All these cases, in which one set of small impulses at proper intervals of time create a large vibration in the body on which they act, are said to be instances of _resonance_. A more perfect illustration of acoustic resonance may be brought before you now. Before me, on the table, is a tall glass cylindrical jar, and I have in my hand a tuning-fork, the prongs of which make 256 vibrations per second when struck (see Fig. 55). If the fork is started in action, you at a distance will hear but little sound. The prongs of the fork move through the air, but they do not set it in very great oscillatory movement. Let us calculate, however, the wave-length of the waves given out by the fork. From the fundamental formula, _wave-velocity_ = _wave-length_ × _frequency_; and knowing that the velocity of sound at the present temperature of the air is about 1126 feet per second, we see at once that the length of the air wave produced by this fork must be nearly 4·4 feet, because 4·4 × 256 = 1126·4. Hence the quarter wave-length is nearly 1·1 foot, or, say, 1 foot 1 inch. I hold the fork over this tall jar, and pour water into the jar until the space between the water-surface and the top of the jar is a little over 1 foot, and at that moment the sound of the fork becomes much louder. The column of air in the jar is 1·1 foot in length and this resounds to the fork. You will have no difficulty in seeing the reason for this in the light of previous explanations. The air column has a certain natural rate of vibration, which is such that its fundamental note has a wave-length four times the length of the column of air. In the case of the rope fixed at one end and jerked up and down at the other so as to make stationary vibrations, the length of the rope is one quarter of the wave-length of its stationary wave. This is easily seen if we remember that the fixed end must be a _node_, and the end moved up and down must be an _anti-node_, or ventral segment, and the distance between a node and an anti-node is one quarter of a wave-length. Accordingly the vibrating column of air in the jar also has a fundamental mode of vibration, such that the length of the column is one quarter of a wave-length. Hence the vibrating prongs of the 256-period tuning-fork, when held over the 1·1 foot long column of air, are able to set the air in great vibratory movement, for the impulses from the prongs come at exactly the right time. Accordingly, the loud sound you hear when the fork is held over the jar proceeds, not so much from the fork as from the column of air in the jar. The prongs of the fork give little blows to the column of air, and these being at intervals equal to the natural time-period of vibration of the air in the jar, the latter is soon set in violent vibration.