358 VIBRATION OF STRINGS 



mulated work is expended in overcoming the resistanc 

 which the tension offers to the flexure of the string 

 then the string returns again, performs the same motioi 

 in the opposite direction, and so on. The vibrations c 

 a string are thus very similar to the oscillations of 

 pendulum, but the former are much sooner brought t 

 an end than the latter, because the work of a vibratin 

 string is soon expended in imparting motion to the soli 

 bodies to which it is attached, and by means of thes 

 to the air. Other things equal, the greater the fore 

 of tension the greater is the number of vibrations pei 

 formed in a given time, and the higher the note prc 

 duced. If the same tension act on two strings of th 

 same length but of different mass, the more massh 

 string would vibrate more slowly, and the note produce 

 would be lower. For the experiments which we ha^ 

 made previously on the relation of forces to the masst 

 moved by them have proved that the motion produce 

 by the same force acting upon different masses is slowt 

 the greater the mass acted upon. The same law hol( 

 good in the case of a vibrating string : the greater tl 

 mass moved by the force of tension, the smaller is tl 

 velocity produced, and the slower are the vibration 

 To prove this relation by direct experiment, and 

 arrive at satisfactory numerical results, a more comple 

 apparatus than our monochord is required. It is (> 

 account of this law that the cords of stringed instr | 

 ments are made thicker for the bass than for the trebl[ 

 and that those for the lowest notes are frequent 

 rendered heavier by being wound round with thin brn 

 or copper wire. 



The string of the monochord may be shortened at w 



