How Does The Speed Of Sound Vary In Solids Liquids And Gases?

The explanation above is incorrect.  The assumption about the spacing of atoms in matter is correct, but the reasoning behind how sound travels through materials is wrong.  Speed travels faster in denser materials.  Since atoms are packed together in solids, any energy imparted upon an atom (a sound wave striking the atom) is transferred to its neighbor atom quickly.  In contrast since atoms are free to move in gases, when it is struck it may have to travel a distance before it strikes another atom, in the process losing total energy  - slowing the sound wave.  If we look up the speed of sound in different materials we see the speed is greatest in solids, then liquids, and finally gases.

Copper 3901(m/s)
Kerosene 1324 (m/s)
Helium 965 (m/s)

Sounds travel fastest in solids.  Think about what you know about molecules
in solids liquids and gasses.  Molecules are farthest apart when in a
gaseous state.  They are zinging around having a great old time. Think of a
box of marbles being dumped on the floor and rolling everywhere.  Next come
the liquids with their molecules, vibrating and much closer together. Same
marbles in a big box with a little less room to roll around.  In solids, the
molecules are much closer together.  Think of all your marbles packed into a
peanut butter jar, full to the top, not too much room to move.

Now about sound...  Sound is a wave that needs something to travel in.
Think the crowded lunch line in the cafeteria.  Someone pushes and then that
person bumps the person in front of them, then the person in front of them
and so on.  Sound travels fastest in solids because the molecules are closet
together and can bump one another easier.  It travels next best in liquids,
and the slowest of all in gasses.  I hope that answers your question.

Good question, share it with your science class.
Happy science!