FREE REED PHYSICS - 5

[ttonon]

Greetings again.  Here we compare steel to a titanium/tantalum alloy, Ti/Ta 70/30 Beta, which is used in surgical equipment and prosthetics.  It interests me, not so much to propose it as tongue material, but because the tantalum increases the density well above the neat material.  The modulus is only a third of that for steel, but its density is a little above that for steel, resulting in a modulus-to-density ratio about 0.3 that of steel. 

 

We can compare these results to those comparing Titanium to steel and find that the higher harmonic amplitudes in comparison to steel are very much less in the Ti/Ta alloy.  The behavior with increasing bellows pressure shows the harmonic amplitudes making up the difference – just what happens in the Titanium/steel comparison; however, since the higher harmonics of the alloy start with such low values, they don’t catch up to those of steel nearly as quickly or as completely as in the case of the neat material. 

 

Comparing these plots with the plots for brass/steel, we see an enormous difference.  If we can discern an audible difference in timbre between brass and steel, according to these plots, and if our basic assumptions are correct, there should be an enormous difference in timbre between either Ti or its Ti/Ta alloy and either brass or steel. 

 

Another interesting outcome in the case of the alloy is that I couldn’t get a convergence with a solution for bellows pressure less than about 2.2 inch w.c.  On the other hand, solutions continue further on for the higher bellows pressure than they do for steel and other materials.  This might indicate a material that may not be able to play at very low bellows pressures, but may perform better than other materials at the highest bellows pressures.  The last plot in these calculations show that the trend of increasing harmonic amplitude with bellows pressure continues for even the highest bellows pressures, for those above solutions for steel become impossible.  

 

We can make such plots for most any feasible tongue material, though at some point, the usefulness tapers off, at least if we are in search of a practical tongue material.  The theoretical interest continues, as a way of getting a good intuitive feel for the effect of material properties on musical tone.  At this point, I think we need wait for experimentalists to compare information they have from work already accomplished or from new work.  There might be other materials I'd like to do calculations on, such as glass, and other geometric factors, such as tongue thickness and plate thickness. 

 

A docx file showing these plots are at: https://app.box.com/folder/79305691686

 

Best regards,

Tom