Hey, everyone. So I want you to imagine in this problem that you and your friend have sort of a rope that is between you. So you've got you like this, you're holding this little bit of rope, and you've got it connected to your friend who's over here. And basically, the idea is that you're going to whip it up and down to create a wave pulse. You're going to whip this string or rope up and down, and that wave is going to travel along until it reaches your friend. If this wave travels with some speed v, then how long does it take for the wave pulse to travel? So how long is going to be a delta t? What we're really looking for is how much time does it take for that wave pulse to travel along the rope and reach the other side and reach your friend. So how do we go ahead and solve for \( \Delta t \)? Well, what happens here is we're going to use an old relationship between the velocity, \( \Delta t \), and the length of the rope, which is \( \Delta x \). This \( \Delta x \) here is going to be the length of the rope, between the two sides, and basically, if the wave pulse is going to be traveling at a fixed speed, it doesn't accelerate, then the relationship is just that \( v = \frac{\Delta x}{\Delta t} \). Right? Displacement over time. We saw that a long time ago in physics. So to calculate this \( \Delta t \), we're really just going to rearrange, and this \( \Delta t \) is going to be the \( \Delta x \), the displacement divided by the velocity. Now what's the displacement? Well, if you could just assume that the rope, which is 7 meters long 7 and a half meters long, doesn't change a whole lot as you whip it up and down, then we can just say this \( \Delta x \) is equal to \( l \), which is 7.5. So what we need to do is have the \( \Delta x \). Now we just need to find the velocity in order to figure out the time. So how do we calculate the velocity? Well, we're just going to use now our velocity equations for waves on strings. Remember, we can always use this equation, that always works, the frequency and wavelength, but we're not given any of that information. Instead, we're going to use this one, which is the velocity force for waves on strings. So we can only use this for strings. This \( v \) here equals the square root of the tension force divided by the mass per unit length. So in other words, I'm just going to expand that. That's the square root of the tension force divided by this is going to be mass per length. Alright? So that's basically what we need because we have the tension. We're told that as you pull this between your friend, there is 30 newtons of tension on the rope, and we've got the mass of it, which is 0.5, and we've also got the length of it. Alright? So we're basically just going to go ahead and plug in a bunch of numbers to calculate this. This is going to be the square root of 30 divided by and this is going to be 0.5 divided by 7.5. Now when you work this out, we remember what you're going to get here is 21.2 meters per second. Now remember, this is not our final answer because we need the velocity in order to plug it back into this equation here to find the time. So this \( \Delta t \) is just going to be the \( \Delta x \), which is, in other words, the 7.5 divided by, this is going to be 7.5 divided by the 21.2 meters per second, and what you'll get here is 0.35 seconds. So that's how long it takes for that wave pulse to travel between you and your friend. That's it for this one, folks.