Hey guys. So let's work this problem out together. So in this problem, we're told that the wave speed for a certain string under tension is 20 m per second. So I'm gonna call this V equals 20. I'm gonna draw this out real quick. That's my sort of wave like this. And this is sort of like my axis right. So now we're asked to calculate, well, if you cut the tension in half, half, so the tension is half of its original value, then what happens to the new wave speed? So let's take a look here because obviously, we're going to be dealing with some kind of a velocity or a wave speed equation. And we know this is going to be a string. So because we have a string, we can, we can always just use this formula over here. So we have that V equals the square root of the tension divided by the mass per length. Now notice how this problem has really no information other than the 20 m per second. And this is a classic kind of proportional reason question because they're asking what happens to something, if something else gets cut in half, right? If you change something, how does another variable respond? So here's what I'm gonna do here. I wanna say that V New is really just gonna be the square root of FT New over the mass per unit length. The only thing we're, we're told here is that the tension is cut in half. So we can assume that the mass per unit length will also stay the same. So here's what happens this FT new here, what they're asking or what they're saying here is that it's gonna be one half of the original tension. So what happens is this equation here, this V equals squared of FT over mu is equal to 20. We actually know that already. But now what happens is V new is gonna be the new tension divided by Mu. OK. And what we can do here is we can basically just replace this FT new with this expression, the one half FT. So it's gonna be the square roots of one half of the original tension divided by the mass per unit length. And what we can do here is we can basically just pull out the one half that's inside of the square root. And this just becomes the square root of one half times the square root of FT over mu, right? That's what happens when you sort of extract it, basically just splitting it up the the square roots. So notice how this piece right here. This equation. This FFT over U is what shows up in our new equation. But now we just have an extra factor of the square root of one half that's on the outside. So that's what usually happens with these proportional reasoning type questions is that you can basically just extract out the same expression in the before case, but with just an extra constant that's out in front. So remember this expression here is equal to 20. We don't know what all the variables are, but we just know that the whole thing equals 20. So really what happens is this just becomes the square root of one half times 20 right? Because this thing is equal to 20. So in other words, the velocity, the new wave speed is actually just gonna be the square root of one half times 20 which is equal to uh this is gonna be 14.1 m per second. Now, this should make some sense that the new wave speed is gonna be less because again, if you look at the equation here, if you reduce the tension, then that means the speed is going to be reduced as well. It's not gonna be half because of the square root that's inside here, but it is going to be reduced. That's it for this one guys.