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(c) The attenuation at high frequencies of the sound wave in the liquid.
(d) The difficulty of setting the crystals up sufficiently nearly parallel if the wavelength is short.
(e) The difficulty of amplification at high frequencies.
Of these (a) and (c) are the most important. A reasonable arrangement seems to be to choose a frequency at which the attenuation in the medium is about 15 db.
With the comparatively low frequencies and with wide tanks the setting up difficulty will not be serious. With long lines we should probably not attempt to do temperature correction, but would rephase the output.
Considerations affecting the pulse frequency are:
(a) The limitation of the pulse frequency to a comparatively small fraction of the carrier frequency if water is the transmission medium, and the limitation of this carrier frequency.
(b) The finite reaction times of the valves.
(c) The greater capacity of a line if the frequency is high.
(d) Greater speed of operation of the whole machine if the pulse frequency is high.
(e) Cowardly and irrational doubts as to the feasibility of high frequency working.
If we can ignore (e) the other considerations appear to point to a pulse frequency of about 3 megacycles or even higher. We are however somewhat alarmed by the prospect of even working at 1 megacycle since the difficulty (b) might turn out to be more serious than anticipated.
Considerations affecting the diameter of the tank are:
(a) That the crystals are most conveniently adjusted to be parallel by bending the tanks and that the diameter should therefore not be too large.
(b) That the diameter should be at least large enough to accommodate the crystal.
(c) That small diameters give phase distortion (p. 40).
(d) That with mercury small diameters are economical. At a price of £1 sterling per 1 lb. avoirdupois of mercury a 1 ms. tank of diameter 1" would contain mercury to the value of about £2-2-6.
A diameter of 1" or rather less is usual in R.D.F. tanks and appears reasonable in view of these conditions.
(xi) Temperature control system.— The temperature coefficient of the velocity of propagation in mercury is quite small at 15 Mc/s, being only 0.0003/degree centigrade. This means that if the length of a 1 ms. line is to be correct to within 0.2 ms. then the temperature must be correct to within two-thirds of a degree centigrade.
