Verified answer

A wave propagates when a motion generates another motion in a neighboring part of the medium. This in turn generates another, neighboring motion, and the disturbance travels through space.

Think of a slinky: You jerk the slinky, so a little bit of it compresses.

This compression generates a force, that pushes a neighboring section to compress.

This compression generates a force...

You see?

Think of a solid. If you compress the solid, the same compression/pushing/compression action happens as with the slinky.

But now if you take a rod of a solid and tap it, so a section is moved transverse to the rod, that section exerts a force on the neighboring sections, and encourages them to move out of line; and so on. So the motion transverse to the rod will generate further transverse motions - but the disturbance will travel parallel to the rod. This is because solids don't like to have their parts moved - even when it doesn't change their density. This kind of motion (called "shear") is resisted by solids.

Now take liquids:

- If you compress a liquid, it "fights back" with a large increase in pressure. This is what happens with sound waves in water: A little compression generates a big increase in pressure, so water is kind of "stiff" (as you know if you've ever belly-flopped onto water). Longitudinal waves depend compression, so they have no problem propagating through liquids.

- But if you shear a liquid, it doesn't care. Try it: Swish your hand through water. It resists, but it doesn't generate a counter-pressure that forces a neighboring section of water to respond, TRANSVERSE to the water's motion. If there are no walls to the water, the water would just shuffle along when you push it. So there is no linkage to the direction transverse to the water's motion, so it just dies out in that direction. That's why transverse waves cannot propagate in liquids (or gases).

Your counter-example does not work, because tides are not waves. Tides are a change in water level due to differences in (apparent) gravity. They do change with time, because of the Earth's rotation and the Moon's orbit; but they do not depend on the dynamics of internal water interactions to propagate, they are generated from the relative motion of the Earth and Moon.

Generally speaking, the earth core is a fluid molten core of red-hot plasma sloshing about in a radial periphery.

You would need fluid mechanics and tectonics to understand the seismology of tectonic waves and what actually happens or indeed what it means that earth's core is "liquid" simply by virtue of the absence of transverse waves traveling through it. This may not just be the "liquid phase" involved but the Plasma-phase, which is now regarded by physical scientists as the fourth distinct state of matter, think LCD-s, for instance..

BUT you have made a mighty good start to the problem by posing very strong mind-numbing questions already. That would fetch you pretty good marks in a physics examination!

They die out very quickly in fluids, that's why!