Chapter 558 - 257: Witness the Miracle! (Part 1)

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.

Among these big shots present, most were graduates of professional schools—only Faraday was an apprentice-turned-"nine-leak-fish" (an online slang term for non-elite students).

Although he’d crammed a lot of knowledge afterwards, math was still a weak spot for this electromagnetism guru.

But to Xu Yun’s slight relief,

the expression on this electromagnetism giant’s face didn’t show much of a ripple. Seemed like he hadn’t lost track—yet.

So Xu Yun kept going with the derivation.

"That means, as long as there’s a function that satisfies f(x, t) = f(x–vt, 0)—i.e., at any time its shape equals the initial shape shifted over a bit—then it represents a wave."

"That’s the purely mathematical description, but it’s not enough. We need to analyze it from a physical perspective, too."

"For example... tension."

As we all know,

a rope lying on the ground is motionless, but if we flick it, a wave appears.

So here’s the question:

How does this wave travel all the way down the rope?

Your hand only holds one end of the rope—you never touch the middle part—yet, when the wave gets there, the rope in the middle moves too.

If the rope moves, that means some force is acting on it. But where does this force come from?

The answer’s just as simple:

This force can only come from the interaction between adjacent points on the rope.

Each point "tugs" on its neighbor a little, and the neighbor moves—just like when we’re lining up and only inform the person next to us. This force inside the rope is what we call tension.

Or, say we pull hard on a rope. I’m obviously applying a force, so why doesn’t the rope stretch out?

Why doesn’t the point right near my hand get dragged away?

The answer is that the points near this spot apply a force—a tension—in the opposite direction and balance it out.

So this point gets pulled on one side, but is also pulled by the neighboring points on the other side. The two forces cancel out.

But force always acts both ways: if the neighboring point applies tension to the endpoint, then the endpoint also pulls back on that neighbor.

Yet, the neighboring point doesn’t move either, so it also must get tension from points further in.

This process can go on and on down the rope, so in the end, every part of the rope is experiencing tension.

From the above analysis, we can sum up a concept:

When a rope lies motionless on the ground, it’s in a relaxed state—no tension.

But when a wave passes through, the rope forms the shape of the wave, and now there is tension.

It’s exactly this tension that makes points on the rope vibrate up and down—so analyzing this tension is the key to understanding wave phenomena.

With that, Xu Yun wrote another formula on the paper:

F = ma.

That’s right.

It’s Newton’s famous Second Law.

As we all know,

Newton’s First Law tells us: "An object remains at rest or moves uniformly in a straight line unless acted upon by a net external force." But what if there is a net external force?

The Second Law covers that:

If the net external force F isn’t zero, the object will have an acceleration a—and F = ma describes the relationship quantitatively.

So,

if we know the mass m of an object, and can analyze the net external force F acting on it,

then, based on Newton’s Second Law F = ma, we can calculate its acceleration a.

Once you know the acceleration, you know how it’s going to move next.

Then Xu Yun picked two random points on a segment of the function graph.

He labeled one A and the other B, marking the arc length between them as △l.

After he finished, he shoved it toward Wheat:

"Maxwell, how about you analyze the net force on this segment? Ignore gravity."

Wheat was stunned, pointed at himself, and asked in surprise:

"Me?"

Xu Yun nodded, sighing inwardly.

What he was about to do today—in terms of Faraday, the field of electromagnetism, or even, more broadly, the whole progress of human history—would have huge significance.

But for Wheat and Hertz, it might not be such a good thing.

Because it meant some credit that was originally theirs had been erased.

It’s like when a salaried worker earning 4,000 yuan a month suddenly learns he could have become a billionaire, only for some reborn person to take away his shot "for the sake of humanity’s common good." How would you feel?

Honestly, it’s a bit unfair.

So deep down, Xu Yun felt a pang of guilt toward Wheat.

How to make it up to Wheat later was another matter—for now, the best he could do was help put Wheat in the spotlight as much as possible among these big names.