Guitar String Theory

I learned how to play the guitar about thirteen years ago, towards the end of high school, because I hypothesized that it would attract the ladies.  Fortunately for me, it attracted one lady in particular, and I ended up marrying her.  Although this case study was limited to one specimen, I think further investigation would lead to a strong correlation between guitars and ladies.

Over time, the guitar has become much more for me than a tool for garnering attention around a campfire.  The six-stringed instrument has sat on my lap for countless hours, as I figure out songs that I enjoy, perform them live, or just sit alone strumming nothing in particular.  It’s amazing what a wonderful diversion those twelve notes can provide.

I have written previously about how a pulse can travel along a string that is in tension.  What distinguishes the behaviour of a stringed instrument is that both ends of the strings are fixed.  The phenomenon that occurs when a taught string is plucked is known as a standing wave.  The note that we hear, its frequency, is dependent on four parameters for the given string: its length (L), tension (T), mass per unit length (µ), and mode number (n).  The frequency in Hz is given by the following equation:

f = [n/(2L)](T/µ)^0.5

A Mechanical Pulse

Can we synthesize a beating heart directly from stem cells?  Did Dorothy’s friend, the Tin Man, have a heart?  Does blood flow through the veins of computer engineers?  Not yet, yes, and not until proven otherwise.

The term pulse has taken on a biological meaning in popular culture.  It is used to describe the gush of blood sent streaming from the heart throughout the body.  You can feel your pulse rate by pressing against your neck.   Fictional characters always check the wrist to see if someone is dead, but the neck seems like a more reliable indicator (if I were a doctor using the wrist to be fancy, I would probably pronounce some living people dead).

In science, a pulse takes on a more general meaning.  It is a single disturbance that propagates through a medium or material.  The source of the pulse may be a beating heart, but it can just as easily be a loud horn.  The loud horn creates a sound of a certain intensity, which travels in all directions through the medium of air.  Sound waves may appear to be mystical, but it is just a game of broken telephone between neighbouring air molecules; information, in this case, longitudinal vibrations on a molecular scale, is being transported.