Waves - Displacement dependent upon time?

[Peter G.]

Hi,

I am reading about how the displacement of a wave can be dependent on both time and position. They use first as an example wave pulses traveling down a rope:

I understand how the time will have an effect: the points on the rope oscillate up and down, therefore, at different moments we will see different displacements.

But I don't get what they mean in terms of position...

Thanks

 

[lewando]

If you freeze time, say by taking a snapshot of your oscillating rope, as you steadily move along the picture of the rope at different positions, the displacement will change in a manner similar to the constant-position, time-varying case. However the perceived frequency of oscillation will depend on how fast your position is changing.

 

[Peter G.]

Oh, ok I got it now.

Could you possibly help me with another doubt?

When a stone is dropped on water, "rays" or rather energy is sent in all directions, correct? And the wavefronts are circular because they have to cover all the points that have traveled the same distance, therefore are in phase?

Thanks.

 

[lewando]

When a stone is dropped on water, "rays" or rather energy is sent in all directions, correct?

Sure, restricted to the surface of the water.

And the wavefronts are circular because they have to cover all the points that have traveled the same distance...

Better to say the wavefronts are circular due to the uniform propagation speed of the wave in the medium (water).

...therefore are in phase?

"in phase" with respect to what? If you imagine a bunch of rays emanating from the drop point, then if you pick one as the reference, say the ray pointing north, and any other ray for comparison, say the ray pointing east, then if the distances from the drop point to the wavefronts along these two rays, as a function of time, is the same, then you can say the east wavefront would be in phase with respect to the north wavefront.