Applications and Methods of Excitation.—As in the case of strings the transverse vibrations of a bar may be excited by striking, plucking, bowing, or by electromagnetic means, the partials present, and consequently the quality of the note being dependent on the method of excitation. The only method of supporting a bar which yields "harmonic partials " is the free free method, which has application in a musical instrument known as the " harmonicon " or "dulcimer" in which freely sup ported bars of graded lengths are struck by a hammer, thus pro ducing an agreeable succession of musical tones. Thin rods or reeds, clamped at one end and excited by plucking, are used in the " musical box" so well known. Used in combination with suit able air cavity resonators, clamped free reeds are fitted in various musical instruments, notably the clarinet group. The combined action of an air blast and a vibrating reed is illustrated in the concertina and the harmonium, whilst in the reed pipes of an organ the reed is combined with a resonant air column. The reed of the telephone earpiece designed by S. G. Brown is operated electromagnetically. It is used in an almost unstable condition, the pull of a permanent magnet being nearly sufficient to over come the stiffness of the reed. This results in a large increase of sensitiveness to the superposed alternating magnetic field.
Frequency Meters form a good example of the electromagnetic or direct mechanical excitation of reeds. The frequency meter consists essentially of a graded series of clamped steel reeds actuated by a common electromagnet supplied with alternating current of which the frequency is required. Such instruments have been made covering various ranges from i or 2 to 1,5oo cycles per second. The frequency of a clamped-free bar may be lowered either by loading the free end or by reducing the cross section near the clamped end. The frequency may be raised either by shortening the bar or reducing the cross section near the free end.
Tuning Forks.—On account of its great purity of tone and constancy of frequency the tuning fork is generally regarded as a standard of frequency and pitch. During recent years it has increased enormously in importance as a frequency standard for controlling electrical circuits, in such a manner as to form an electrical standard of great accuracy and of extensive range.
The tuning fork may be regarded either as a development from a free-free bar bent into the form of a U, or as consisting of a pair of symmetrical clamped-free bars attached to a common block of metal. Numerous patterns are in existence approximat ing to one or other of these two forms. It will be sufficient here to regard each prong as a clamped-free bar. In consequence of the oscillation of the centre of gravity of the two bars as they vibrate there will be communication of vibration to the block to which they are clamped. To reduce the amplitude of this vibration, which is in the direction of the prongs, the block must be firm and massive. The frequency of a fork of this construction with
prongs of rectangular section of thickness t will therefore be that is, N= 8.24 X if the prongs are of steel in which (E/p) = 5I X cms./sec. The frequency of a fork will therefore vary directly as the thickness of the prongs and as the velocity of sound in the material, and inversely as the square of the length of the prongs. The first and second overtones of a fork will have frequencies 6.25N and 17.6N respectively. These overtones may easily be excited in a large fork by bowing at suitable points.
The fundamental tone of a tuning fork may be selectively rein forced by attaching the stem to a resonance box of the same fre quency—the overtones of the fork and the air cavity are widely different and do not reinforce each other. Two forks of nearly the same pitch may be compared by the method of beats, which gives in a very simple and direct manner the difference in fre quencies. This method is also useful in studying the effect of temperature on the frequency of a fork—the one fork is kept under standard conditions whilst the temperature of another is varied. The temperature coefficient of frequency for a steel fork determined in this way is approximately — per degree C rise of temperature. The temperature coefficient of a fork made of elinvar steel is about one tenth of this.
Electrically Maintained Forks.—The vibrations of a low frequency fork may readily be maintained by means of electrical contacts controlled by the prongs and an electro-magnet situated between them. The mode of operation is similar to that of an electric bell. Forks of higher frequency (of the order of a ,000 p.p.s.) are maintained by means of electromagnets arranged in a special form of 3-electrode valve circuit devised by Eccles. Electrically maintained forks may be used to drive what are known as phonic motors (see Figures 7 and 8 on Plate), the vibratory motion of the fork being thereby converted into a rotary motion of combined accuracy and constant speed. Elec trically maintained forks and phonic motors, with their applica tions in standard frequency determinations, are described in A. B. Wood's Textbook of Sound. Forks are now in common use as sub-standards of time. The period of a fork is a very constant quantity and serves as a convenient sub-division of a second when time intervals have to be measured with accuracy. As a con sequence of the increased application of the tuning fork for this purpose, methods have been devised for increasing the accuracy and perfection of electrically maintained forks. Low-frequency forks of this character giving an accuracy greater than I in io,000 are in common use. If particular care is taken with the choice of material, design, and control of the fork, an accuracy of I in Iob or even I in a million is possible.