Final answer:
The solution given by ( u(x,t) = f(x+at) + g(x-at) ) is for the wave equation, demonstrating the principle of superposition in wave theory.
Step-by-step explanation:
The expression ( u(x,t) = f(x+at) + g(x-at) ) corresponds to a general solution to the wave equation. This form of solution utilizes the principle of superposition, where two individual wave functions combine to form a resultant wave function that still satisfies the wave equation. This concept is pivotal in understanding phenomena such as interference, where two or more waves overlap to form a new wave pattern. The functions f and g represent two waves traveling in opposite directions along the x-axis, with a denoting the wave speed.