Re: [Harp-L] Description of Harmonica Reed Physics (Was: Johnston or Johnson)

[Vern <jevern@xxxxxxx>]

It seems to me that there are several subjects to be studied.

The reed itself is a cantilever beam of non-uniform cross section.  Its natural frequency will be a function of the square root of the ratio of the restoring forces as  it deflects to the mass of the portion that deflects. These parameters are distributed along the length of the reed.  

 Determining natural pitch, deflected shape, and local stresses can be done with finite element analysis (FEA). Fortunately we don’t have to develop that method, just obtain the software and run it on the computer.  To start with the desired pitch and determine reed shape is not practical because there are multiple solutions for any set of parameters……e.g. a stiff, heavy reed and a limber, light reed can have the same pitch. 

Another subject is how the air excites the vibration.  Trying to understand the motion of every air molecule is beyond the scope of our investigation, but we can start with some general principles.  The air must exert time-varying force on the reed that is out of phase with the deflections. (Ideal excitation is 90 degrees out of phase with the deflection.)  It seems reasonable to assume that  bernoulli effect near the surfaces of the reed can exert such forces as the reed passes back and forth through the slot and the flow paths vary in size and direction.  This is confirmed by the fact that a reed must have a gap to allow initial flow in order to start. The natural frequency of the reed determined by plucking isn’t very different when excited by breath in the harmonica.

The resonance of the player’s embouchure coupled to the reed resonance effects the sound that emanates from the slot and seems to me to be least understood and of greatest interest to me.  I have connected a large syringe to reed chambers and observed huge changes as the volume is changed. At some settings, the reed will not start and at others it peaks in loudness. My experiments were not quantitative.

The coupling of another reed in the chamber as in bending has been studied.  I believe that I have that paper in my files and a VCR of Bahner’s imaging of Howard Levy’s embouchure.  I would send that to you if you will convert it to DVD and return me a copy.

Vern

On Apr 30, 2014, at 10:14 PM, Music Cal <macaroni9999@xxxxxxxxx> wrote:

> Hi Robert
> 
> Thanks for your comments and suggestions.
> 
> I think that the system to be modeled is not simply the reed but the air
> column plus reed, possibly as a coupled set of second law equations.
> 
> MusiCal