How do waves propagate?

Answer 1

To understand how electromagnetic (EM) waves propagate, you first need to know some background information. The most important piece of information that you need to understand is that a time-varying electric field produces a magnetic field, and a time-varying magnetic field produces an electric field. Additionally, both of these produced fields are perpendicular (900 apart) to each other.

The last thing to understand may be a little difficult, so pay attention. If either time-varying field, the magnetic or the electric, is always changing in the same manner, the field produced from that change will either be constant, or will itself be changing in one particular way over time.

For example:

Say an electric field continuously gains 1 unit of strength for every 1 unit of time; i.e., its strength is 1 after 1 unit of time, 2 after 2 units of time, 3 after 3 units of time, etc. The magnetic field produced from this change will be constant, or uniform; i.e., not changing at all, or better yet, it will be a number, like 1. And, since this magnetic field isn't changing, it won't produce an electric field.

Now let's say that this electric field was gaining strength proportional to the cube of the unit of time; i.e., its strength is 1 after 1 unit of time, 8 after 2 units of time, 27 after 3 units of time, 64 after 4 units of time, etc. The magnetic field produced from this change will be proportional to the square of the unit of time; i.e., its strength will be proportional to 1 after 1 unit of time, 4 after 2 units of time, 9 after three units of time, etc. Continuing further, that magnetic field will produce an electric field proportional to the one I first described, where it's gaining 1 unit of strength for every 1 unit of time.

The point to gain from all this is that were EM waves described as above, they wouldn't be able to indefinitely propagate through space, because they would eventually stop producing fields. However, were the fields produced changing, not in the same fashion over time, but in a variable manner, the fields produced by those fields would be changing in a variable manner as well, and so on, and so on. Well, since we know that EM waves do in fact exist, we have to figure out a way to mathematically describe these field changes in such a way that the fields produced from them can perpetually continue producing other fields.

The way this is done is by describing these waves using the sine function. The reason being that the field produced from a field changing proportionally to a sine function is proportional to the cosine function, whose field produced is once again proportional to the sine function. Thus the field keeps varying from sine to cosine to sine to cosine, and so on, indefinitely.

All of that above was basically an explanation as to how EM waves are able to propagate in the first place. Now, the direction in which they propagate is a much shorter explanation.

As stated above, the fields produced by time-varying electric or magnetic fields are perpendicular to each other. Additionally, the field produced from this previously produced field is perpendicular to it, but it remains in the same 2-dimensional plane as the other two fields. Similarly, the next field produced is in the same 2-dimensional plane, and so on, and so on. Well, fortunately, we live in a 3-dimensional universe, which leaves us a spare dimension for the EM wave to use, which it does. In other words, the oscillating electric field, the oscillating magnetic field, and the direction of propagation for an EM wave are all perpendicular to each other. Thus, an EM wave travels in a single direction.

Two quick notes:

When an EM wave travels from one medium to another, like say from air to glass, it changes its direction of propagation at the boundary of the two mediums, and then continues moving in a straight line. This is known as refraction, and I've added a related link below if you want to read more about that.

Also, there is an effect from the General Theory of Relativity, called gravitational lensing, in which a powerful gravitational field can bend EM waves towards it. I linked a website about that below as well.

Answer 2

Waves propagate through the transfer of energy from one point to another without the physical transfer of matter. As a wave moves, it causes particles in the medium to oscillate back and forth, transferring the energy along the wave's path. The medium itself does not move with the wave but rather serves as a mechanism for energy transfer.