ber of vibrations, for we cannot begin to count them? We will take a tuning-fork, D, 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
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 "middle C" below. In the same way each of the other tones doubles its vibrations 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 produced 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-