Mechanical waves are the product of a perturbation of a medium caused very often by a vibration. What is characteristic of the different types of mechanical waves is that their propagation does not involve a real displacement of the particles of the medium. The particles just oscillate a bit around their initial position, returning to the starting point as the energy goes away. That means that mechanical waves' propagation involves a displacement of energy and not a displacement of the substance of the medium where they propagate.
Mechanical waves always propagate in the same way, no matter what the density of the medium in which they propagate is, being the speed of propagation the only exception: the denser the medium is the faster they propagate. At 20ºC, sound will propagate in the air at 343 m/s, in water at 1484 m/s, and in brass at 4700 m/s.
From the point where the initial vibration occurs mechanical waves will propagate in all directions, loosing intensity with the distance until the energy dissipates. That's why we see rings on the water when rain or whatever object falls in it.
A little note about frequencies: mechanical waves lose intensity with the distance and when encountering surfaces, being the trebles the range of frequencies suffering the most. Think of a concert of pop or rock music you are going to: as you get closer you'll be able to hear more and more instruments. From afar, you won't hear anything but the bass. The shorter and less disturbed the way of mechanical waves is, the clearer will be the sound you hear. The longer and more disturbed that way is, the darker will be that sound.