Chapter 558 257 Witness the Miracle! (Part 1)_2

But that is not enough.

The world is full of things that change with time and space.

For example, an apple falling, or an author being shaken by a reader, how do they fundamentally differ from waves?

The answer is equally simple:

When a wave propagates, though its position changes at different times, its shape remains the same.

That is, if one second ago the wave had this shape, one second later, although it is not in the same position, it still has the same shape.

This is a very strong restrictive condition.

Since we use f(x, t) to describe waves, the initial shape of the wave (shape at t=0) can be represented as f(x, 0).

After time t, the wave speed is v.

The wave then moves a distance vt to the right, which means the initial shape f(x, 0) is shifted vt to the right.

Thus Xu Yun wrote down another equation:

f(x, t)=f(x-vt, 0).

Then he glanced at Faraday.

Among the bosses present, most came from professional backgrounds, only Faraday was an apprentice-born 'underdog.'

Although he later caught up with a lot of knowledge, math was still a weakness for this electromagnetic boss.

However, Xu Yun was slightly relieved.

This electromagnetic boss's expression showed no fluctuation, so it seemed he still hadn't fallen behind.

So Xu Yun continued his derivation.

"That is to say, as long as a function satisfies f(x, t)=f(x-vt, 0), ensuring the shape at any time equals the initial shape shifted by some amount, then it represents a wave."

"This is purely a mathematical description, but it is not enough, we also need to conduct some analysis from a physical perspective."

"For instance... tension."

As everyone knows.

When a rope is placed on the ground, it is motionless, but when we give it a flick, a wave appears.

Then the question arises:

How does this wave propagate to distant places?

Our hand only pulls one end of the rope and does not touch the middle, but when the wave reaches the middle, the rope indeed moves.

The movement of the rope indicates that force is acting on it, so where does this force come from?

The answer is equally simple:

This force can only come from the interactions between adjacent points of the rope.

Each point 'pulls' its neighboring point slightly, and the neighboring point moves—just like when we queue up and only notify the person next to us, this internal force within the rope is called tension.

Also, for example, when we pull on a rope with force, I clearly apply force to the rope, but why doesn't this rope lengthen?

Why doesn't the point closest to my hand get pulled?

The answer, naturally, is that the points near this point exert an opposing tension on this mass point.

In this way, this point is pulled on one side and pulled by its adjacent points on the other, with the effects of the two forces canceling each other out.

But force is mutual, and if nearby points exert tension on the endpoint, then those nearby points also experience a pull from the endpoint.

Yet, the nearby points don't move either, so they must also experience tension from deeper points.

This process can propagate continuously, with the final result that tension exists throughout the rope.

Through the above analysis, a concept can be summarized:

When a rope is still on the ground, it is in a relaxed state, with no tension.

But when a wave reaches there, the rope takes on the wave's shape, and then tension exists.

It is this tension that causes points on the rope to vibrate up and down, so analyzing the effect of this tension on the rope becomes the key to analyzing wave phenomena.

Then Xu Yun wrote down a formula on the paper:

F=ma.

Exactly.

It is Little Niu's second law.

As everyone knows.

Little Niu's first law tells us "an object will remain at rest or in uniform straight-line motion unless acted upon by a force or with a net external force of zero." So what if the net external force is not zero?

Little Niu's second law continues:

If the net external force F is not zero, then the object will have an acceleration a, and their relationship is quantitatively described by F=ma.

That is to say.

If we know the mass m of an object, as long as you can analyze the net external force F acting on it.

Then we can calculate its acceleration a using Little Niu's second law F=ma.

Knowing the acceleration, you know how it will move next.

Afterward, Xu Yun randomly took two points on a segment of the function graph.

He labeled one as A and the other as B, and marked their arc length as △l.

After writing, he pushed it toward Little Niu:

"Maxwell, could you analyze the net external force received in this interval? Without considering gravity."

Wheat was stunned by these words, pointed at himself, and said in astonishment:

"Me?"

Xu Yun nodded, letting out a slight sigh in his heart.

What he was trying to achieve today would greatly promote Faraday, the field of electromagnetism, or, on a larger scale, the entire human historical process.

Yet for Wheat and Hertz alone, it might not be so favorable.

Because it means some contributions originally belonging to them would be erased.

Like one day when a person earning a monthly salary of 4000 suddenly learns that they could have been a billionaire, only to have a reborn individual take your opportunity in the name of 'human common development,' what would you feel?

To be fair, it's somewhat unfair.