I was watching an XKCD “What-If” video recently and Randal off-handedly mentions the title fact as a given. Upon a further Google search I see explanations about why sound moves faster in liquids than gasses but nothing for my specific question. Is there an intuitive explanation for that fact or is it just one of those weird observable facts with no clear explanation
Do incompressible materials therefore have extremely high speed of sound?
Yes. Nothing is truly incompressible. The speed of sound can be viewed as a measure of how much a material can squish on the atomic level before the next atoms move.
Exactly. One usually speaks of quasi-incompressibility when the resistance against compression (bulk modulus K) is much greater than the resistance against shear (shear modulus G), which is often the case for liquids such as water (strictly, fluids like water don’t have any resistance against static shear deformation, i.e. G = 0).
However, water has a lower bulk modulus (K =2 GPa) than e.g. steel (K = 160 GPa), which is considered a compressive material, as its shear modulus and bulk modulus are in the same order of magnitude (G = 81 GPa).