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What is the difference between using $y=A\sin\omega t$ and $y=A\sin(ct-x)$ in a wave formula?

I am not a math student and I am not getting this.

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  • $\begingroup$ I suggest you to take the function $y(x,t)=A\sin(ct-x)$ and plot it for different values of $t$. You'll then see what the $x$ dependence does. $\endgroup$ – eranreches Nov 28 '18 at 17:54
  • $\begingroup$ But does it make a huge difference if I use wt in my derivation instead of ct-x? $\endgroup$ – Faaiza Ibrahim Nov 28 '18 at 17:56
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    $\begingroup$ These are different things. Note that the first is independent of the position coordinate - so if you're trying to calculate the interference pattern at a specific point in space, then that's what you need. $\endgroup$ – eranreches Nov 28 '18 at 17:57
  • $\begingroup$ The first is constant in space, the second is not. Am I understanding this correctly? $\endgroup$ – Aaron Stevens Nov 28 '18 at 18:01
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When you use the equation $y(t)=A \sin(\omega t)$ to describe the motion of a particle what you get is the oscillation of a particle located at a particular point in space and just vibrating in the perpendicular direction to and fro. But when you use $y(x,t)=A \sin(\omega t-kx)$ you assign time-varying $y$ coordinate values to each particle in space . As at any point say $x=x^0$ we can substitute it in equation and obtain the equation of motion of a particle if it was located at $x=x^0$. To summarise I just want to say that the first equation is just a dime dependent equation of motion but the second equation is varying with both time and $x$ coordinate and if you observe a particular point only then you fix the value of $x$ and both equations can be used after phase correction

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    $\begingroup$ Try to learn and use math formatting for readability. I edited your answer to get you started with the basics. $\endgroup$ – ja72 Nov 28 '18 at 20:53

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