Why do sound waves travel faster in denser substances?
They don’t. They travel faster in stiffer substances. Some denser solids happen also to be stiffer, so if the stiffness increase is proportionately greater than the density increase they would conduct sound faster. As an illustration of the fact that high density alone does not guarantee higher sound speed, the speed of sound in glass ~= 5640 m/s, and in much denser lead ~= 1960 m/s (1st ref.). Solids in general conduct sound faster because their molecules are closer together, so you can say that sound travels faster in materials with a higher
