Mechanism of mechanical transverse wave in solids

[vcsharp2003]

Homework Statement

Why does a solid medium allow transverse wave to propagate through it?

Relevant Equations

None

I am not sure, but below is my attempt.

In solids the force between adjacent atoms/molecules is very strong. So, when a part of the solid medium is displaced perpendicular to the solid medium like a rope, the atoms/particles in the medium just ahead of the displaced part will tend to bring the displaced part back to its original equilibrium position. At the same time, due to Newton's Third Law, the displaced part will exert an equal and opposite force on the part just ahead of it; consequently, the part ahead will start to move in direction of displaced part.

Thus, we see two things happening.

1. displaced part of medium starts moving towards its original position
2. the part of medium just ahead of displaced part starts moving

 

[haruspex]

Looks ok to me, except that you mean perpendicular to the direction of travel of the wave.

 

[vcsharp2003]

Looks ok to me, except that you mean perpendicular to the direction of travel of the wave.

Yes, displacement is perpendicular to direction of wave travel.

Also, could I say that transverse mechanical waves cannot exist in liquids and gases because the force between adjacent atoms/molecules is weak so that displaced part of such a medium cannot be pulled back to its equilibrium position by adjacent atoms/molecules? Or there is something else happening in liquid or gaseous medium.

Edit: Probably, forces that restore original position of atom/molecule is completely absent in liquids and gases.

 

[haruspex]

Yes, displacement is perpendicular to direction of wave travel.

Also, could I say that transverse mechanical waves cannot exist in liquids and gases because the force between adjacent atoms/molecules is weak so that displaced part of such a medium cannot be pulled back to its equilibrium position by adjacent atoms/molecules? Or there is something else happening in liquid or gaseous medium.

Edit: Probably, forces that restore original position of atom/molecule is completely absent in liquids and gases.

The term you are looking for is "shear force".

 

[Lord Jestocost]

Also, could I say that transverse mechanical waves cannot exist in liquids and gases...

"Transverse waves cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave."

http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/tralon.html

 

[vcsharp2003]

The term you are looking for is "shear force".

So, is the presence of shear force in liquids and gases responsible for perpendicularly displaced sections of medium to not come back to original position?
Shear force seems to be a force parallel to the plane being cut/sheared. It seems to prevent elasticity by exerting a force pointing away from equilibrium position of the displaced part.

 

[vcsharp2003]

"Transverse waves cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave."

http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/tralon.html

I am trying to understand why perpendicular motion is not possible in liquids or gases.

The above link doesn't explain why perpendicular motion is not possible in liquids or gases.

 

[hutchphd]

I am trying to understand why perpendicular motion is not possible in liquids or gases.

You need to be careful here. This is true for waves in the bulk of an infinite fluid/gas lacking rigidity. At a surface, the surface tension allows a host of different types of waves, but the details are complicated. FYI

 

[Lord Jestocost]

I am trying to understand why perpendicular motion is not possible in liquids or gases.

The case with liquids and gases is that liquids and gases don't have that much shear strength. Transverse waves need a medium rigid enough to propagate, which liquids and gases can't provide.

 

[vcsharp2003]

You need to be careful here. This is true for waves in the bulk of an infinite fluid/gas lacking rigidity.

So, it seems there is no restoring force like tension in a rope or surface tension on liquid surface, that can pull back a perpendicularly displaced part of the medium. The rope tension or the surface tension provide the restoring force as well as a force to displace perpendicularly the next part of the rope or liquid. That is why a transverse wave can exist on the surface of a pond but not deep underwater.

Is above explanation valid? Mechanical waves should follow the Newton's laws of motion. (Unlike electromagnetic or light waves).

 

[haruspex]

So, is the presence of shear force in liquids and gases responsible for perpendicularly displaced sections of medium to not come back to original position?
Shear force seems to be a force parallel to the plane being cut/sheared. It seems to prevent elasticity by exerting a force pointing away from equilibrium position of the displaced part.

No, it's the near absence of shear force. If of two adjacent blocks of water one moves sideways there's not much force dragging the other with it.