Page:
1 2 3
4 5 6 7 8 9 10
device which is often used in
tensity measurements is due to Rayleigh (Sound, Vol. II., p. 44). A delicately suspended disc (a small mirror about 1-in. diameter) will tend to face a stream of air (or other medium) flowing past it, whether the flow be direct or alternating. The torque M on the disc tending to diminish 0, the angle which the normal of the disc makes with the stream, is given by M = 4- •
sin 20, "a" being the radius of the disc, p the density of the medium and v the velocity of the stream. If the stream be alternating instead of steady, it is only necessary to employ the mean value of
The maximum torque is obtained when 0=
A light gal vanometer mirror suspended on a fine quartz fibre provides a very sensitive arrangement, particularly when used inside a double resonator (see fig. 13) tuned to the frequency of the sound it is desired to measure. When accurately tuned to the sound falling upon the open end of the resonator R, the instru ment can be used to compare the intensities of sounds of the same frequency. The sensitiveness is comparable with that of the ear. The deflections, if small, are proportional to the square of the particle velocity in the undisturbed field. It is important that the diameter of the disc should be small compared with the wave-length of the incident sound. As the double resonator and disc system is very sharply tuned, a large number of instruments would be requir _.d to cover a moderate range of frequency and intensity. A disc mounted in the mouth of a single resonator of continuously variable tuning is more generally useful, but is less sensitive.
When the incoming sound-waves have a predominant frequency it is clearly advantageous to "tune " the receiver to obtain maximum sensitivity. The tuning of a receiver, e.g., an air cavity or a diaphragm is similar to the tuning of a sound transmitter. In many electrical cases the same device may serve either as a transmitter or a receiver, e.g., a telephone ear piece (magnetophone), a Fessenden electro-magnetic oscillator or a piezo-electric oscillator. Under these circumstances it is possible for the tuning to be very exact. A resonant air cavity develops a relatively large amplitude of vibration at its mouth, this amplitude being considerably in excess of that in the sur rounding medium. The sound-field near such a resonator is affected by its behaviour as a secondary source, the energy which the resonator emits being drained from the other parts of the sound-field. It can be shown that the area of wave-front from which energy is extracted (and re-radiated) by a small resonator is
where X is the wave-length of the incident sound to which it is tuned. This area may be considerably greater than the area s of the resonator, the energy amplification being Mks. In actual resonators, however, only a part of this energy is re radiated, the remainder being absorbed. The latter portion is partly dissipated in viscous damping and partly converted into a useful form, i.e., is utilised in operating a detector, such as a microphone, or a magneto-phone, or in deflecting a mirror. The efficiency of the receiver is dependent on the proportion of the total energy which is usefully absorbed. Absorption of energy involves damping. The receiver is inefficient if it is underdamped, little or no energy being absorbed, or if it is over-damped, too much or all the energy being absorbed. If the receiver is under
damped it re-radiates too large a proportion of the received energy back into the medium. Overdamping reduces the sharp ness of resonance and consequently reduces the area from which energy is obtained, the main advantage of tuning being lost. The most efficient receiver lies between these extremes, i.e., the energy absorbed is equal to the energy re-radiated. In other words, in an efficient tuned receiver the damping due to the medium must be equal to the internal damping in the receiver. It is of course, equally important that the internal damping must be useful damping, i.e., the absorbed energy must be used efficiently. Thus if the receiver is electro-magnetic (a telephone receiver) it is important that the ratio of motional impedance (measured electrically) to total electrical impedance should be as great as possible. A solid resonator such as a tuned metal diaphragm in air is necessarily inefficient, for a large proportion of the incident energy is reflected or scattered from its surface as from a rigid obstacle. The energy re-radiated to the medium due to the vibration of the diaphragm is extremely small.
It is sometimes desirable to convert an oscillation of large displacement and low pressure to one of small displacement and high pressure; a mechanical process analogous to the electrical transformation of a large alternating current at low voltage to a small current at high voltage. Hahneman (Inst. Radio Eng. Proc., II., Feb. 1923) has employed this principle in the design of sound-transmitters and receivers for use under water. As a rule, in such apparatus, one part of a vibrating system is actuated in air whilst another, coupled to it, vibrates in contact with water. In transferring vibratory pressure from air to water a "step-up" pressure trans former is required, and conversely. For this purpose Hahneman employs a mechanical lever of a novel type, the ordinary pivoted lever and link system being useless at even moderate frequencies. He also considers it desirable, as far as possible, to separate the mass and spring factors of the vibrating system, like a weight on a spring, rather than .a combined mass and spring as in the prong of a tuning fork. The lever principle is as follows: Two masses m and M are connected as in fig. 14a by a spring of stiffness s. At resonance, neglecting energy radiated, the system will vibrate about its centre of gravity, the amplitudes a and A of m and M being inversely proportional to the masses, i.e., al A= M I m. The spring will be undisplaced at the centre of gravity of the system, i.e., at some point 0 such that
The natural frequency of the two parts on opposite sides of 0 is In applying this principle to under-water sound transmitters, Hahneman replaces the diagrammatic helical spring by an elastic rod or tube, as in fig. 14b, which combined with the loads m and M tunes to the required frequency. The masses may be pistons or diaphragms suitable for electro-magnetic excitation and for the transmission of vibrations to the water (see fig. 3, plate, and Technical Applications: Sound-Signalling). S. T. Williams (Journ. Franklin Inst., Oct. 1926) refers to the use of mechanical "transformers " in the design of a gramophone sound-box.