The base of the inner tube of the whistle is the foremost end of a plug, that admits of being advanced or withdrawn by screwing it out or in; thus the depth of the inner tube of the whistle can be varied at pleasure. The more nearly the plug is screwed home, the less is the depth of the whistle and the more shrill does its note become, until a point is reached at which, although the air that proceeds from it vibrates as violently as before, as shown by its effect on a sensitive flame, the note ceases to be audible.
The number of vibrations per second in the note of a whistle or other "closed pipe" depends on its depth. The theory of acoustics shows that the length of each complete vibration is four times that of the depth of the closed pipe, and since experience proves that all sound, whatever may be its pitch, is propagated at the same rate, which under ordinary conditions of temperature and barometric pressure may be taken at 1120 feet, or 13,440 inches per second,--it follows that the number of vibrations in the note of a whistle may be found by dividing 13,440 by four times the depth, measured in inches, of the inner tube of the whistle. This rule, however, supposes the vibrations of the air in the tube to be strictly longitudinal, and ceases to apply when the depth of the tube is less than about one and a half times its diameter. When the tube is reduced to a shallow pan, a note may still be produced by it, but that note has reference rather to the diameter of the whistle than to its depth, being sometimes apparently unaltered by a further decrease of depth. The necessity of preserving a fair proportion between the diameter and the depth of a whistle is the reason why these instruments, having necessarily little depth, require to be made with very small bores.
The depth of the inner tube of the whistle at any moment is shown by the graduations on the outside of the instrument. The lower portion of the instrument as formerly made for me by the late Mr. Tisley, optician, Brompton Road,[28] is a cap that surrounds the body of the whistle, and is itself fixed to the screw that forms the plug. One complete turn of the cap increases or diminishes the depth of the whistle, by an amount equal to the interval between two adjacent threads of the screw. For mechanical convenience, a screw is used whose pitch is 25 to the inch; therefore one turn of the cap moves the plug one twenty-fifth of an inch, or ten two-hundred-and-fiftieths. The edge of the cap is divided into ten parts, each of which corresponds to the tenth of a complete turn; and, therefore, to one two-hundred-and-fiftieth of an inch. Hence in reading off the graduations the tens are shown on the body of the whistle, and the units are shown on the edge of the cap.
The scale of the instrument having for its unit the two-hundred-and- fiftieth part of an inch, it follows that the number of vibrations in the note of the whistle is to be found by dividing (13440 x 250)/4 or 84,000, by the graduations read off on its scale.
A short table is annexed, giving the number of vibrations calculated by this formula, for different depths, bearing in mind that the earlier entries cannot be relied upon unless the whistle has a very minute bore, and consequently a very feeble note.
The largest whistles suitable for experiments on the human ear, have an inner tube of about 0.16 inches in diameter, which is equal to 40 units of the scale. Consequently in these instruments the theory of closed pipes ceases to be trustworthy when the depth of the whistle is less than about 60 units. In short, we cannot be sure of sounding with them a higher note than one of 14,000 vibrations to the second, unless we use tubes of still smaller bore. In some of my experiments I was driven to use very fine tubes indeed, not wider than those little glass tubes that hold the smallest leads for Mordan's pencils. I have tried without much success to produce a note that should be both shrill and powerful, and correspond to a battery of small whistles, by flattening a piece of brass tube, and passing another sheet of brass up it, and thus forming a whistle the whole width of the sheet, but of very small diameter from front to back. It made a powerful note, but not a very pure one. I also constructed an annular whistle by means of three cylinders, one sliding within the other two, and graduated as before.
When the limits of audibility are approached, the sound becomes much fainter, and when that limit is reached, the sound usually gives place to a peculiar sensation, which is not sound but more like dizziness, and which some persons experience to a high degree. Young people hear shriller sounds than older people, and I am told there is a proverb in Dorsetshire, that no agricultural labourer who is more than forty years old, can hear a bat squeak. The power of hearing shrill notes has nothing to do with sharpness of hearing, any more than a wide range of the key-board of a piano has to do with the sound of the individual strings. We all have our limits, and that limit may be quickly found by these whistles in every case. The facility of hearing shrill sounds depends in some degree on the position of the whistle, for it is highest when it is held exactly opposite the opening of the ear. Any roughness of the lining of the auditory canal appears to have a marked effect in checking the transmission of rapid vibrations when they strike the ear obliquely. I myself feel this in a marked degree, and I have long noted the fact in respect to the buzz of a mosquito. I do not hear the mosquito much as it flies about, but when it passes close by my ear I hear a "ping," the suddenness of which is very striking. Mr. Dalby, the aurist, to whom I gave one of these instruments, tells me he uses it for diagnoses. When the power of hearing high notes is wholly lost, the loss is commonly owing to failure in the nerves, but when very deaf people are still able to hear high notes if they are sounded with force, the nerves are usually all right, and the fault lies in the lining of the auditory canal.
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Notes:
[Footnote 28: Mr. Hawksley, surgical instrument maker, 307 Oxford Street also makes these.]