Can sound travel in the form of transverse waves? We all know that sound travels in longitudinal waves but in some books, I have found that sound travels in the form of both longitudinal and transverse waves while passing through rocks. Can anybody explain this to me? 
 A: The difference between a fluid and a solid is the following: fluid's have zero shear modulus, so they cannot carry a shear force, but solids have non-zero shear modulus, so they can carry shear force.
Fun little way to visualize this: let's say we line up a bunch of second graders on rectangular grid. Now we push one of the students along one row. That student will push the next student in the same row and so the push will move through the row. However, the students in the other rows are unaffected. That's how a fluid behaves.
Now we ask the students to hold hands with their neighbors in the adjacent rows. If we push one student, not only will the push travel through the same row, but since the student are holding hands with their neighbors, these kids will move as well, so the the push will also travel laterally along the columns through the other rows. That's how a solid behaves.
In a solid, molecules are "holding hands" with their neighbors, in fluid they do not. This enables transversal waves in a solid.
Of course, in reality all the second graders would fall over each other giggling hysterically. The branch of physics dealing with kids is neither solid mechanics nor fluid mechanics, but probably chaos theory.
A: According to this website:

Sound is transmitted through gases, plasma, and liquids as longitudinal waves, also called compression waves...Through solids, however, it can be transmitted as both longitudinal waves and transverse waves.

This means that through most forms of matter (gases, plasma, liquids), such as water, or the air, sound travels as longitudinal waves. Through solids (such as rock), though, it can be transmitted as both longitudinal and transverse waves. A diagram that compares a transverse wave to a longitudinal wave is shown below:

The reason sound can travel as a transverse wave through a solid is because, as this website says:

Say that you hit a big steel block on top with a hammer. Just picturing how the atoms are displaced by the blow, you can see that there should be a compressional (longitudinal) wave going downward. Out to the sides, there should be transverse waves.

Since liquids are non-compressible, sound can't travel as a transverse wave through liquid. Also, the compression/rarefaction of gases facilitates longitudinal waves as opposed to transverse waves. According to this website:

An example of rarefaction is as a phase in a sound wave...Half of a sound wave is made up of the compression of the medium, and the other half is the decompression or rarefaction of the medium.

Since this is true, the rarefaction of gases clearly makes longitudinal waves a better choice in gases.
Hope this helps!
(Picture from http://msascienceonline.weebly.com/waves.html)
A: Treating a medium as continuous (which works for our purposes), for sound to travel through the medium the motion of one unit of it has to affect the motion of the next unit, and so on and so on. Sound in a gas or liquid does this by varying pressure: the air pressure next to a speaker suddenly increases, pushing a unit of air outwards towards the adjacent lower-pressure unit. That unit's pressure increases, pushing it out towards the next unit along, and so forth. Bingo: longitudinal sound wave.
But, if you move the air side to side without varying the pressure, the next unit along will feel no force, and so will not in turn move, so the incipient transverse sound wave dies aborning.
(This is not completely true, as viscosity and turbulence can pass force between adjacent sliding units of gas. However, the effects of these are dissipative rather than elastic, so there will be no recoil and thus no continuing vibrations.)
In a solid, however, transverse motion can be passed along through the elasticity of the medium. For example, if you take a long fiberglass rod and shake one end side to side, the displacement will travel down the rod in a wave. Even if you stop shaking, the existing waves will continue until they reach the end of the rod.
So, fluids cannot propagate transverse sound waves, but elastic solids can.
