ON THE SOURCES AND EFFECTS OF SOUND. 379 



Musical sounds are, however, most frequently produced by the alternate ^^.at-^*^-h^^ 

 motions of substances naturally capable of isochronous vibrations, and these 

 substances may be either fluids or solids, or instruments composed of a com- 

 bination of fluids with solids. The resonance of a room or passage is one of UMin^^^^'^ / 

 the simplest sources of a musical sound; the walls being parallel, the impulse 

 is reflected backwards and forwards continually, at equal intervals of time, 

 so as to agree with the definition, and to produce the eflfect, of a musical 

 sound. When we blow obliquely and uniformly into a cylindrical pipe 

 closed at one end, it is probable that the impulse or condensation must lyJtf^ t^^-Ci-'-i 

 travel to the bottom and back, before the resistance is increased ; the cur- 

 rent of our breath will then be diverted from the mouth of the pipe, for 

 an equal time, which will be required for the diminution of the resistance 

 by the discharge of the condensed air, so that the whole time of a vibration 

 will be equal to the time occupied by an impulse of any kind in passing 

 through four times the length of the pipe. An open pipe may be considered 

 nearly as if it consisted of two such pipes, united at their closed ends, 

 the portions of air contained by them being agitated by contrary motions, 

 so as always to aft^brd each other a resistance similar to that which 

 the bottom of the stopped pipe would have furnished. It is probable 

 that when an open pipe is once filled with air a little condensed, the oblique 

 current is diverted, until the effect of the discharge, beginning at the remoter 

 end, has returned to the inflated orifice, and allowed the current to reenter the 

 pipe. Where the diameter of the pipe is different at different parts of its 

 length, the investigation of the sound becomes much more intricate; but it 

 has been pursued by Daniel Bernoulli with considerable success, although 

 upon suppositions not strictly consistent with the actual state of the motions 

 concerned. 



In the same manner as an open pipe is divided by an imaginary basis, 

 so as to produce the same sound with a stopped pipe of half the length, a 

 pipe of any kind is capable of being subdivided into any number of such 

 pipes, supposed to meet each other's corresponding ends only; and in 

 general the more violently the pipe is inflated, the greater is the number of 

 parts into which it subdivides itself, the frequency of the vibrations being 

 always proportional to that number. Thus, an open pipe may be divided not 

 only into two, but also into four, six, eight, or more portions, producing 

 the same sounds as a pipe of one half, one third, one fourth, or any other 



