LESSONS IN PHYSICS. 53 



weight; strike the cord near the center and notice the vibra- 

 tions. Add another brick as a weight and strike it again, and 

 compare the vibrations in the two cases. Stretch a heavier cord 

 and compare the vibrations of the two cords when stretched 

 with the same weight. Stretch a light wire and experiment with 

 it, and compare the vibrations of the wire with vibrations of 

 the cords. Shorten the strings, by putting a brick in the middle, 

 and then test the vibrations again; then shift the brick either 

 way, so that one end of the cord is longer than the other, and 

 again test the vibrations. Vary the weights, causing tension in 

 different ways, and notice and compare the vibrations in each 

 case. The result of these experiments will convince one that the 

 shorter the string, the cord or wire, the more rapid the vibra- 

 tions; and second, that the greater the weight or tension the 

 more rapid the vibrations; and that the heavier the cord or wire 

 the slower the vibrations. Experiments with more delicate appa- 

 ratus show that in the second case the vibrations vary as the 

 square root of the weight producing tension ; and in the third 

 case that they vary inversely as the square root of the weight of 

 the cord. 



Musical sounds differ in pitch; the pitch of sounds is that 

 which distinguishes them as being high or low. It depends en- 

 tirely upon the rapidity of vibrations; the more rapid the vibra- 

 tions the higher the sound produced. Two sounds made by the 

 same number of vibrations per second, however they may differ 

 in other respects, will have the same pitch. With pitch as a guide, 

 test the laws of vibrating cords just given. When the num- 

 ber of vibrations which produce one sound is twice as great 

 as that which produces another, we do not say that the sound is 

 twice as high, but rather that it is an octave higher. The term 

 octave is used to designate the tone which is made by twice the 

 number of vibrations needed to produce the lower tone, called the 

 fundamental. The difference in pitch between a fundamental note 

 and its octave is very great. To fill up this interval sounds have 

 been chosen which blend and harmonize most perfectly with the 

 fundamental or with each other. These placed between the fun- 



