Resonance
§ 8 Experiments With Resonant Jars. Analysis and Explanation
The series of tuning-forks now before you have had their rates of vibration determined by the siren. One, you will remember, vibrates 256 times in a second, the length of its sonorous wave being 4 feet 4 inches. It is detached from its case, so that when struck against a pad you hardly hear it. When held over this glass jar, A B, Fig. 90, 18 inches deep, you still fail to hear the sound of the fork. Preserving the fork in its position, I pour water with the least possible noise into the jar. The column of air underneath the fork shortens, the sound augments in intensity, and when the water has reached a certain level it bursts forth with extraordinary power. A greater quantity of water causes the sound to sink, and become finally inaudible, as at first. By pouring the water carefully out, a point is reached where the reinforcement of the sound again occurs. Experimenting thus, we learn that there is one particular length of the column of air which, when the fork is placed above it, produces a maximum augmentation of the sound. This reinforcement of the sound is named resonance.
Operating in the same way with all the forks in succession, a column of air is found for each, which yields a maximum resonance. These columns become shorter as the rapidity of vibration increases. In Fig. 91 the series Fig. 90. of jars is represented, the number of vibrations to which each resounds being placed above it.
What is the physical meaning of this very wonderful effect? To solve this question we must revive our knowledge of the relation of the motion of the fork itself to the motion of the sonorous wave produced by the fork. Supposing a prong of this fork, which executes 256 vibrations in a second, to vibrate between the points a and b, Fig. 92, in its motion from a to b the fork generates half a sonorous wave, and Fig. 91. as the length of the whole wave emitted by this fork is 4 feet 4 inches, at the moment the prong reaches b the foremost point of the sonorous wave will be at C, 2 feet 2 inches distant from the fork. The motion of the wave, then, is vastly greater than that of the fork. In fact, the distance a b is, in this case, not more than one-twentieth of an inch, while the wave has passed over a distance of 26 inches. With forks of lower pitch the difference would be still greater.
Our next question is, what is the length of the column of air which resounds to this fork? By measurement with a two-foot rule it is found to be 13 inches. But the length of the wave emitted by the fork is 52 inches; hence the length of the column of air which resounds to the fork is equal to one-fourth of the length of the sound-wave produced by the fork. This rule is general, and might be illustrated by any other of the forks instead of this one.
Let the prong, vibrating between the limits a and b, be placed over its resonant jar, A B, Fig. 93. In the time required by the prong to move from a to b, the condensation it produces runs down to the bottom of the jar, is there reflected, and, as the distance to the bottom and back is 26 inches, the reflected wave will reach the fork at the moment when it is on the point of returning from b to a. The rarefaction of the wave is produced by the retreat of the prong from b to a. This rarefaction will also run to the bottom of the jar and back, overtaking the prong just as it reaches the limit, a, of its excursion. It is plain from this analysis that the vibrations of the fork are perfectly synchronous with the vibrations of the aërial column A B; and in virtue of this synchronism the motion accumulates in the jar, spreads abroad in the room, and produces this vast augmentation of the sound.
When we substitute for the air in one of these jars a gas of different elasticity, we find the length of the resounding column to be different. The velocity of sound through coal-gas is to its velocity in air about as 8:5. Hence, to synchronize with our fork, a jar filled with coal-gas must be deeper than one filled with air. I turn this jar, 18 inches long, upside down, and hold close to its open mouth our agitated tuning-fork. It is scarcely audible. The jar, with air in it, is 5 inches too deep for this fork. Let coal-gas now enter the jar. As it ascends the note at a certain point swells out, proving that for the more elastic gas a depth of 18 inches is not too great. In fact, it is not great enough; for if too much gas be allowed to enter the jar the resonance is weakened. By suddenly turning the jar upright, still holding the fork close to its mouth, the gas escapes, and at the point of proper admixture of gas and air the note swells out again.45