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If this wave is created on &n 6.00 an long rope that is fixed at both erds, will the wave fom stanaing wave &n the rope?Select one: Yes; with antinodes_Yes;...

Question

If this wave is created on &n 6.00 an long rope that is fixed at both erds, will the wave fom stanaing wave &n the rope?Select one: Yes; with antinodes_Yes; with antinodes_Yes; with antinodes:No standing wave will form:Not enough information:which direction the part of the medium at Tm moving at tSelect one;DownTo the leftTo the right This point on the wave not moving this time

If this wave is created on &n 6.00 an long rope that is fixed at both erds, will the wave fom stanaing wave &n the rope? Select one: Yes; with antinodes_ Yes; with antinodes_ Yes; with antinodes: No standing wave will form: Not enough information: which direction the part of the medium at T m moving at t Select one; Down To the left To the right This point on the wave not moving this time



Answers

Consider again the rope and traveling wave of Exercise 15.24 . Assume that the ends of the rope are held fixed and that this traveling wave and the reflected wave are traveling in the opposite direction. (a) What is the wave function $y(x, t)$ for the standing wave that is produced? (b) In which harmonic is the standing wave oscillating? (c) What is the frequency of the fundamental oscillation?

So party is asking us for the amplitude frequency period and thie wavelength. So Oh, also the propagation speed. So we should just just immediately right this equation down. Why accept t is going to be equal? Tio point seven five zero centimetres. So remember, very keep track of your units there. Obviously, extremely important on this will be times pi, um, point four zero zero centimeters to the negative First X and then oh, rather, this pie is actually distributed to the entire term here, so we'LL say text plus two hundred fifty seconds to the negative first, See? Okay. And we can compare this to why of x t. The standard equation would be a co sign k X minus omega t. So we know that this value right here is going to be okay. And we know that this value right here is going to be omega or the angular frequency so automatically we know that this variable right here is going to AA corresponds of this variable. So this would be a and put a amplitude is going to be point seven five sir of centimeters or point zero zero seven five zero meters. Always convert to s I u nits. And then we know that the angular frequency is equal to two pi over f, which means that the frequency is going to equal to the angular frequency divided by two pi. We know that the angular frequency is going to be two hundred fifty pie radiance per second and it's gonna be over to pie, which means that we have a privacy of one hundred and twenty five hertz. The period is simply one over the frequency or the reciprocal of the frequency. So one over one hundred twenty five and we have a period of point zero zero eight seconds and then we want the wavelength as well. So the wave The wave number is equal to two pi over the wavelength thie wavelength is going to be equal to two pi over the wave number, so this will be equal to two pi over point for pie. Wave length is going to be equal to five centimeters or point zero five meters again. That's why it's in. It's very important to know that this is a point four zero zero of centimeters too negative first pie. So that's why that's why the wavelength is measured in centimetres and then we obviously have to convert to Rs I units. And then finally we confined the propagation speed by multiplying the wavelength by the frequency point zero five times the frequency of one hundred and twenty five. And we get a propagation speed of six hundred and twenty. Sorry, six point two five meters per second. So this will be our V. This is our A. This is our f and this is our wavelength here. And this is our period here. Okay. And at this point, they're asking us. Okay, what's let's sketch a graph. Robert B. It's sketch a graph such that t equals zero seconds. So we have why of X t equals zero seconds and this is going to be point seven five zero centimeters. And then we'll have co sign of point for pi Centimeters to the negative first acts and our Graff is gonna look something like this. It doesn't have to look, it's definitely a sketch. Doesn't have to look perfect, but you do have to get these critical values and so it will be here. It will be a zero comma point seven five and this is why in centimeters this is X and centimetres and I'm we are going Tio Graf and centimetres simply because it's giving us a bit easier values to work with. And then this point right here will be one point two five comma zero. This point right here will be two point five common negative point seven five and then this point right here will be three point seven five comma zero. They're asking us to graph it at X T equals point zero zero zero five seconds. So extremely small time interval. And this is going to be equal two point seven five zero centimeters and it will be co sign of point for pie Centimeters too negative First X plus point three nine to five. Let's again, Charlie, this sex and centimetres, why and centimetres. And let's draw this shape of this curve again. We just need to get these critical values. So this one right here is going to be zero comma point six nine three. This value right here will be point nine three eight, divided by zero. This value right here is going to be two point one eight eight comma, negative point seven five And then this value right here will simply be three point brother. This value right here will be three point three, three point four three eight comma zero apologize. And the final graph is asking us to find, um Why of X t equals point zero zero one second So double what we had last time. And rather this is simply going to equal point seven five zero centimeters. This will be Times Co sign and then of again point four pi centimeters to the negative first X But instead we'LL have plus point seven eight five So once we have this, we can Now again Graff and again we're going Tio, draw the general shape again. This is a sketch, but we do need to have these four points at least So and this is all found with a graphing calculator and then eso this point at this point is point zero comma point five three one. This is going to be point six to five comma zero this is going to be one point eight seven five comma negative point seven five And then we have here three point one two five divided by zero and this will be it again. Let's label our axes. Okay. And then the final, the final three parts asking us, Ah, what direction is the wave moving in? So as T increases, we find that acts is decreasing. So the wave is obviously moving in the X and the negative X direction and then for part D, they're asking us for the attention. So we have the linear density of point zero five zero zero kilograms per meter and we simply need to find the force tension. We know that those those propagation speed is equal to the square root of the force. Tension divided by the linear density. We can isolate the force tension and find that this is going to be equal to the propagation speed squared times, the linear density. And we know the propagation speed of six point two five. We found it in the first lied squared times that point zero five and this is going to be one point nine five Nunes. So this will be the fourth tension. And then for part ee, they're asking for the average power. So the average power is going to be equal to one over two time's a linear density, times of propagation, speed times, omega squared times the amplitude squared. We have all of these. Um, we have all of these values. And again as a reminder, the amplitude is simply point zero zero seven five meters. So we can say that the average power is going to be one over two point zero five and then the propagation speed of six point two five and then we have our omega squared is going to be two hundred and fifty. I squared, and then our amplitude, of course, point zero zero seven five squared and we find that the average power is going to be five point for to watts. So this will be your answer for part ee and that's the end of the solution. Thank you for watching.

This problem covers the concept of the standing wave and for a standing wave on a string tied at both ends. The fundamental frequency Fs uh one upon to, well, I'm steve uh they speak pretty okay. So the frequency, the fundamental frequencies, the Wave speed is 16 m four seconds Upon to into the length of the string that is two m are. The frequency of the standing wave is 15. Coach of the way violent equals the waves feed upon the frequency. What we can be, the equivalent is 60 m or second of all. The frequency that is 15 March so the violent is four metre.

So in this problem, we need to make use of the given way function while Frank's d, which is right written right here to derive the master important properties of function. So first property is the altitude on from the given form of the function, we can see that the opportunities right here on that we can state immediately that a equals 0.75 70 m altitude. We also know the way number which is 0.41 over centimeter. And we also know the angler frequency which is given us 2250 one over second. From here, we can also find other important properties such as frequency which were related to the angular pregnancy in the manner that Dubai Times frequency equals 250 Hi, one over second from here when you arrived at basically the frequency but will be 250 or two on one more. Second richest hurts Andi f equals 125 hertz or cycles per second. So the the other important properties a period which is D equals one over f, and that equals in this case one over 125 seconds on the Sequels. 0.8 seconds. This is the period of the coal situation for the good wave Onda. Also, we need the way late and the Vaillant is equal to Dubai. Over Kate. Now we know. Okay, it is zero point forward times Pi centimeters. I think I Yes, it is. So the Sequels to buy over 0.4 times by on bean eaters. So when we put this virus into a calculator, you obtain that. Oh, and I equals five centimeters. Andi, Finally, we need to make use of all of these variables. All of these para meters do evaluate the last e or the wave propagation. So the last time we on the main propagation is able to Well, we can use frequency time. Slam that since we know about the frequency and the railing, I have time slammed, which equals 125 times five. So remember that this is five centimeters and that this is 125 seconds. So we need to make times 10 to the mind second power meters because this is in seconds and substituting this into or placing this policy into calculator obtain, devalue that V equals 625 means there's centimeters, uh, centimetres per second because this wall here will be 106 m per second on this is it for the party of the problem. Now for the barn to be of the problem, we need to sketch. We need to sketch the shape of the robe as the way displacement is being passed. Truly So at a zero, for example, we can say that is this is going to be why access, which is the access of displacement, vertical displacement. And this is XX is Andi. This access is going to be classics minus eggs and the vertical displacement. So in the beginning, the vein will be symmetrically around the shape of the rope. For doing this. Now, observe that the name is moving from the rifle inside to the left hand side or to the negative X direction. So this is for the D equals zero. Now, another sketch that Trinity's 40 equals for D equals 0.5 seconds. So very small Dia period. How do we obtain this? Well, we just follow the amplitude, the altitude, the move Move along and the position of the operative can be obtained from exactly this function. When we say that that t equals zero, aptitude is on X equals zero. So then we just basically fixed our exc according to be the coordinate of the amplitude and we just smoothing time which is substitute different bodies for time. So we'll be we just substitute here. We can substitute if we want to see how the app it'll change. For example, with time we just need to substitutes zero where the axes Andi will attain the function of t and we want to see how the vague propagates in space. Then we need to find the specific time D and substituted into here and then graph basically this whole function for different finance effects and find where the maximum is where the opportunities and create this sketch. The is a rough sketches. They're just here to show you how the function behaves. So now the object of them removed slide to do glad. So it would be like this from the left, from the right hand side to the left inside. Clearly the wave is moving in the negative X direction. This is where t equals 0.5 seconds and for double the time of that, it was only moving on the further the left hand side so it could be silver like here. So these bloods can be even to me. Block is using computer softer berry will just substitute dysfunction into the sulfur and substitute that given time t and then make X view of arable. And then the soft revealed American flocked every point for every possible X on the real axis. And for this is for the part of deal this problem now for Depart, see of this problem we need to make use off two. Very important for most of recorded transfers ways. So the relationship that stays it's the lost in wave transfers. May is going to be f over the leaner density off the video or the string of the role for any kind of meeting for the transfer spade. And from here this far, no, I was supposed to find the result of force or the tension that is in the robe while the the waves get disease being propagated, and from that we can find the average power, which is speed average, which is given by the formula on its own. And these four relays one have off square old density, leaner times. Pension force times, omega squared times eight squared. So first we need to find the detention force or the result first components. So it's going to be equal to we lost the Square times, destiny and both of this wiser. Give it some dissident to be six pulling 25 which the second squared times 0.5 kilograms per meters and this gives together meter several seconds. Scared over second square times kilograms. So this is new dance, Andi. Finally, when we put this piracy to calculator, we obtain that half because 1.90 five unions for the average power off the murders powers is created to the energy that is being moved from one place to another with the wave balls or with debate motion propagation through the medium or to the rope, we will be, Yeah. I mean, if you we have every term that we need. So here on the horizontal force, we can does it. Do we have altitude? We have anger, frequency, everything. So we could just substitute one because square in golf, 0.5 times, 1.95 times 250 pie squares times 0.0 0 75 squared, and this is going to be in what's or jewels per second. So the final answer is the average equals to five points for two, but on this is

Frequency of the N it normal mood is given by end times V over to ed and frequency of the interest wanted normal motives and plus one re over too well so we can find that this is if this is 400 hearts, then that is 480 hearts. So from here, we can figure out that if we take a difference, then really, what do well comes out to be for a T minus 4400? It was 80 hearts, so we find that and it was 400 hearts divide by fee over to end. So who you getting in from here? Overview. Want to at least 80 hearts? We have an inquest. Five. Now we have them. The end. It was to end over end length of the string is four meters or two times four meter over five equals 1.6 major and them the end. This one equals two is over and plus one equals a meeting over six equals 1.33 major. Finally, velocity is given by two l a friend of what n equals Squared off t over mu. So from here we see that the over mu on that the square do It comes out to be to l and Ephron over Eni's we overdo in which is 80 hearts. So we find that tension in the string to be two times as it was four meters times 80 hearts times Munich was 0.6 You know Graham by me. Dad squared off this on. This is outside the square. So we find the tension in the string to be 2.457 times 10 to the three new good.


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