So, I have to self-teach myself part of my class. However, there's one part of my book I can't understad at all. First, I would like to understand, why does a transverse motion has 3 variable, y,x, and t . In my book they give the explanation y=h(x,t) and when we find the formula of the wave we get y=Asin(kx +/- wt). I'm wondering, if y is the displacement of one element of a string, then what does x represent? I'm all confused :/
Yes, y represents displacement, x specifies at what point along the x-axis. Just think about a picture of the wave... obviously displacement is not the same at every x position, and even if you stay at one x position, the displacement varies in time, hence the need for both variables.
No, it specifies the position in the direction that the wave is traveling. If you just have a function y(x), what does x represent? What does y represent? Nothing changes for y(x,t) except that y now changes as time passes, meaning if you say at the same x position, the displacement (y) changes (periodically, in this case). In the terms you put it, x is the position of a particular "element" of the string.