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tuning fork over the upper end of the tube, and push the lower end into the water, as shown in Fig. 189, until the air in the tube responds to the tone of the fork and strengthens it.

207. Principle of the Resonator. The tube in the above demonstration is called a resonator. While the prong A is producing a condensation on one side, it is producing a rarefaction on the other. In order that the sound of the fork may be strengthened by the resonator, it is necessary that the condensation started by the prong A in its downward vibration (Fig. 183) shall go to the bottom of the tube, which is the surface of the water at B, and be reflected to A in time to join the condensation produced by A in its upward vibration. If, instead, the distance AB is such that the reflected condensation meets a rarefaction, the result will be interference instead of resonance, and the sound of the fork will be weakened.

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208. Relation of Velocity, Number of Vibrations, and Wave Length. - When a body is sounding continuously, the air be


FIG. 190

tween it and a person who hears it is filled with a continuous series of waves.

The condensations are a wave length apart, consequently the wave length may be defined as the distance the sound travels while the vibrating body is making one complete vibration. The number of these waves that strike the ear each second will depend upon the rate of vibration of the sounding body, and the velocity of sound in the air

will be the product of the wave length by the number of vibrations per second. That is,

v = NL.


For example, if the wave length is 4 ft. and the vibrating body sends out 280 waves per second, then the front of the first wave will be 1120 ft. away from the sounding body when the 280th vibration is finished.


209. Measurement of the Velocity of Sound by a Resonance Tube. It is possible to compute the velocity of sound in air by measuring the length of the air column in the resonance tube, and combining this properly with the number of vibrations per second. A convenient form of tube and support for this measurement is shown in Fig. 191. The glass tube A is connected by a flexible rubber tube to a similar glass tube fastened to the movable wooden arm B. This arm moves with so much friction that it will stay in any position. The support for the tuning fork is so arranged that forks of various lengths may be held in position. By pouring water into the tube and moving B toward or from the vertical position, the length of the air column in A can be so fixed that it will give a maximum reënforcement to the sound of the fork. When this is carefully determined, the length of the air column can be read on the millimeter scale


FIG. 191


back of A, which is graduated from the position of the fork as zero. To find the velocity of sound from this measurement it must be remembered that since the pulse of air first given out by the fork must go to the bottom of the tube and back, that is, twice the length of the tube, while the fork is making half of a complete vibration, it will go four times that length while the fork is making a complete vibration. This means that the wave length of the fork is 4 times the length of the air column. Calling the length of the air column l and substituting the value 4 l in Formula 43, we have v = 4 IN. Experiments with tubes of different diameters, however, show that a correction must be made for the diameter; that is, in order to get correct results a certain fraction of the diameter must be added to the length of the air column to give one fourth of the actual wave length. Lord Rayleigh finds this fraction to be nearly four tenths the diameter. Including this correction in the formula, we have

v = 4N(+0.4 d).

(44) 210. Sympathetic Vibrations. Whenever a sounding body is near another that has the same time of vibration, it is found that the pulses of air sent out by the first will put the second in motion.

FIG. 192

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lect two tuning forks that are mounted upon reso

nance boxes, and that give the same number of vibrations per second. Place them parallel to each other at opposite ends of a table, and put one of them in vibration with a heavy bow. Stop its vibrations with the fingers, after a few seconds, and the second fork will be heard. Its vibration may also be shown by sus

pending a light ball by a thread so that it will just touch one Iside of the fork.

The minute and rapid blows of the condensed waves of air striking upon the fork have enough energy to set it in motion, provided that the rate of the blows is the same as that of the vibrations. That this is also the case with a heavy swinging body may be shown as follows:

Demonstration.-Suspend from a hook in the ceiling a 20-pound weight, and find the time in which it will vibrate as a pendulum. Strike the weight light blows with a cork hammer, when it is at rest, timing the blows to the same rate as that in which it vibrated. If the blows are given at the right times, the result will be to set the pendulum swinging.


211. Forced Vibrations. Demonstrations. - Hold a toy music box in the hand and play it. Place it upon a table and play it. Hold it against the glass door of a bookcase and play it. Describe the differences in the effects.

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When the music box is played upon the table, there is a greater volume of sound because the vibrations of the box are communicated to the table top and put it in motion. although their rates of vibration are different.

Since all the tones played are increased in volume, it is evident that certain parts of the table were forced to vibrate in time with the tones given by the box. If the end of a vibrating tuning fork is pressed upon a table, the sound will increase in volume but will soon die out, showing that the energy of the fork is rapidly used up in making the table vibrate.

A thin tone is produced by any vibrating body that puts only a small quantity of air in motion. Fullness of tone can be secured only by putting a large mass of air in motion. For this reason, in all stringed instruments, as the violin,

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Sound wave reflected by an elliptical mirror, second position


Sound wave reflected by an elliptical mir- Sound wave reflected by an elliptical mirror, third position

ror, fourth position

FIG. 193. Photographs of cylindrical sound waves made by Professor Arthur L. Foley and Mr. W. H. Souder, Indiana University. The source of sound was an electric spark, directly behind the black center and perpendicular to the page. Used by permission.


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