V. VIBRATIONS AND WAVES. 



123 



V. VIBRATIONS AND WAVES. 



54O, Apparatus for the Composition of two parallel 

 simple vibrations. Dr. F. G. Groneman, Groningcn. 



1. Principle. If the point C moves with constant velocity through the 

 circumference of the circle AC, it is known that its 



projection B upon the diameter GH performs a motion, 

 which is called a simple vibration. 



If in this variable point B a string is fixed, which 

 is put through the pulley D, and from this hangs 

 down to E, so that BD + DE is the constant length of 

 the string, it is easy to see that the point E will per- 

 form quite the same motion as B. 



If this string is not attached in B, but in the 

 moving point C itself, E will have a motion which is 

 not strictly, but nearly that of B, the difference re- 

 sulting from the difference of the .two variable lines 

 BD and CD. This difference can be diminished to 

 any degree, by increasing the distance between the 

 pulley and the centre A. 



2. Two discs of the same diameter are placed in the 

 same vertical plane, and can turn round the horizontal 

 axes, one of which has a handle.' The motion of the 

 first disc is communicated to the second by means 

 of crown wheels and cog wheels. One of the latter 

 can be fixed at any point of its axis, so that it may 

 correspond with each of the six crown wheels of the 

 second disc. By this arrangement the velocity of the 

 second disc can be made equal to that of the first, or 

 the i, f , f , f , or the f part of it. For changing this 

 velocity, or for changing the difference of the phases, 

 when the velocities of the discs are the same, the 

 washer at the end of the axis of the second disc must 

 be a little loosened, and this axis pushed forward. 



3. The discs have one knob each. If the distance of the knob of the first 

 disc to the centre of it is called 1, that of the knob of the second disc can 

 be made 1 , , or -^. From the knobs proceed two strings, which are put 

 through the pulleys on the top of the instrument, and bear the hooks 

 A and B (Fig. 2). 



It is easy to understand that these hooks, when 

 the handle is turned, perform two simple vibra- 

 tions, the one being invariable, the other variable, 

 in amplitude, phase, and velocity. 



4. From A and B proceed two strings, passing 

 through the pulleys C and E, and fixed in F and H. 

 These pulleys have strictly the same motions as 

 A and B, at a rate of one half. A third string 

 proceeds from A to B, passing through D. At 

 any moment the displacement of D will be the 

 sum of the displacements of A and B, at a rate 

 of one half. Its motion is therefore the resultant 

 of those of C and E. 



The motions of the three pulleys are shown 

 by the little white balls, placed on the front of 

 the instrument. 



