94 BROOMALL : 



the corresponding angle. The angle increases from o° to 360° 

 and so on through successive cycles, while the sine passes 

 through various values between plus and minus one as its 

 limits. The result of plotting such values of the sine in the 

 manner described is to produce a wavy line called the sine 

 curve. The sine curve is typical of almost every kind of 

 vibrational motion met with in nature, the ordinates repre- 

 senting displacement and the abscissas representing angle, 

 time or length as the case may require. Another name given 

 to the curve is the harmonic curve, from the fact that a 

 vibrating elastic string or cord, as for instance, a violin 

 string, swinging back and forth, in some cases takes the 

 form of an almost perfect sine curve. Although the vibra- 

 tions in any particular phenomenon may not be truly sinu- 

 soidal, it has been found possible by assuming the superposi- 

 tion of a number of sine curves of varying amplitude and 

 period, to exactly represent the resulting motion. This has 

 given rise to a branch of mathematics known as harmonic 

 analysis. This combination of a number of sine curves is 

 shown very nicely in the case of the violin. In this case, for 

 a given note, the string vibrates powerfulh' back and forth at 

 a rate corresponding to its pitch. This is the fundamental 

 vibration. At the same time the string is vibrating weakly 

 back and forth in 2, 3, 4, 5, etc., segments. These faint 

 vibrations are called harmonics, and their effect added to the 

 fundamental note is to produce the peculiar timbre of the 

 violin tone. Each vibration in itself is a perfect sine curve, 

 while the actual resulting motion of the string is more or less 

 "writhing" in character. 



In the field of electricity the sine curve is likewise of 

 great application in analysing and examining the phenomena 

 of alternating electric currents. 



The vibration of the perfect (cycloidal arc) pendulum, 

 is often termed harmonic, as a pen or marker fastened to the 

 bob would describe the sine curve on a piece of paper moving 

 uniformly under it at right angles to the plane oi vil)ration. 



