Hey, guys. Hopefully, you're able to work on this problem on your own. So we're given that some wave is on some stretch horizontal rope, and we're told in this problem that the vertical and horizontal distances from crest to trough are some of these values here. So in my opinion, the best thing you can do is actually draw this out and sort of see for yourself what these distances correspond to. So I've got this sort of wave like this. I'm gonna draw the little sort of sketch this out. It doesn't have to be perfect. But basically what I'm told here is that the vertical distance from crest, remember that's the top of the wave, to the trough, which is sort of like the bottom of the most minimum part of a wave, is equal to 15 centimeters. So let's figure this out. Right? So I've got this distance over here is equal to 15 centimeters. And then I'm told that the horizontal distance from crest to trough is 20 centimeters. So is that gonna be from here to here or is that gonna be from crest to trough? That's actually just gonna be this distance because this is the crest and this is the trough. So this horizontal distance here represents 20 centimeters. Right? It's obviously not scale, but that's just the distance, right?

So basically we have to figure out the amplitude and the wavelength here. So I've got the amplitude and the amplitude is what? The definition for the amplitude is it's the height of the wave off of the axis or the midline. It's not the entire height of the wave. It's just basically how high the wave gets off of this middle axis here. So this is actually this distance right here represents the amplitude. So that's actually just gonna be 12 of the total distance from crest to trough. So it's gonna be 152 centimeters. This is just 7.5 centimeters. Or if you want to convert this to SI units, you can shift the decimal place back and this will be 0.075 meters. Since the problem didn't specify, we can just write it either way.

Alright. So now we have to figure out the wavelength for this wave. This is the wavelength. Remember, that's lambda. Now remember, the definition for lambda is that it is the distance between the same sort of 2 identical points, for the different waves. So for example, crest to crest or trough to trough, or let's say this point over here to the next point where it's going up again. Either one of these horizontal distances all represent the wavelength. So how do we figure that out? So I'm just gonna label this here. This is gonna be my lambda. Well, the only thing I'm told about horizontal distances is that this distance here is equal to 20 centimeters. So what is this 20? Is this an entire wavelength here? If you think about it, it's not because you have to go all the way from the crest down to the trough and then go all the way back up again to complete one cycle. One up, down, up. So really this distance here actually only represents 12 of the wavelength. So this Lambda here is actually 2×20 centimeters and this is equal to 40 centimeters. And again, we can just rewrite this as 0.4 meters, and so those are the correct answers. So this distance here represents the wavelength and this represents the amplitude. Hopefully that makes sense. Let me know if you have any questions.