The mathematical concept of function is used in physics to represent different physical quantities. For example the air pressure variation with time and space is called an acoustic wave. We use a function to represent a charge distribution (or even electric field strength) in space and time.In gravitation we use it to represent a mass distribution (and momentum distribution) in space and time. In Quantum mechanics we use it to represent a Quantum state and hence the probability distribution of position and momentum of a particle in space and time. Most of the time we do a variety of mathematically well defined operations on these functions to make some conclusions and to answer some questions regarding a physical system.Even the fundamental laws of physics give the mathematical relation between functions representing different physical quantities. Now if i ask a question on the mathematical nature of a function that represents a physical quantity (say for example a mass distribution in space and time), would it be possible to find an answer ? Does every such question has a physical interpretation ?
Here i give a sample question ?
Q. let a function $p(t)$ represent the acoustic pressure variation at a given point in space.Is the function well behaved ? Mathematically speaking "Is $p(t)$ a smooth function ?"