hertz's experlments. 209 



roHected motions rciiitbrcc, wliilr the lattc'i" are where tlu^sc iiiotioiis 

 arc o]>i)()S('(l. if we iiioasure the distaiicc between two nodes, we know 

 tliat it is hair the distance a wave tra\-els durini;- a single ^•il)ration of 

 the string, and so can calcnlate the velocity of the wave if we know 

 the rate of vibration of the string. This is the se(;ond method men- 

 tioned above for finding the ^■elocity of sound. There are so many 

 things illustrat<'d by this \ibrating chain that it may be well to dwell 

 on it for a few moments. We can make a wave travel up it, either 

 rapidly or slowly, by stressing it much or little. If a wa\e travels 

 rapidly, we must gi\'e it a \eiy rajtid vibration if we Avish to have 

 many loo[)s and nodes between our source and the reflector; for the 

 distaiu'c fronrnode to node is half the distancje a wave travels during 

 a vibration, and if the wave goes fast the vibration must be rapid, or 

 the distance from node to node will be too great for there to be many 

 of them within the length of the chain. 



Another i>oint to be observed is the way in which the chain moves 

 when transmitting a single wave and wlien in this condition of loops 

 and no<les, /. c\, transmitting two sets (»f waves in opposite directions. 

 There are two ditterent motions of the parts of the chain it is worth 

 considering separately. There is in the f.rst place the displacement 

 of any ]\\\k up or down, and in tlie second i)lace there is the rotation 

 of a link on an axis which is at right angles to this up and down 

 nn)tion. Xo\a , when waves are going nj) the cliain those links are 

 rotating most rapidly which are at any tinn^ most dis])laced; it is the 

 links on the tops and bottoms of waves that are rotating most rapidly. 

 On the other hand, in the case of looi)s and nodes the links in the 

 mi(hlh» of hjops never rotate at all; they are much displaced uj) and 

 down, but they kec)) ])aralh'l to their original direction all the time, 

 while it is the links at the nodes where there is no displacement up 

 and down that rotate first in one direction and tlien l)ack again; 

 there is. in tiie loops and nodes c(»ndition, a separation of the most 

 rotating and the most dis])laced links which does not occur in the 

 simi)le wa\c. 'iliere is a corres])onding relation between the most 

 rotat<Ml and tiie most rapidly moving links. Tiiese are tlie same 

 links haltway up tlie simple waves, but in the loo])s and nodes the 

 most rai»idly moving links never rotati^ at all, while those at the 

 nodes that get most lotated are not displaced at all. These remarks 

 will be seen hereaft<'r to throw light on some of the phenomena ob- 

 served in connection with Hertz's experiments; hence their importance. 



It Mill be observed that the method of measuring the velocity at 

 which a disturbance is ])i()pagated along a string, and which depends 

 on measni'ing the distance between two nodes, is really only a moditica- 

 tion of tin- direct m<'thod of linding out how long a disti'.i'bance takes 

 to go from one )>lace to another: it is on<' in which we make the waves 

 register ujion Themselves how long they took, and so does not iciiuire 

 us to have at our dis|)osal any method of sending a message from one 

 II. Mi.s. 114 II 



