A 1.50-m-long rope is stretched between two supports with a tensi...

Question

A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of (c) the fourth harmonic?

Accepted Answer

Hey everyone welcome back in this problem. We have a copper cable and it's tied between two trees. Were told the horizontal distance between the two trees is three m. Okay? And we have transverse waves traveling at a speed of 80 m per second. They were asked to calculate two things first. The wavelength and then the frequency. Okay. Of the third Overtone. Guys we have these trees And we have a rope tied between them or a copper cable. Sorry, in the distance between these trees is three m. Alright. We're also told the speed is 80 m/s. Whereas to find the 3rd overtone wavelength and frequency. Alright. So let's recall when we're talking about wavelength, we have the following formula. The wavelength lambda N. Is equal to two L. Over N. In this case we're talking about the third overtone. So N. Is going to be four. Okay, three plus one. So using that information we can find the wavelength of the third overtone. Lambda 42 times L. The length which we know is three m divided by N. Which is four. So the wavelength is going to be six m divided by four, which is 1.5 m. Okay, so that's it for part one. Let me just hear part one. We found the wavelength of the third overtone. Now let's go ahead and find the frequency of the third overtone. Okay, similarly to the wavelength formula, we also have one for the frequency. So let's recall we can write the frequency F N. As V over land N. Okay and again it is four in this case. So we have F four. It's going to equal to V. R. Speed which is 80. Okay. And then lambda four, the wavelength of the third overtone, which in this case we found to be 1.5 m and the 80 has a unit of meters per second. So I missed that. Okay. And doing this calculation, we're going to get 53. and our unit is going to be Second in verse K one over second and we can write this as 53.33 hurts. Okay, so this is going to be our frequency of the third overtone. So our answer is going to be C. We have a wavelength of 1.5 m and a frequency of 53.3 hertz. Thanks everyone for watching. See you in the next video.

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