Sound waves propagated as transverse waves

Who said they can't?

 

Think about how a transverse wave propagates. For this example, don't worry about EM waves (which propagate differently than sound), just consider transverse waves moving down a string as you oscillate one end of the string up and down. What force makes the string as a whole propagate the wave? Why is it that when I pull up on one side of the string, other pieces of the string also move up?

Is this force present in air?

 

if that's true, your textbook is using a restricted definition of sound waves.

 

Sound waves in a gas cannot support transverse waves. This is because a gas is not resistant to shear forces. berkeman asked about molecules. What are the properties of molecules in a gas, and what is shear force?

Sound waves in a solid can be transverse waves.

 

Since you are new to the forum you may not realise that you can search the forum for lots of answers.

Have a look here.

https://www.physicsforums.com/showthread.php?t=386490

 

This is a classwork question so you have to do some work first. What is a shear force?

 

Recently the people of Haiti and Chile called them earthquakes. They are all too real.

Did you read my linked thread?

If you don't understand the difference between shear and normal force then try this explanation.

In a fluid (liquid or gas) the particles are distributed at random as in my first sketch. They can move freely in any direction and there will be local 'clumps' where the molecular density is temporarily higher or lower than average.
A pressure or longitudinal wave is nothing more than organising these clumps to form a regular pattern of higher and lower density (pressure).

In a solid there is a regular array and the molecules are not free to move about. Instead they can 'vibrate' about their mean positions, as dictated by the bonds with their immediate neighbours.
Vibration along the bonds axes is energetically preferred.

So if we can organise a wavetrain of vibrations to pass down the array it can be either longitudinal or transverse as shown.

 

Search on "shear wave" and there will be a Wikipedia article. Go to the article. The first animated picture is a shear wave.

Note, it might look like a the waves on the surface of water, but all the motion is in the plane of your video monitor. The motion of the grid is perpendicular to the direction the wave propagates.