[Illustration: FIG. 327.--An air column of the proper length reinforces the sound of the tuning fork.] =339. Sympathetic vibration= is explained as follows: Sound waves produce very slight motions in objects affected by them; if the vibration of a given body is exactly in time with the vibrations of a given sound each impulse of the sound wave will strike the body so as to increase the vibratory motion of the latter. This action continuing, the body soon acquires a motion sufficient to produce audible waves. A good illustration of sympathetic vibration is furnished by the bell ringer, who times his pulls upon the bell rope with the vibration rate of the swing of the bell. In the case of the resonant air column over which is held a vibrating tuning fork (see Fig. 328), when the prong of the fork starts downward from 1 to 2, a condensation wave moves down to the water surface and back just in time to join the condensation wave _above_ the fork as the prong begins to move from 2 to 1; also when the prong starts upward from 2 to 1, the rarefaction produced under it moves to the bottom of the air column and back so as to join the rarefaction _above_ the fork as the prong returns. While the prong is making a _single_ movement, up or down, it is plain that the air wave moves twice the length of the open tube. During a _complete_ vibration of the fork, therefore, the sound wave moves four times the length of the air column. In free air, the sound progresses a wave length during a complete vibration, hence the resonant air column is one-fourth the length of the sound wave to which it responds. Experiments with tubes cf different lengths show that the diameter of the air column has some effect upon the length giving best resonance. About 25 per cent. of the diameter of the tube must be added to the length of the air column to make it just one-fourth the wave length. The sound heard in seashells and in other hollow bodies is due to resonance. Vibrations in the air too feeble to affect the ear are intensified by sympathetic vibration until they can be heard. A tuning fork is often mounted upon a box called a _resonator_, which contains an air column of such dimensions that it reinforces the sound of the fork's sympathetic vibration. [Illustration: FIG. 328.--Explanation of resonance.] Important Topics 1. Musical intervals: octave, sixth, fifth, fourth, third. 2. Major chord, 4:5:6. 3. Use of sharps and flats. Tempered scale. 4. Resonance, sympathetic vibration, explanation, examples. Exercises 1. What is a major scale? Why is a major scale said to be built upon three triads? 2. Why are sharps and flats necessary in music? 3. What is the tempered scale and why is it used? What instruments need not use it? Why? 4. Mention two examples of resonance or sympathetic vibration from your own experience out of school.