Diaphragms form one of the most convenient means of pro ducing and receiving sounds in air or in water. Numerous forms of diaphragm telephone receivers and microphone transmitters are in daily use. Large diaphragms are used as sources of sound power for signalling over large distances in air or under water. A diaphragm operated at resonance by electro-magnetic methods may become an efficient generator of sound. By suitably choos ing its dimensions the frequency of the sound may have any value up to the limits of audibility. A thick diaphragm of small diameter excited by an electro-magnet provides a very con venient source of high frequency sound as an alternative to a bird call, etc., in experimental work.
Directional property of Membranes and Diaphragms.—If a mem brane or a diaphragm be mounted on an annular ring it will possess definite directional properties used either as a transmitter or receiver of sound. Regarding it as a transmitter, the sound emitted from opposite sides will be of the same intensity but in exactly opposite phase. Consequently an observer "edge-on" to the diaphragm will hear nothing at all, for the sounds proceeding from opposite sides of the disc will exactly neutralize each other. In the " broadside-on" position, however, the sound from the back of the diaphragm will be partially screened by the annular ring and by the diaphragm itself, whereas the sound from the front will reach the observer unobstructed. As the transmitter is rotated through 360° therefore, the observer will hear two dis tinct maxima, 180° apart, separated by two corresponding minima, or zero positions. The maxima will, of course, be of smaller intensity than that observed with one side of the dia phragm completely screened (in which case it is non-directional). The directional properties of an unscreened diaphragm may be simply demonstrated as a receiver of sound by means of a "but ton " granular microphone attached at the centre. The micro phone gives maximum and zero response in the "broadside-on and "edge-on " positions respectively, relative to a fixed source of sound.
bowing and touching certain points on the edge of the plate covered with fine sand, is well known. The nodal figures are very striking in their appearance and wonderful variety—nothing further is needed to testify to the complexity of the problem. Chladni preferred to use glass plates, as their transparency per mits of the fingers being used to damp points underneath which are shown to be nodal by the sand above. Simple figures cor respond to low frequency tones, and the more complicated figures to the higher tones. Chladni obtained 52 different figures with a square plate and 43 with a circular plate. Metal plates of moderate thickness when struck with a hammer are sometimes used as gongs. The Submarine Signalling Company have used such a gong under the sea, describing it as a "disc-bell " for life boats.
Curved Plates, Cylinders and Bells.—The complex problem of the flat plate is still further complicated when the plate is curved—for it becomes increasingly difficult to separate the various possible modes of vibration. Rayleigh has calculated the fundamental frequency N of vibration of a thin cylindrical shell, obtaining Noc where e is an elastic modulus in p volving bulk modulus and rigidity, h the thickness, a the radius, and p the density of the cylinder.
A bell may be regarded as a progressive development of a curved plate or, in certain forms, it may be treated as a cylindrical shell with one end closed. The possible variety of forms is far too numerous even to mention here. In practically all cases the bell is supported at the centre of symmetry and is excited by striking near the free edge. Rayleigh made a particular study of the vibrations of church bells, and distinguished five characteristic tones: Lowest tone (4 nodal meridians, no nodal circle), second tone (4 nodal meridians, one nodal circle), third tone (6 nodal meridians, sound best produced when the clapper strikes the bell on the lower thick part termed the "sound bow "), fourth tone (6 nodal meridians, best elicited by striking half way up), fifth and highest tone (8 nodal meridians). Bell founders in England recognise five chief tones in a church bell, reckoning from the highest they are termed the "nominal," "fifth," "tierce," " fundamental," and " hum-note." By suitable distribution of metal in the bell the founder aims at making the hum-note, fundamental and nominal successive octaves—but seldom suc ceeds. Massive bronze bells are used in charted positions, e.g., lightships and buoys, under the sea as a means of signalling to ships suitably fitted with hydrophones (underwater microphones) to receive the sound. Sound travels for long distances under water and these bells can be heard many miles away, if the conditions are favourable.