We take for granted these fundamental understandings of how the universe works, and it leads me to my curiosity toward civilizations that existed before understanding these basic scientific principles. Specifically the nature of sound waves (and maybe Doppler effect if anything existed to display the phenomenon)
As early as Aristotle's On Things Heard, we find the idea that sound is vibrations pushed through the air on a wave. Aristotle also argued that higher pitched sounds travelled through the air faster than lower pitched sounds. This idea was incorrect, but it does show that Aristotle conceived of sound as something which not only implicitly had speed, but which also implicitly had speeds which might vary. So basically, the slowness of sound was something Alexander The Great would have known about (Aristotle having personally tutored the young conqueror).
Aristotle's natural philosophy was all about observation, but it wouldn't have occurred to Aristotle to mathematise those observations, in order to figure out the exact speed of sound; it would take until the Scientific Revolution for that to happen.
In terms of the Scientific Revolution, Galileo Galilei did experiments with glasses of water and sound, and in A Dialogue Concerning Two New Sciences he agreed with Aristotle that sound was propagated by the vibration of the air (based on analogy to the movement of waves in water which occur when glasses vibrate, as the props department of Jurassic Park could no doubt tell you).
Others following Galileo specifically tried to measure the speed of sound. Marin Mersenne tried to measure the speed of sound via measuring the time it took for an echo to return, and got a value of 316 m/s. In 1656 Borelli & Viviani estimated it at 350 m/s. A measurement in Paris in 1738 produced the reasonably accurate 332 m/s, based on cannon fire. Isaac Newton, using his theory of physics (rather than observations), and based on Galileo's prior observations, came up with a value of 298 m/s for the speed of sound. The variability in observations was a bit of a puzzle, and Branconi showed that the temperature of the air had something to do with it in 1740.
However, it wasn't until Laplace in 1812 that there was a clear/basically correct explanation of why the speed of sound was so variable from experiment to experiment even in experiments where measurement was more precise: the speed of sound was heavily dependent on the properties of the air it was moving through. How humid that air was, the composition of the air, and the pressure of the air all mattered; if Newton had factored these into his calculations his theorising would have been essentially correct.
Laplace's formula took into consideration the elasticity of the air, which itself depended on temperature changes as a result of the vibrations of air. And once Laplace revised his understanding of the elasticity of air in 1825, his formula for the speed of sound - given a particular temperature, air pressure and the nature of the gas - was satisfactorily well-correlated with observations. Since 1825, scientists have refined Laplace's formula slightly, and the measurement of the speed of sound has progressively become more precise because instruments have gotten more precise, but Laplace's basic formula still reliably explains the speed of sound (which the Bohn article cited below says is 331.45 m/s (+/- 0.05 m/s) in dry air at 0 degrees celsius).
Sources:
Dennis Bohn, 1988, 'Environmental Effects on the Speed Of Sound', in the Journal Of The Audio Engineering Society
Caleon & Subramaniam, 2007, 'From Pythagoras to Sauveur: tracing the history of ideas about the nature of sound', in Physics Education