In a wave problem in physics, it is important to understand the concept of phase and how particles vibrate in relation to each other. In the given figure, particle b is shown to be at its highest displacement, or crest, while particles c and d are also at their respective crests. This means that they are all vibrating in phase with each other, meaning they are all moving in the same direction and at the same time. This is because they are all located at points on the wave with the same amplitude and wavelength, causing them to vibrate in unison.
To answer the question, yes, it is correct to say that particles c and d vibrate in phase with particle b. This can also be observed by looking at the wave pattern in the figure, where the crests of particles b, c, and d are all aligned.
Moving on to the second question, the spongy lining at the edges of a ripple tank serves as a boundary for the water waves that are generated. This helps to contain the waves within the tank and prevent them from reflecting off the edges. This allows for a more controlled and accurate observation of the wave behavior, as the waves will not be affected by any external factors. Additionally, the spongy lining also helps to reduce any interference from external vibrations, ensuring that the waves being observed are solely generated by the device in the tank.