Response to Posting on Waves and Trig Functions

Here is a response to the previous posting form a pal and his son:

Mike,

So...one way to try to understand a complicated idea is to attempt to reverse engineer

it using your knowledge and physical intuition.  Kudos for that.  If you reach a dead

end, you would at least have the satisfaction of uncovering the area you need to focus

on next in your education.

In this case you are in luck. Since the harmonic wave function is a product of hundreds

of years of brilliant mathematicians describing what they've observed in nature

(everything vibrates: light, sound, objects, people, etc.), it is an incredibly elegant

way of representing exactly what is going on.



In order to resolve the apparent conundrum in your mind that the units don't match in the

harmonic wave function, you have only to realize that they must match, obviously, or it

wouldn't be a world-renowned description of how things work. This should encourage you to

continue your quest to understand the nuts and bolts of how and why.



To your credit this is not a simple subject.  There is a lot going on in that equation so it

is good that you are intrigued by the fact that a single equation or a single argument in an

equation can describe a position, a time and modulation from the pattern with all the units

still matching.  The good news is that thousands of people teach and learn this very equation

every year.  For example, a class in structural dynamics can be all about vibrations and learning 

exactly how to manipulate the harmonic wave equation to efficiently design complex physical structures. 

In fact there is a book, Fundamentals of Vibrations by Leonard Meirovitch, that might be just the ticket.

Apparently the current version is rather expensive but you can get an older one, used, online for

considerably less.

It is cool that you are challenging these equations based on your intuitions; however, with a little more

background...chances are good that you'll come to realize the true elegance of the harmonic wave function.

Respectfully Submitted,

Randy Brown paraphrasing son Alex, a graduate student in aerospace engineering