either microphone or magnetophone (electro-magnetic) attach ments have been used extensively in under-water signalling. Lamb has shown theoretically that for diaphragms having the same frequency in water the amplitude at resonance is inversely proportional to the area of the diaphragm. When an additional damping factor, such as a granular microphone, is introduced there is a "best size of diaphragm, increasing with increase of the added damping. (See Powell, Phys. Soc. Proc., Feb. 1925.) Electromagnetic Receivers.—The vibrations of a diaphragm may be employed to excite currents in an electrical circuit em bracing or lying in a magnetic field. The iron diaphragm of a telephone earpiece by its vibrations varies the magnetic flux passing through a coil and consequently induces alternating cur rents of the same frequency as the sound vibrations falling on the diaphragm. Similar results are obtained when an iron reed clamped at one end is set into vibration by sound-waves falling on a stiff cone attached to the free end of the reed. In an alter native form the diaphragm or reed, which now may be of non magnetic material, is attached rigidly to an annular coil of wire which lies in a strong magnetic field. Vibrations of the diaphragm and coil induce currents in the latter of the same frequency as the sound-waves. Telephone, microphone, and loud speaker movements are constructed on these principles. Such instru ments can also be used to generate sound-waves by supplying the coil with alternating current of the required frequency. Diaphragm and reed receivers have usually marked resonant frequencies, the sharpness of resonance increasing with the load attached to the diaphragm (see p. 8). They may if required be used as "non-resonant" receivers, provided their natural resonances are reduced by damping or are far removed in frequency from that of the sound it is desired to receive. The
efficiency of electro-magnetic receivers is determined from ob servations of damping and motional impedance (see p. 9).
Resonant Air Cavity. Hot-Wire Microphone.—One of the most sensitive and metrical forms of resonant receiver for sounds in air, is a Helmholtz resonator fitted with a hot-wire microphone. In the hands of Tucker and Paris (P1.1!. Trans., 221. 1921) this combination has proved of great value in its technical applica tions and as a laboratory instrument for sound-measurement. It consists essentially of an electrically heated grid of fine platinum wire (o•0006 cm. diameter) placed in the neck of a Helmholtz resonator, or in the second neck of a "double-resonator" such as that shown in fig. 13. The oscillating air currents in the neck at resonance cool the hot grid, the extent of this cooling being measured (by a Wheatstone's bridge) as a change of electrical resistance. This resistance-change is a measure of the intensity of the sound. The instrument is calibrated by observing the cooling produced by steady air streams of known velocity. The sensitivity increases with increase of heating current. The tun ing of the microphone and resonator is fairly sharp; in a typical example the response fell to one tenth of its maximum by "detuning" 7%, i.e., nl p=1-± 0.07. In common with other forms of Helmholtz resonator receivers, therefore, a series of instru ments is required to cover a moderate range of frequency. The hot wire-microphone increases in sensitiveness towards the lower frequencies (say ioo per second) ; its upper limit being about Soo to i,000 cycles/sec. The device has proved extremely useful in measurements of intensity and distribution of sound, particularly for testing trumpets, lenses, mirrors and other sound-concen trating devices and also for investigating the reflection and dif fraction of sound-waves generally. Used in connection with resonators of very low frequency the hot-wire microphone proved of great value during the war in detecting and locating the posi tions of enemy guns. (See p. 22.) Non-Resonant Receivers.—The ideal non-resonant receiver, equally sensitive at all frequencies, is not known. The best approximations aim at uniform sensitivity over a limited range of frequency—the better the receiver the more extended the range. Non-resonant receivers are, as a general rule, consider ably less sensitive than the resonant type at a particular fre quency but have a good average sensitivity over a wide range.