Why does sound travel faster in steel than in water?

Question

I understand that sound travels faster in water then in air. Water is a liquid, and air is gas.

Water still has the ability to roll the molecules over each other (so water can flow), it has some flexibility.

But I do not understand how a solid that is inflexible can make sound waves travel faster then in a flexible liquid.

In fact, sound waves travel over 17 times faster through steel than through air.

Sound waves travel over four times faster in water than it would in air.

Question:

1. Why does sound travel faster in steel than in water? I am interested in the quantum mechanical level.

Answer 1

the speed of sound (a compression wave) in steel is given by the square root of (the ratio of the sum of the bulk compressive modulus and 4/3 times the shear modulus divided by the density of the material). Since steel is very stiff, this makes the numerator very big and even though the density of the steel is significant, the ratio remains big and so does the square root- so the speed of a compression wave in steel is big.

For water, the expression is similar: the square root of (the bulk elastic modulus divided by the density). In this case, the result is smaller because water is less dense than steel and not as stiff.

You say you want this explained at the quantum level. To do so requires a quantum treatment of the physics of interatomic bonds, intermolecular bonds, electron orbital shapes and sizes, and strong force bonds so that the resistance of the materials to compressive stresses and their bulk densities can be accounted for on a quantum level. This is a huge job for which I am not qualified, and I invite the experts to weigh in on these matters.