The real answer is "because this is the universe we found ourselves in"
Our study of physics has allowed us to model this universe mathematically, with models that not only describe what is happening but also can predict what will happen in the future given initial conditions, as well as previously not detected pbenomena.
All "why" questions in physics end up on the axioms and postulates we have discovered for these mathematical theories. Physics answers "how" from the axioms and postulates we arrive at a given observation.
We get waves because we have found that in the microcosm there is an exchange of bosons that transfers impacts between elementary particles of the standard model for all three forces ( strong, weak and electromagnetic) and hypothesize the same for gravity. These bosons, photons, in an ensemble create the electromagnetic waves we observe macroscopically and at the limit are described by Maxwell's equations that describe wave propagation and information transfer macroscopically.
Sound is a collective effect described by classical physics, it is a meta level based on innumerable electromagnetic interactions which hold solids and liquids together and transfer impulses statistically in gases too. The wave equations for sound arise naturally in the framework of classical statistical mechanics.
So the ultimate answer to the "why" is "because this is what we have observed".