HOW SOUND AND WORDS ARE PRODUCED. 45 



ber of vibrations, for we cannot begin to count them ? We will take a 

 tuning-fork, _Z>, Fig. 2, that gives the same tone as middle C, thus having 

 the same number of vibrations, and attach with a bristle fastened to one 

 prong by a little wax. This will trace the vibrations, P, on the smoked 

 paper L. The wave-forms of the marking, counted along either one side, 

 indicate the number of vibrations. We count these wave-forms, and 

 divide by the number of seconds the vibration lasted, and we have the 

 number of vibrations per second corresponding to the tone of the fork. 

 In this case we find " middle C " to vibrate 264 times in a second. In 



Fig. 2. 



the same way, we find D to vibrate 297 ; E, 330 ; F, 352 ; G, 396 ; A, 

 440 ; B, 495 ; and C, again, 528 times per second, just double of " mid- 

 dle C" below. In the same way each of the other tones doubles its vi- 

 brations going up, and halves them going down. Thus, from the first 

 A of the bass of a seven-octave piano, to the last A of the treble, we 

 have a range of from 27 vibrations, or pulses, per second to as many as 

 3,520. The number of vibrations is the same for the same note on any 

 instrument. 



We have thus proved, in a simple way, that a musical tone is pro- 

 duced by rapid, regular vibration, as shown by the marking the air- 

 waves, set up by the vibration, seeming to blend in the ear in a manner 

 similar to that in which the vibrations of the string blend to the eye, 

 which makes the tone seem continuous. In this experiment we notice 

 that tones are high or low, according to the number of their vibrations 

 the higher the tone the greater the number of its vibrations per second. 

 Again, we observe that we can make the same tone loud or soft, without 

 making it higher or lower. We notice that loudness is obtained by 

 striking with greater force, making the string or fork swing farther from 

 side to side, but still swing the same number of times in a second. This 

 force of the swing is given to the air, and carried to the ear, beating it 

 with greater violence than before, but still only the same number of 

 times a second. This width of swing, which makes the loudness of a 

 sound, by a greater compression in the air-wave, is called the amplitude 

 of vibration, and corresponds to the height of water-waves, where the 

 amplitude is up and down. In water, the greater the force the higher 

 are the waves. Now, let us turn to the sound-wave in the air, which we 

 will study by the aid of Fig. 3. Here we take an ordinary A tuning- 



