a-rope-of-length-5-m-is-stretched-to-a-tension-of-80-n-if-its-mass-is-1-kg-at-what-speed-would-a-10-

Question

A rope of length 5 m is stretched to a tension of 80 N. If its mass is 1 kg, at what speed would a 10 Hz transverse wave travel down the string?
(A) 2 $\mathrm{m} / \mathrm{s}$
(B) 5 $\mathrm{m} / \mathrm{s}$
(C) 20 $\mathrm{m} / \mathrm{s}$
(D) 200 $\mathrm{m} / \mathrm{s}$

Sachin Rao · Accepted Answer

problem. We have given a rope of land five m and tension in the room is 18 of them. It may, if it&#x27;s mass is one case. At what speed without 10 hurt frequency is 10 harsh. We have traveled down the string so we have to find this feed. So we know that we know that formula for the spirit is equal to V is equal to undergo TV. I&#x27;m you were amused. A mass per unit length and bile. So the speed will be equal to under road 80 divided by mass which is one kg into l l is five m. So this is a call to underwrote 400 So speed will be called to 20 m. But they can now we will check the options of options civil. We were correct option of Sun Sea

Ze-Han Lee · Answer

So in this problem we need to know that the wave speed on the string equal V because screw t over Landa So tes attention force an alumna is the density of the rope which equals the total mass of the rope over the lands of the rope. Okay, so according to this problem can see that the Lambda equal 0.2 kilograms lemaitre intention is 80 new toe. So we can&#x27;t in that to this sequel. 20 meters per second, okay?

Averell Hause · Answer

So for party, the mass per unit length um, you This would be the linear density is the mass over the length and so this would be 0.60 kilograms or 600 kilograms. So three significant figures divided by 5.0 meters again, three significant figures. So this is giving us 1.20 times 10 to the negative second kilograms per meter. And so we know that then the required tension in the string f would be equaling, the velocity squared multiplied by the linear density. So this would be 50 0.0 meters per second quantity squared multiplied by 1.20 times 10 to the negative second kilograms per meter. And we find that the required attention it is equal in 30 0.0 Newton&#x27;s and then for part B, the velocity is gonna be equal in the square root of the force divided by mu, the linear density. And here we have a force instead of 30 Newton&#x27;s only eight Newtons. So this would be 8.0 Newton&#x27;s divided by that same linear density 1.20 times 10 to the negative second kilograms per meter and we find that the speed is gonna be equaling 25 0.8 meters per second. This would be our final answer for part B. That is the end of the solution. Thank you for watching.

Kai Chen · Answer

so it question lighting. We have trust, Worsley. Um, it has being a rope and sands. This world has unanswered off two meter. It has a massive 60 grams. So is that tells us of the mass density of the graph of rope is that we also know that it&#x27;s a real pissed atia of five contributor and we are looking for two speeds as away is traveling. Okay, that is quite straightforward. Uh, we are givens, attention working on the mass density. So speed is the way this traveling is tension over mass density. So we don&#x27;t have a not remember to play with us, and then we can just directly puts it into it. Um ever sink wrist? We do not know. We need to. Captain. It was mass testes, and that can be done by have total nous over total nets. So 500 newton and then mass density is total. Mess is 60.0 guerra. Um, but it&#x27;s used as a unit. So this is pseudo points there. 06 kilogram over. This is to be here. This gives us if you could get your calculator. Ah, 100 Tony and I meters per second

Neil Pandya · Answer

all right, so let&#x27;s write down the tension of the string. Tension is 80 Neumann&#x27;s The string has a length of 2 m, and the mass of the string is 5 g, which is five times 10 to the minus 3 kg. So if we want to find the speed of a trans verse wave that would propagate through this string here, then we&#x27;ll be using this equation. We write down the equation in general, that one, and that is going to be 80 times to over five times 10 to the minus three. So that is, um, 1 60 which is 1.6 times 10 to the second power over five. Better yet, let me just write it as 16 times 10 to the first power over five times 10 to the minus three, and that is four on the outside here over 10 time. I mean, I&#x27;m too scared to 10 over five times 10 to the minus three, right, So that is gonna be, um, 10 of the first minus. Negative three is actually 10 to the fourth 10 the fourth here, 10 to the fourth square. Root is gonna be So we have four times 10 squared, right, cause 10 of the fourth is 10,100 times, 110,000. And then we have the square root of 1/5 year that will stay in the radical. And so this is We can keep it like that. Now we want to. So this is, um, meters per second, right? It&#x27;s the speed of the wave. We want to now calculate the power required to generate these waves if they have a wavelength of 16 centimeters, so it&#x27;s copy that wavelength equals 16 centimeters, which is of course, um, 16 times 10 to minus two meters, which is 1.6 times 10 to the minus 1 m. And then we got that. The amplitude is four centimeters. Amplitude is for centimeters, which is four times 10 the minus 2 m. So this and that All right now we want to find the power right, so we can use this equation. Power is one half times mu times omega square times amplitude squared. Sometimes we now we have new, but we don&#x27;t have the angular frequency Omega. So in order to get that will be using the fact that velocity is Lambda Times new, and we want to use this new here. So new, actually is velocity over Lambda. And that will be what we have over here, which is four times 10 of this. The second power times the square toe 1/5 four times, 10 to the second power times Spirit of 1/5 and everything divided by, um, Lambda, which is 1.6 times 10 to the minus one. Everything divided by I, um I would rather write 16 time to 10 of the mines, too. 16 times, 10 to the minus two. Mhm. Um, yeah. So what is this? Tend? The Tu minus negative too is actually 10 in the fourth. Ah, and then So that&#x27;s 10 of the fourth. Keep the skirt over fifth year and then for over 16 is 1/4 so that it&#x27;s just on everything over four. Mhm. Cool. So that is the frequency. Um, Now we need to find the angular frequency. So, actually, and you have frequency is two pi nu that it will be two pi times 10 to the fourth time. Scared of fifth. I was 1/4 but this makes it a half. So we have pie over to time of the spirit of the fifth times 10 to the fourth. Great. Um, that is our English frequency. Next we have. So we need to square it. Arrogance. Yeah, well, okay, let&#x27;s just put everything into the to the power now. So power equals one half times new, which we said waas. Well, Mu is five times 10 to the minus third over to Yeah, right. So five halves times 10 to the minus third. Then we have omega squared, which is this whole quantity squared. So that&#x27;s gonna be I squared over four and then the 1/5 in 10 of the eighth. Then we have the amplitude squared, which is four times 10 to the minus two. So that&#x27;s squared. Will be actually four times 10 to the minus four. Uh huh. Oh, actually, it&#x27;s 16 times 10 to the minus four, That is, um the amplitude squared. Next, we have the velocity, which we&#x27;ve calculated to be, uh, four times 10 square times a squared of 1/5. Right. So can we simplify this? Um, so we have this right here is 5/4, but this four cancels with these guys. Eso that&#x27;s just once, right? So? So that&#x27;s just five. That&#x27;s left 10 to the minus. Three times. Tend to be eighth is 10 to the fifth. I understand. The minus fourth is just 10 to the first. And then times 10 to the second is times 10 to the third. Gets rid of all of these. Um, we&#x27;ve got We&#x27;ve covered that. Now we have this four in this 16. That simply puts a four here so you can get rid of that in this, Then we have hi square. We have. We&#x27;re getting rid of a five on the bottom there. Just get rid of it from here, okay? And then So that gets rid of that one. And we&#x27;re left with the spirit of the fifth. This is this is the final, and this is the final power. And this isn&#x27;t Watts. If you want, we can put that into a calculator. Um, yeah, why not? So So that is about 1766 Watts. Power is about 1700 66 wants

Arghya Mukherjee · Answer

it. The velocity off Trans first wave on a string is expressivity, given by the formula. He&#x27;s called Scott of P by row, where these attentions Andrew is the mosque part unit land and it is given is that the velocity here is equal to 200 meter. But second and it is asked that what is the new velocity or in the tension? New tension becomes four times be so. Therefore, the new velocity will be the new square. Root off two times TV Row has called a Pierrot is 200. So therefore squared off two into 200 Mr Gore Second, which is given us to 82 point eight for 27 meter per second, and this is the final answer.

Problem

A transverse wave on a long horizontal rope with …

Problem 2 Easy Difficulty

A rope of length 5 m is stretched to a tension of 80 N. If its mass is 1 kg, at what speed would a 10 Hz transverse wave travel down the string?
(A) 2 $\mathrm{m} / \mathrm{s}$
(B) 5 $\mathrm{m} / \mathrm{s}$
(C) 20 $\mathrm{m} / \mathrm{s}$
(D) 200 $\mathrm{m} / \mathrm{s}$

Answer

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