Wave problem in Physics

[Johnny Leong]

From the figure, please see the attachment. Which particles vibrate in phase with particle b and why?
Can I say that particle c and d vibrate in phase with particle b?

Another question: What is the function of the spongy lining at the edges of ripple tank when we generate water wave in the ripple tank?

[HallsofIvy]

Assuming that you mean you picture to represent a wave with the two endpoints fixed, then d is in phase with b (they will always be at the same height). c is not.

As for the spongy lining, it is there to absorb the wave so you won't have reflections confusing the situation.