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Surface Acoustic Waves Explained

What are Surface Acoustic Waves?     

     "Surface Acoustic Waves" ("SAWS") are minute physical wave deformations (tiny "ripples") on surfaces which behave much like waves on an ocean or lake.  The biggest difference between SAWS on musical instruments and ocean waves is their extremely small size and weak energy on musical instruments.  (Earthquake waves and Tsunami waves are also surface acoustic waves.)

     Surface acoustic waves on musical instruments are simply too small to be seen except for the trace of their maximum/minimum positions of their "standing waves" on strings.  You can see them between the instrument's "bridge" and the instrument's "nut", (or the player's finger tip position, or "fret").  This trace is usually visible in good lighting when viewed from the side because the string's vertical velocity is zero at the moments when it is changing directions at the top and bottom of its trace.  

     Surface acoustic waves also cannot be felt except for very low frequencies of standing waves on surfaces of the instrument which the player feels as "vibrations".  (A person in a boat with his or her eyes closed will also feel waves as vibrations, but with eyes open will see the rows of waves passing beneath the boat and moving on into the distance, and so will understand what has actually occirred.) 

     Surface acoustic waves also cannot be heard since our ears can hear only waves of pressure in air, not wave deformations on surfaces.  

     Given these difficulties of seeing, feeling and hearing surface acoustic waves, it is not surprising that many musicians, musical instrument manufacturers and craftsmen have never even heard of surface acoustic waves, much less know of their potential to easily improve the volume and sound quality of musical instruments.

     For no reason other that I am both curious and persistent, I learned from about 10 years of experiments with my own banjo, acoustic tenor guitar, violin and mandolin that surface acoustic waves not only exist on stringed acoustic musical instruments but can be controlled using very simple, inexpensive, movable devices which can be temporarily attached to the instrument.  More important, they can impressively improve the volume and sound quality from the instrument.  

     This is possible primarily because of a well-known physics principle related to all waves called, "Constructive Interference", which is explained below.  Significantly, I also learned from my experiments that the surface acoustic waves on acoustic stringed musical instruments are accurate representations of the music being played on the instrument.  I  learned this because I learned how to amplify the harmonics of surface acoustic waves, (frequency multiples of a tone's basic frequency), which are widly known to improve sound quality, and also how to convert the inaudible surface acoustic waves into audible sound in the instrument's sound chamber.   Because, once in the sound chamber, this newly created, harmonic-rich  audible sound mixes with the sound already there allowing everyone present to hear the improved volume and sound quality.

     Because the surface acoustic wave devices which accomplished this improvement, (or its surface wave input components), are movable by the player, the appropriate portion of the device can be easily moved about on the instrument to achieve maximum performance in the opinion of the player.

The General Wave Principle of "Constructive Interference" Explained. 

     This principle posits that when waves in air, on a surface of a musical instrument, or on an ocean or lake, meet coming from different directions, their behavior will depend on the relative frequencies of the different waves before they meet.  If meeting waves have the same or similar frequencies (timing between wave peaks) when they meet their heights (called amplitudes) will add algebraically.  If they have different frequencies the waves simply pass through each other, "ghost-like", without changing either wave.

     This characteristic of wave algebraic addition between waves having the same or similar frequencies, and the ability to remain free from distortions when the waves meet when they have different frequencies, is ideal for control of sound volume and quality.  This is because waves having many different frequencies on musical instruments almost always share the same surfaces.  More important, amplification of waves, which is so important in achieving high quality sound by amplifying harmonics, is as simple as causing waves of the same or similar frequencies to meet coming from different directions!  This means that putting a random bunch of different surface acoustic waves on a 3/8" x 1" thin steel rectangle will amplify ALL similar frequencies on the rectangle!  All frequencies will amplify, (or, more correctly, "add algebraically"), because all will reflect from edges to meet themselves and/or similar frequencies at an angle, and so be amplifyied by the principle of "Constructive Inteference".  And they will not be changed by waves with other frequencies but will pass through them without changing either wave!  

     The principle of "Constructive Interference" almost seems to be "heaven-sent" to improve musical instruments!  How could we have not known about this behavior and then exploit its possibilities before now?  (Perhaps a collective lack of imagination?)  Does this mean that every rectangle which can conduct surface acoustic waves is an exquisitely simple surface acoustic wave amplifier?  Answer:  Yes, and so is a standard steel staple!

     The points of a staple in a sheet of paper touch the paper very close to each other on the back side of the paper.  A surface acoustic wave traveling on that side of the paper will enter both points of the staple essentially at the same time, travel on the staple in opposite directions (away from each point) and meet "head on" on the staple's flat on the opposite side of the paper as two separate waves having the same frequency.  This causes them to add algebraically (amplify) when they meet by the "Principle of Constructive Interference".  Since the staple flat is in firm contact with the paper a new, larger wave will flow out from under the staple on the side of the paper with the staple flat.

     The important point to be made here is that it is incredibly easy and cheap to make a surface acoustic wave amplifier by stapling a piece of paper.  Now all we need is a cheap and easy way to make the inaudible surface acoustic wave audible.  - Something like a mechanical loudspeaker.  No worries, Mate!  That's easy and cheap to make, also!

     My first mechanical loudspeakers were simple cantilevers - rectangles with one fixed end and one free end like a diving board.  Surface acoustic waves were input at the fixed end and when they got to the free end they had nowhere to go so reflected onto themselves causing the free end to vibrate and move adjacent air in an analogous manner to the surface acoustic wave on the cantilever.  

     This idea was improved by using cantilevers in different shapes, some causing the surface acoustic wave to grow in height as it moved down the cantilever.  Some were shaped like vibration traps seen in the center of all violin bridges (which are shaped like fish traps), to maximize wave intersections.  (Like fish in a fish trap, the waves could go in but couldn't come out.)  Eventually, a more efficient loudspeaker was tried which had a small five-sided polygon of thin steel taped along one edge over a similarly shaped piece of cardstock.  The idea was to allow the surface acoustic waves on the steel to squeeze the air between the steel and cardstock in an analogous manner to the surface acoustic waves on the steel.  That idea worked great and even amplified harmonics improving both high notes and sound quality, but it needed to be bigger to amplify low notes.  

     The next iteration to improve low notes was a simple fold of compressed Kraft paper cut from a small coin envelope, which made a very impressive bass note amplifier.  The simple fold of Kraft paper seemed logical at the time because one would suspect that the surface acoustic waves would make the equivalent of a "U-turn" going around the fold, and compress the air in the fold between the diverging planes of Kraft paper.  It probably did, but experiments proved what was required was not a "U-turn" but an accurate "mirroring" of the input surface acoustic wave on the opposite plane of paper.  This was easily done by placing a row of four closely-spaced staples just 1/8-inch from the fold and 1/8-inch from both edges.  This greatly improved the loudspeaker, so it was decided to cut off the fold which was suspected of degrading the mirrored wave.  

     As soon as the fold was cut away I heard the beautiful low tones that I had been hoping for.  Mirroring the wave to the opposite diverging plane of Kraft paper was the key to achieving an undistorted (and growing) analogous wave form of air in the diverging air space between the planes of Kraft paper.  Making an equivalent high frequency amplifier was simply a matter of making one with a fold of thin brass foil, which could mirror high frequency waves to the opposite side simply by creasing the brass with a thumbnail.  The input surface acoustic waves could be deposited inside the fold of brass foil with a few staples with their flats placed anywhere inside the fold.  It worked great!

   Yea!  I now had both low and high frequency loudspeakers and they sounded fantastic!  Now the problem was psychological.  Who would buy something that looked so...and was so... CHEAP?  I was already anticipating the question that I had heard many times before, "Why didn't you make one out of brass?"  "Ugh..Mmmm.."