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 (a) the fundamental?

Accepted Answer

everyone in this problem, we're told that the speed of transverse waves in a stretch guitar string is m per second. Okay, we're told that the string length is 75 centimeters and we're asked to find the wavelength and frequency of the first harmonic. Okay, Alright, so let's go ahead and write out what we know. We know that V the speed is 417 m per second And that the length of the string is 75cm. So we can write this as 0.75 m to have consistent units. Okay, Alright, now we're talking about first harmonic. When we hear first harmonic, we can think of fundamental frequency and in this case we're going to take an end value equal to one. Alright, so let's start with the wavelength. Now recall, we have a formula for the wavelength that says lambda N equals two L over N. Okay, in this case and is one. So we have lambda one is equal to two L. Which makes sense because we know that the fundamental frequency has a wavelength that's two times the length. Okay, so so far so good Plugging in our length. 0.75 m. Okay, and we get a wavelength for the first harmonic of 1. m. Alright, now, for part two we need to find the frequency. So similarly to the wavelength for the frequency we have a formula, let's recall the frequency F N equals V over lambda N. Okay, so in this case and is one. So F one is going to be V R Speed m per second over lambda one, which is a wavelength we just found 1.5 m. We have units of meters per second divided by meters. So we're gonna be left with the unit of one over seconds, which we can write us hurts. Okay, So this is going to give us 278 hertz And that is the fundamental frequency or the frequency of the first harmonic that we were looking for. And so our answer is going to be see the wavelength is 1.5 m. The frequency is 278 hertz. Thanks everyone for watching. See you in the next video.

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