Pulse does not reach the other end instantly, it takes time for it to reach it, in both cases and it will take more time for it to travel in the metal rod than in the rope

When we do not change the distance that our hand moves, but we shake the rope faster and faster amplitude will stay the same along with the velocity, but wavelength will decrease which will cause period to decrease as well, and frequency to increase.

We can show that by making transverse wave with a rope, and we can tie some cloth at the middle of the rope, for example. We will hold one end of the rope and the friend will hold another one and by shaking it up and down we can make a wave.

While observing moving of the wave, we can notice that the cloth that we have tied previously did not change its position, which means: the wave did not transport matter (cloth in this case)

We can do it by making transverse wave with a rope which has cloth tied in the middle of it.

In a longitudinal wave the particle displacement is parallel to the direction of wave propagation.

All media : Solid, liquid and can gases transmit longitudinal waves

This does not happen since the swimmer, as he jumps in the water, transfer his energy to the water in a small space and it takes short time for that and raindrops are spread out on the greater surface and it takes more time.

Because the raindrops are spread out on the greater surface and it takes more time for them to transfer energy to the wave.