Understanding the Phase Constant in y(x,t) Equation

[Sciencer]

Hi,

In the equation
y(x,t) = ym * sin(kx - wt - PHI)

I thought I understand why we have that phase constant atleast mathmetically but after thinking about it I don't think I understand it completely like here in my book it says the phase constant moves the wave forward or backward in space or time. Now let's say
we have wave at t = 0 and x = 0;

we would have y(x,t) = ym * sin(-PHI) that wouldn't really move it forward or backward in space or time if we had y(x,t) = ym + PHI then yeh it would have but I don't see how it would moves it backward or forward in that case ?

I can see how they derived
y(x,t) = ym * sin(kx - wt) but that PHI keeps confusing me.

 

[Philip Wood]

You might try sketching a 'snapshot' of the wave (that is a graph of y against x) at t = 0, first for the case \phi = 0, then for the case \phi = \pi/2. The shift (in the x direction) of the wave profile brought about by \phi should then be clear.

The purpose of including \phi is so we have an equation which fits the general case: when y doesn't happen to be zero when x = 0 and t = 0. [An alternative, sometimes permissible, sometimes not, is to choose our zero of time (or of x) expressly to ensure that y = 0 and \frac{\partial y}{\partial x} > 0 when t = 0 and x = 0. Then we don't have to bother with \phi.]