68 DYNAMICAL THEOKY OF SOUND 



In the latter case one of the intervals of rest vanishes*. 



It is of course with the vibrations of a finite string that 

 we are chiefly concerned in acoustics. The string is usually 

 stretched with considerable tension between the two points which 

 limit the vibrating portion. At one at least of these points the 

 string passes over a bridge resting on a sounding-board, whose 

 function it is to communicate the vibrations to the surrounding 

 air. The direct action of the string in generating air-waves 

 is quite insignificant, but by the alternating pressure on the 

 bridge the whole area of the sounding-board is set into forced 

 vibration. This implies of course a certain reaction on the 

 string itself, which is however, in the first approximation, 

 usually negligible, for the reason given in 4. 



For experimental purposes an arrangement called a " mono- 

 chord " is used. The sounding-board here forms the upper face 

 of a rectangular " resonance chamber." The distance between 

 the bridges can be varied and measured, and the tension, being 

 produced by a weight attached to one end of the wire, which 

 passes over a smooth pulley, can be regarded, at all events 

 approximately, as known. For purposes of comparison one or 

 more additional wires may be stretched alongside the former, 

 their tension being adjusted, as in the pianoforte, by means of 

 pegs at the extremities. 



25. Normal Modes of Finite String. Harmonics. 



The preceding investigations have been given on account of 

 their historical importance, and for the sake of the analogies with 

 other types of wave-motion which we shall meet with later. 

 From the purely acoustical point of view they are however of 

 secondary interest. The ear knows nothing of the particular 

 geometrical forms assumed by the string, and is concerned 

 solely with the frequencies and intensities of the simple- 

 harmonic constituents into which the vibration can be resolved. 



* The theoretical vibration-forms have been verified experimentally by 

 Krigar-Menzel and Kaps, Wied. Ann., vol. L., 1893, so far as the initial stages 

 of the motion are concerned. After a few vibrations the form is seen to be 

 undergoing a gradual change. This is attributed to a slight yielding of the 

 supports of the string, in consequence of which the normal frequencies are not 

 exactly commensurable, and the resulting motion therefore not accurately 

 periodic. The construction in Fig. 27 is also due to these writers. 



