we have the wave equation as follows with non zero phase constant:

y(x,t) = ym * sin(k( x - PHI/k) - wt)
or

y(x,t) = ym * sin(kx - w(t + PHI / w))

I don't understand where did the PHI /k or PHI / w came from ??

I understand how did we derive the wave equation but I don't understand this part.

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 Quote by Sciencer we have the wave equation as follows with non zero phase constant: y(x,t) = ym * sin(k( x - PHI/k) - wt) or y(x,t) = ym * sin(kx - w(t + PHI / w)) I don't understand where did the PHI /k or PHI / w came from ?? I understand how did we derive the wave equation but I don't understand this part.
You just substitute in and both equation are the same.

But the more basic thing is, I never seen any book write it this way, that is very confusing. The three terms are totally independent. $\omega t$ is the time dependent, kx is distance dependent, and $\phi$ is a phase constant. You don't confuse this more by mixing them together as if they are related.

People usually set either t=0 or x=0 as a reference and generate two separate equations that relate t or x with $\phi$. With this, you can generate two separate graphs of (y vs t) or (y vs x).

 I see but what is then the reason for putting it in this form? What is the logic behind it ?