Difference between two harmonic motion equations

[Rorshach]

Homework Statement

Hello, folks:) I'm currently having problem with properly understanding the difference and aplications of two equations which resemble each other greatly, but the difference makes it difficult for me to tell exactly which one is for what.

2. Homework Equations
Those two equations are given below:
(1) x(t)=Asin(ωt+φ)
(2) y(x,t)=Asin(kx-ωt)

The Attempt at a Solution

I know it is silly, but it's like I have brick wall in my mind that just prevents me from getting it right.
My initial conclusions told me that first one describes dependence of displacement of a body(in my particular case I was interested in acoustic wave) from beginning of coordinates system from time. Second one describes displacement of a body on axis perpendicular to the axis of direction of propagation of a wave I am interested in (in the dircetion of an amplitude, so to speak). Now I am just confused, and cannot place my conclusions in any real life illustrations. Please help me in getting this right.

 

[Doc Al]

Those two equations are given below:
(1) x(t)=Asin(ωt+φ)
(2) y(x,t)=Asin(kx-ωt)

The second equation describes a traveling wave moving in the +x direction with some speed. y is the displacement of the wave at some position x and some time t.

The first equation can be used to describe the displacement of something in simple harmonic motion, where x is the displacement from equilibrium.

Let me know if that helps.