HANDBOOK OF ACOUSTICS - online book

A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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62
HAND-BOOK OF ACOUSTICS.
consequently the air particles in the latter will crowd into the former, causing a rarefaction in 0 D. In this way the rarefaction is transmitted back to A 0. As the pressure of the external air will now be greater than that in A C, air particles from the former will crowd in, forming a condensation in A C. If at this moment, the prong is a second time beginning its descent, this condensation will be increased, and the same series of changes will take place as before. It is evident, therefore, that the sound wave must make two complete journeys up and down the tube, while the fork is executing one vibration; that is, in order that a stopped tube when excited by a fork, may give its maximum resonance, it must be £ as long as the sound wave originated by that fork.
"We have already seen, that the length of the sound wave pro­duced by a sounding body, may be ascertained by dividing the velocity of sound by the vibration number of that body; con­sequently it is easy to calculate the length of tube, either open or stopped, which will resound to a note of given pitch. The rule evidently is: divide the velocity of sound by the vibration number of the note; half this quotient will give the length of the open pipe, and one fourth will give the length of the stopped one. It is necessary that the tube should be of moderate diameter, or the rule will not hold good, even approximately.
The resonance of stopped tubes may easily be illustrated, by means of glass tubes, corked, or otherwise closed at one end. On holding a vibrating tuning-fork over the open end of a sufficiently long tube, held with its mouth upwards, and slowly pouring in water, the sound will swell out when the vibrating column of air is of the requisite length, the water serving the purpose of gradually shortening the column. For small forks, test tubes, such as are used in chemical work, are very convenient.
It is by no means necessary that the resounding masses of air should be in the form of a cylinder; this shape was selected for the sake of simplicity in explanation. Almost any shaped mass of enclosed air will resound to some particular note. Everyone must have noticed, that the air in a gas globe, vase, &c, resounds, when some particular sound is loudly sung near it. The following is an interesting method of optically illustrating this phenomenon. A, fig. 34, is a cylinder 3 or 4 inches in diameter, and 5 or 6 inches long, with an open mouth, B. The other end is covered with an elastic membrane, D, such as sheet india-rubber slightly stretched, thin paper, or membrane. At C is fastened a silk fibre, bearing a