Phase difference of 2 points in a same graph

[kelvin macks]

Homework Statement

since point P is ahead of point O, why the displacement , y , of P shouldn't be Asin(wt + 2pi/(x)) ?

Homework Equations

The Attempt at a Solution

 

[Jilang]

Be careful, the graph is against x not t.

 

[kelvin macks]

Be careful, the graph is against x not t.

sorry, stil don't unseratand . can you explain further?

 

[NascentOxygen]

Homework Statement

since point P is ahead of point O, why the displacement , y , of P shouldn't be Asin(wt + 2pi/(x)) ?

Think of the figure as a snapshot photo of an ocean swell.

Imagine O and P are corks floating on the ocean, and they rise and fall as the wave gently passes. At the moment captured in the photo, cork O is falling and crossing the zero line. How far must the wave move along (sliding along to the right) before cork P in turn finds itself falling through the zero line?

So P is lagging O by ...?

 

[kelvin macks]

Think of the figure as a snapshot photo of an ocean swell.

Imagine O and P are corks floating on the ocean, and they rise and fall as the wave gently passes. At the moment captured in the photo, cork O is falling and crossing the zero line. How far must the wave move along (sliding along to the right) before cork P in turn finds itself falling through the zero line?

So P is lagging O by ...?

so are you assuming falling downward dispalcement is positive? floating upward dispalcement is negative since you said P is lagging behind by O. how do we know which direction is positive and which is negative (falling downward or floating upward) ?

 

[NascentOxygen]

so are you assuming falling downward dispalcement is positive?

Defintely not assuming anything. I described how you could see things were you to imagine this as an ocean swell; I used an analogy.

Floating upward dispalcement is negative since you said P is lagging behind by O. how do we know which direction is positive and which is negative (falling downward or floating upward) ?

You are told that movement is described as A.sin(ωt), so that's where you might choose/assume '+' direction if it's not explicitly indicated.

Any and every motion of O will be emulated at a time Δt later by a point which lags O by that amount of time, regardless of what that instantaneous motion of the sinusoid may be. Whatever O is doing will be copied by P a short time later.