352 



CHAPTER V. 



PROBLEM OF THE SOUNDS OF PIPES. 



IT was taken for granted by those who reasoned 

 on sounds, that the sounds of flutes, organ-pipes, 

 and wind-instruments in general, consisted in vibra- 

 tions of some kind ; but to determine the nature 

 and laws of these vibrations, and to reconcile them 

 with mechanical principles, was far from easy. 

 The leading facts which had been noticed were, 

 that the note of a pipe was proportional to its 

 length, and that a flute and similar instruments 

 might be made to produce some of the acute har- 

 monics, as well as the genuine note. It had further 

 been noticed 1 , that pipes closed at the end, instead 

 of giving the series of harmonics 1, ^, ^, , &c., 

 would give only those notes which answer to the 

 odd numbers 1, ^, , &c. In this problem also, 

 Newton 2 made the first step to the solution. At 

 the end of the propositions respecting the velocity 

 of sound, of which we have spoken, he noticed 

 that it appeared by taking Mersenne's or Sauveur's 

 determination of the number of vibrations corre- 

 sponding to a given note, that the pulse of air runs 

 over twice the length of the pipe in the time of 



1 D. Bernoulli, Berlin. Mem. 1753, p. 150. 



2 Princip. Schol. Prop. 50. 



