De site over het instrument alpenhoorn
Pipes and frequencies - application to the alphorn
 
Conclusions
  
  • In the first instance we are inclined to conclude that it is the combination of model 4 and the bell effect that makes that blowing the alphorn (with mouthpiece) results in a full harmonic series, with the fundamental missing. But, the fact that we used a mouthpiece in the previous investigations cannot be neglected. We have to assume that the well-known effect of the mouthpiece has also its influence on the sounding frequencies. The mouthpiece forces the upper resonances progressively down. I think the used measuring-method is not enough precise to show this effect clear.
     
  • The sounding frequencies of the alphorn are:

    2f, 3f, 4f, 5f, ..........


    The formula 2f = v / L' proves to be a reasonable approximation of the second natural mode of the alphorn.
    In the case of our alphorn in E this formula gives:
    2f = v / L' = v / (L + 0,3 d2) = 343 / (3,97 + 0,3 x 0,23) = 84,9 (Hz), which equals almost the value 82,4 (Hz) of the pitch E2.
     
  • Now we see how strong the suggestion is that model 3 is a correct physical model for the alphorn! Unfortunately, this interpretation is not tenable. The physical backgrounds are more complicated.
    A more serious fallacy is to see model 1 as a physical model for the alphorn. This cannot be the case, since the mouthpiece end of the tube behaves acoustically like a closed end. At this end the pressure variations are not zero but a maximum.
     
  • We have seen that the applicability of the four models is limited. Only model 4 (with formula 2 of Neville Fletcher) gives a good, but only partial contribution to the understanding of the acoustical working of the alphorn. The mouthpiece effect and the bell effect play a significant and indispensable role. This role is well-known with respect to the acoustics of the trumpet.
    However, many questions regarding the mouthpiece effect and the bell effect are still open and require more physical research. In my opinion a highly fascinating question is the following one:
     
    As we saw, under certain conditions a tube (cylindrical, conical, cylindrical-conical), with mouthpiece and bell, will have resonances  2f, 3f, 4f, 5f, .....
    Which conditions?

  
 
dr. J. de Ruiter

Diever
The Netherlands
 
© 2007 J. de Ruiter