The world is full of things that change with time and space.
For example, apples falling, or the author being strung up and shaken by readers—what's the fundamental difference between those and waves?
The answer is just as simple:
When a wave propagates, although its position is different at different times, its shape always stays the same.
In other words, the wave has this shape at one second, and even though it's no longer here after another second, it still keeps the same shape.
This is a pretty strong constraint.
Since we use f(x, t) to describe a wave, the initial shape of the wave (that is, at t=0) can be represented by f(x, 0).
After time t has passed, and the wave speed is v,
that means the wave has moved a distance of vt to the right; in other words, the initial shape f(x, 0) has been shifted right by vt.
So Xu Yun wrote down another formula:
f(x, t) = f(x – vt, 0).
Then he glanced at Faraday.
