For the birthday of this problem, we will derive detention for us from the general formula. Is the end mode on the frequency order for the mental frequency that were given in this case so ever Neagle's and over if you ill and then a squared off detention for us over the density linear distance. So since and because one for the given case we know that have it was one over to L over the dance T When me arise, vote both sides to the power of to and your range the equation of brackley you obtained that f equals four times Franklin C squared time slain square times leader density Also believe your density is mess over L, which is then said the more evidence determines the area times the length over length For this to cancels out than your pain road times A. Which is this case for the given string radius. There's the times five times, right, He's squared so we can say that af equals. We know the frequency four different demand full and first harmonic. So it is his four times 247 herd's times. No, we need me to square of course. Now we need to apply the body of the linked he meters and square it and then we should have this. So this is equal. Do 7800 kg permitted skew times by times on this will be the radiance is very small. So radius for this problem. He's basically how the older given diabetes which is zero point for 06 millimeters over two and then squared. And when we evaluate this your pain that this this linear audacity is one 01 kilograms meters. But I'm just that this will be times 10 to the negative. Terry Power kilograms for meters killed just meters. Sorry. So this way you can that be substituted here they can say this 0.1 constant negative third power squared and course the end dimension will be Newtons. And when we place this foot, it's into calculator. You obtain that people's 99 point or Newton's now for depart, be within two bruv relationship between the small change. Delta uh f frequency somehow relates to changing and exactly how it relates. And to prove that given four million the problem. So we'll start from the general for for the frequency and then we will express the changes. The frequency will be the change of the whole function. No dessert. This is the cost of term. So this is just want to l No, no. The square of the bath off the leaner density. This is also cost the term. So it is one over to l square off the density Andi have here Delta off square off. Scared off. Now, since we need to go to the other half, we should note that if we have some function off, some worry able, resemble ffx Delta affects the small change in his function will be the first derivative love that functional Rex times Delta X So for the force have here we can say that this is the derivative of the square. The fast over f times are tough and now it is. It is the real issue here. He's actually derivative of F off on one half over the and these derivative from the elementary rules, self motivation will be one cause f minus wrong. Half the F which is this minus is plastic pieces one over F. So this is a good one one over square. The fast. I don't have. This should be substantive back on. Then we finally turned. The delta frequency is one over to l square into the density. And then one powerful changing force square with force. The ratio from here we go that the ratio delta frequency or frequency will be one over to l squared density among Karpov does ask whole Graf and then all of this over one. There were do now and then this square with half over the nasty. What? We cancel out everything as we can cancel up this term this term this term busy going to everything except one half. And this racially intended. This is ableto one from Delta F over half. And by this the formula is proven before they're given in the problem for the bar to be for the barn. See, we have this change in the temperatures on and this change in temperatures are contributing. Teoh the linear expansion that we hear letting their expansion coefficient given as well. So we can first relates the changing tension force with the linear expansion. You too be the change off the temperature. So we need to. Why? Coefficient of expansion, Cross sectional area and the change in temperature. We can also substitutes what is since that, given the problem. Some incident to be two times despite insurrection early This is the young young's Mothers off steal this scary. We shouldn't maybe better say this week, expressing with big Why, so that it doesn't get may stop weed the function of a function or vertical displacement. So here we have two times stand for 11 power basketballs. Since next models, he has seen dimension so pressure times. And here we have this professional in every expansion which is 1.2 times and the negative fifth power one ourselves years and then we can the area cross sectional area, which is by times zero point tree 20 to 3 times 10 to the negative third power meters and then squared from then times. The changing deputy reaches from the daughter of the late changes basic 11 degrees. This that is obtained then be subtracted given bodies from temperature so 11 degrees tells use. This isn't one over Celsius. We can use cells is here. And when we put this forest into calculates, we obtained that this change forced entry means negative three points for Newton's. Now we know the relation that I have over after is one off off Delta Force over force frequency and forced change relationships so we can use this relationship and say the frequency or frequencies able to well, one half of negative one point for mutants own word 99 point for mutants. Of course, one half of this is in the product, so this will be equal to this. Will people just somewhere around 0.34 over two. Negatives on Finally, when it could, despite the car crashed through a fence. Zero Negative 0.0 70 No, from this body you you obtained that the frequency is pregnancy times negative 0.0 self team, which is equal June 247. It's times negative, 0.0 17. And when we place this one isn't a calculator and evaluate, we obtained that the change frequency is negative. Four points to hurts. This is the end of the problem. I hope you find it's helpful and they hope to see you in another lesson.