a. What are the three longest wavelengths for standing waves on a 60 cm long string that is fixed at both ends?

Video transcript

Hey, everyone. So this problem is dealing with harmonics, consider a rope that is anchored at both ends with a total length of 72 centimeters. Using the concept of standing waves, calculate the four longest wavelengths that can be produced on this rope. You can see we have four multiple choice answers here ranging from the longest wavelength of 1.44 m to the shortest wavelength of 0.22 m. OK. So in harmonics or standing waves, we can recall that the fixed string wavelength is given by Hamda and equals two L divided by N where N is the number of nodes. So we can see as an increases our wavelength is going to decrease. So the longest four wavelengths are going to be when N is the smallest. So that's from N equals one, two, N equals four and has to be an integer. So from here, we're just going to solve this equation four times from, for N equals one, all the way through to N equals four. So that looks like lambda one equals two, multiplied by the length. Now, they did give it to us in centimeters, 72 centimeters So we are going to want to put that into standard units of meters. So that becomes 720.72 m divided by one, 1.44 m. And we'll do that for the second node two multiplied by 20.72 m divided by two equals 20.72 m. For the third node two multiplied by 20. m divided by three is 30. m. And lastly for that fourth node four, um lambda four equals two multiplied by 20. m divided by four. And that equals 0.36 m. And so those are the four longest wavelengths that can be produced on a rope that is anchored at both ends that has a length of 72 centimeters. So when we look at our multiple choice answers, the correct choice is answer choice. A all right. So that's all we have for this one. We'll see you in the next video.