builds up to the noticeably larger value that you see here. Under these conditions, the new energy w Now the initial adjustment w I could just as well have produced resonance by leaving the line at its original length and tuning the frequency of the generator instead. And I can destroy the resonant pattern that I have here by changing the value of either of these parameters a little bit in either direction. Another way of looking upon a resonant system is to regard it as a reservoir for energy. Thus the escape wheel of a watch, a c They ex Now from here I want to go on to the subject of the impedance of the wave medi The generation of waves on a transmission line of any kind, electrical, optical or what have you, involves two parameters, an originating cause and a resulting effect. In an electrical transmission line for example, the cause of the waves is an AC voltage applied to the input end of the line. W The ratio of the cause to the effect is called the impedance. You're probably most familiar with the term impedance through your studies in the field of electricity. But t On our mechanical wave machine there for instance, the cause of the waves is the oscillating torque which I apply to the first cross arm and the result is the oscillating angular velocity imparted to the medi On that structure then the impedance, the mechanical impedance, is the ratio of the applied torque to the resulting angular velocity. In terminating the other end of a transmission line, we frequently seek to adjust the impedance of the terminating load to equal the impedance of the line itself. When the load is then said to be matched to the line. Now t Such a mechanical impedance is afforded by t Simply a tin can full of water with a little piston p By sliding this dashpot in or out along the last cross arm I can control the counter torque with which it resists the displacement of the medi When t Now instead of using single waves suppose we have a look at t Here you see such a train of waves traveling down the mac Now suppose I spoil the impedance of the load now no longer matches the impedance of the transmission line and a partial reflection of the wave energy occurs. Let's have a look at t We expect some kind of standing wave pattern to appear on t After all we have running waves going in this direction and returning waves coming in this direction at the same period on the same medi Well, I do see a standing wave pattern of sorts. Here are the nodes half a wavelength apart. Only notice now that the nodes are no longer standing still as they were in the case of 100% reflection. Suppose I have the camera speed up the picture for you so that you can see what the envelope of this standing wave pattern looks Now let me draw you a sketch of that standing wave envelope. The amplitude at this point I'll call A sub maxim Now in wave theory the ratio of A max to A min has a particular significance. It is called the standing wave ratio abbreviated SWR. On the wave mac Now recall that when we had 100% reflection when the end of the mac The standing wave ratio in that case was infinity. On the other hand when I had a perfect impedance match there was no reflection at all and no standing wave pattern. In that case A max and A min were the same and the standing wave ratio was unity. Now I the punchline is t In any practical case of reflection a measurement of the standing wave ratio on the medi The complete expression is percent reflection is equal to the standing wave ratio minus 1 squared divided by the standing wave ratio plus 1 squared times 100. Now just for fun let's measure the percent reflection that's taking place here. With these identical scales I can measure the amplitude at a maxim If you and I agree the maxim Therefore the standing wave ratio is 5 halves. Substituting in the percent reflection formula we obtain percent reflection is equal to 5 halves minus 1 w Now note that I have just calculated the percent reflection on a mechanical wave system using an expression that was first developed in the field of AC electricity. Now this is a perfectly valid and logical thing for me to do since waves of all kinds behave a Now let me develop for you another idea. Waves are partly reflected not only at mismatched terminations but also at places where the impedance of the transmission medi Suppose I connect these two wave mac Together they give me a single transmission line made up of two pieces having different impedances. At t A wave traveling slow along this medi T Now before I show you what I want to show you let me clip t It's t Alright here comes a wave and there it goes. Again. Do you see the reflected waves coming back from the midpoint here? Now that I've warned you what to look for t Here it comes. And once more. There goes the main wave. Here comes the partly reflected wave. Electric waves, light waves, sound waves, mechanical waves are partly reflected when they encounter impedance discontinuities. Usually in situations of t After I connect up t As we might expect a partial standing wave is produced. If I wanted to determine how much energy is reflected there I could measure the maxim That expression is equally good for calculating the energy loss at any kind of impedance mismatch or discontinuity. Often in our technology this partial reflection of wave energy by impedance discontinuities in the transmission path is economically wasteful and we seek to avoid it by inserting some kind of impedance matching device between the sections of the medi Here is an example of such a mechanical impedance matc It is simply a short section of the wave medi It is called a quarter wave matc I'll sandwich it in here and then show you how it operates to promote the transmission of wave energy across t Alright, here come the waves and now you watch what happens. And there they go. There is no perceptible partial standing wave on the input portion of t Apparently then I have matched the impedances of these two mac The non-reflecting coating on the lens of t It works in precisely the same way with light waves. Now unfortunately t It operates only for continuous waves and it is effective only for a narrow range of frequencies including the particular one for w For applications in acoustics, mechanics, short wave radio and the Now the megaphone smooths over the impedance discontinuity between the air col The mechanical analog of a megaphone is a section of the wave medi A tapered section transformer such as t It is effective also for use with single waves and pulses. Watch what happens now when I send a n Here comes a short quick one and you see that hardly any perceptible reflection comes back. Here comes a somewhat longer one and again only a small amount of reflection returns. You see the tapered section transformer is really a relatively broad band device. Here is another example of a tapered section transformer. It is a piece of wave guide used to couple a section of rectangular cross section wave guide to another one of a smaller cross section in such a way as to prevent the reflective loss of radiation. In electricity we employ transformers ranging all the way in size from t Even nature herself is in their pitc Inside the mammalian ear there are three tiny bones called the hammer, the anvil and the stirrup. Their task is to provide an impedance linkage between the low impedance of the air in the outer ear and the And in addition to all these transforming devices that are used with pulses and waves there are others that are employed with unidirectional motion. For example in mechanics all of the mechanical advantage machines such as gear trains and levers and pulleys and the Now in t One t Waves of all kinds behave and if through any process you choose you can learn the fundamentals of wave behavior either through the study of some discipline in w Then you will always feel at home in any branch of physics or engineering where the main show has to do with waves and how they behave.