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 (b) the second overtone?

Video transcript

Hey everyone, welcome back in this problem. We have a violin string K. It's 0.51 m and it's fixed at both ends and we have a transverse wave on this string traveling at 600 m per second. And we're asked to find two things first. The wavelength and then the frequency of the third harmonic. Okay. Alright, so we know L 0.51 m. Okay. The length of the string that were given, can we have V. The speed is 600 m per second And we want the 3rd harmonic. Alright, so let's start with the wavelength. Now our call, we have a formula for the wavelength, lambda end equals two L over end. Okay, and in this case we're looking for the third harmonic. So we're gonna want N equals three. Okay, so if we're finding λ three we have two times r length is 0.51 m. R N is three. This is going to give us a wavelength of 0. m. Okay, so the wavelength of the third harmonic, 0.34 m. And now for part two, let's do the frequency. So similarly to the formula we have for the wavelength, we also have one for frequency. So the frequency F N can be written as V over lambda N. Okay, now in this case again and is three. So we have F three is equal to V. The speed which is 600 meters per second divided by lambda. And so lambda three in this case which we just found to be 0.34 m. Okay meters per second, divided by meters. We're gonna be left with the unit of one over second. Okay, We're gonna have 1764.71 over second. We can write this as hurts. Okay, So this is the frequency of the third harmonic. And so we have, our answer is b. The wavelength is 0.34 m. The frequency is 1,764.7 Hz. Alright, that's it for this one. See you in the next video.