Differences Between EM Waves & Pulses: Comprehensive Analysis

[ZeroCool77]

What is the difference between EM Waves and EM Pulses and how are they related to one another? When trying to look up info on this, I always get a full article on either just one or the other so that no comparison is ever made between one and the other, the definitions alone seem a little lacking when it comes to thinking of both of them and how they are related, at least, when looking this up online, as my experience has shown me, which is why I've turned to this forum after extensively searching for comparative definitions of these two for months! I'd appreciate any comparative info that will help me to understand these two a little better. Thank you.

 

[bjacoby]

What is the difference between EM Waves and EM Pulses and how are they related to one another? When trying to look up info on this, I always get a full article on either just one or the other so that no comparison is ever made between one and the other, the definitions alone seem a little lacking when it comes to thinking of both of them and how they are related, at least, when looking this up online, as my experience has shown me, which is why I've turned to this forum after extensively searching for comparative definitions of these two for months! I'd appreciate any comparative info that will help me to understand these two a little better. Thank you.

First off, get a handle on mathematics vs reality. So far as is known all EM radiation is pulsed. We say that because so far as we can tell every wave has a beginning and will have an end. In other words it is an infinite wave that has been "amplitude modulated". Thus, the commonly described things such as "TEM plane waves" or even waves of a single pure frequency are abstract mathematical constructs and not real objects. Real waves are not infinite in extent nor in time.

But now here is the interesting mathematics. It can be shown that one can construct a real wave (mathematical function) by a sum of orthogonal functions. For example Fourier analysis shows that one can construct a wave finite in both time and space (modeling real waves) which does NOT have a single frequency with a summation of a set of mathematically abstract "pure" infinite waves. Thus one can get some insight into mechanisms by which the parameters of a pulsed EM radiation relates to other parameters such as the frequencies contained within the pulsed wave and the bandwidth needed to pass it.

The key is that mathematics gives you insight but is not reality. Mathematics is imaginary and abstract. And indeed when using mathematics to study EM radiation is it a common occurrence to encounter what are known as "non-physical solutions". These are cases where the mathematics simply has no correspondence to reality. In those cases practical designers and engineers simply summarily throw out these results without a second thought. The problem one often has (as you have encountered) is that in articles and textbooks one is assumed to know that things like infinite waves are not real but just mathematical models and the reader is left to sort out what is what on their own.

 

[Claude Bile]

EM Pulses are sometimes described as wave packets. This is because you can describe an EM pulse as the sum of an infinite number (or continuum) of EM waves spanning some frequency interval. The larger the frequency interval, the shorter the pulse.

Claude.

 

[ZeroCool77]

The problem one often has (as you have encountered) is that in articles and textbooks one is assumed to know that things like infinite waves are not real but just mathematical models and the reader is left to sort out what is what on their own.

I feel you, one would think that the purpose of reading these textbooks is precisely so that one is NOT left to sort out what is what on their own and waste time re-inventing the wheel.

The key is that mathematics gives you insight but is not reality.

As I suspected, this means that all the popular visual representations of EM Radiation (as waves or particles) out there are just visual representations of mathematical functions and not of reality. Do I dare ask if any attempt has ever been made to visually represent EM Radiation as it is propagating in reality and not just in the abstraction of a mathematical construct?

 

[Claude Bile]

As I suspected, this means that all the popular visual representations of EM Radiation (as waves or particles) out there are just visual representations of mathematical functions and not of reality. Do I dare ask if any attempt has ever been made to visually represent EM Radiation as it is propagating in reality and not just in the abstraction of a mathematical construct?

I suppose you could graph it using a computer quite easily, but the truth is, the mathematical formulae contain all the information that is contained in the graphical representation.

I suppose people have different preferences regarded equation-like representations and something that is a bit more visual, but the notion that a visual representation would offer more insight into the actual physics is an illusion.

Claude.