Speed of sound in steel vs air

[Thecla]

I saw on a web page a video of tiny Agnes Scott College vs Princeton University from 1966 on GE College Bowl.Agnes Scott won (!), but one of the questions that both schools got wrong was
asked by the moderator:
The speed of sound in air is about 1,100 feet/sec. The speed of sound in steel is about 16,400 feet/sec.
Why does sound pass through steel faster than air?
Princeton answered because steel was denser.
Agnes Scott said that the molecules of steel were closer together.
The moderator said both answers were incorrect.
The moderator said the correct answer was that steel was more elastic than air.
Can someone explain this answer of the moderator?

 

[davenn]

hi Thecla

Princeton answered because steel was denser.

that is incorrect without other comments ... increasing density decreases the speed of sound through it

Agnes Scott said that the molecules of steel were closer together.

that is partly correct but again needs further insight

The moderator said the correct answer was that steel was more elastic than air.

The moderator is correct

Elasticity is the materials ability to rebound after the sound wave passes through it. In a rigid material like steel, the atoms are tightly
bound together by strong forces and this allows them to come back to their original position quickly. This high elasticity. Don't confuse this with high flexibility, eg. as in a piece of rubber ... it is highly
flexible, but has low elasticity. that is, it won't return to its original position/shape as quickly, if at all.

Sound does move through a denser material/medium better than a less dense material/medium

eg through a solid better than a liquid and through a liquid better than through air/any gas
But the elasticity of the material is the overriding factor.


hope that helps


Dave

 

[Doc Al]

To add to Dave's comments, check this out: Speed of Sound

 

[Thecla]

I had no doubt the moderator was correct and density seems like a good guess.The students must have been thrown off by the general statement that speeds are faster in solids than liquids and faster in liquids than gasses.

 

[jbriggs444]

The moderator said the correct answer was that steel was more elastic than air.

The moderator was incorrect as well. The property of elasticity is not the right one either. The ability to rebound from a deformation is not key for the speed of sound. The stiffness of a material is key.

The property of elasticity is what allows a tuning fork to vibrate for a long time.
The property of stiffness is what allows a tuning fork to vibrate rapidly.

 

[russ_watters]

The moderator was incorrect as well. The property of elasticity is not the right one either. The ability to rebound from a deformation is not key for the speed of sound. The stiffness of a material is key.

The property of elasticity is what allows a tuning fork to vibrate for a long time.
The property of stiffness is what allows a tuning fork to vibrate rapidly.

Right; it's large forces (in the bonds) that cause rapid acceleration and deceleration, not conservation of elastic energy.

There could be a secondary meaning of "highly elastic" though, meaning high modulus of elasticity.

..but either way, the colloquial use of "elastic" is basically the opposite of what it would mean scientifically/in an engineering sense. Steel is more elastic than rubber in both ways.

 

[Chestermiller]

The moderator was incorrect as well. The property of elasticity is not the right one either. The ability to rebound from a deformation is not key for the speed of sound. The stiffness of a material is key.

The property of elasticity is what allows a tuning fork to vibrate for a long time.
The property of stiffness is what allows a tuning fork to vibrate rapidly.

Yes, I totally agree. For the isentropic expansions and compressions characteristic of ideal sound waves in air, air can be regarded as being just as elastic as steel (or at least in the same sense as steel).

 

[sophiecentaur]

The speed of sound in a solid is
c_s = √(κ/ρ) (κ = modus and ρ is density)
so the speed relies on two factors and not just one.
The speed in air is given by
c_a = 20.05√(T/K) (T is the absolute temperature and K is Boltzman's constant)
So the question was poorly chosen if the quiz required a simple answer because there are a different set of quantities involved in the simple classical values of both speeds. I can't think of a straightforward answer to this but the question gets asked and the phenomenon gets "explained" a lot in elementary Science.
Yet another example of where Physics gets trivialised. I imagine that the speed in steel vapour (i.e. very hot) could be more similar to the speed in air of the same temperature - the factor 20.05 would be different I guess.