The wave speed on a string under tension is 200 m/s. What is the speed if the tension is halved?

Video transcript

Welcome back, everyone. We are making observations about waves that are traveling on a strand wire. Now, we are told that the waves travel with an initial velocity of 225 m per second. And we are told that the tension or the final tension of the strained wire will be 1/5 of the initial tension applied to the wire. And we are tasked with finding what is going to be the new speed of the waves on the wire. Well, the formula for our original velocity is going to be the square root of T knot divided by our linear density here. Now, what I'm going to do is I'm now going to say that V of F is equal to the square root of T F F divided by our linear mass density here. So what I can do is I can sub in our value for our final tension. What we get is the square root of 1/5 divided by T knot over mu. I can take that 1/5 out and it'll be one times the square root of five times the square root of T knot over mu. But as you can see T knot over mu is just one over the square root of five times our initial velocity. So let's go ahead and calculate that. What we get for our final velocity is we get one divided by the square root of five times to 25 which gives us a final answer of 101 m per second corresponding to our final answer. Choice of D Thank you all so much for watching. I hope this video helped. We will see you all in the next one.