M. Greenspan and C. E. Tschiegg 89 
down the sample liquid in a time //c, where c is the speed of sound and / is the 
path length. The received pulses are amplified and shaped and are used to syn- 
chronize the original pulse-forming circuit. If t, is the sum of the electrical 
delays and the time lost in the noise, the total time delay is 
jo (1) 
The prf, f, is measured and perhaps recorded. Both t, and / are obtained 
by direct calibration with a liquid in which the speed of sound is known. If the 
velocimeter is to be used in the sea, for example, a suitable calibration liquid 
is distilled water. Readings of f with distilled water at various temperatures 
between 0 and 60°C cover the range which would be obtained in the sea where 
the extremes of temperature are 0 and 40°C and the salinity reaches perhaps 
4%. Corresponding to each temperature of the distilled water is a known speed c 
and an observed prf, f. These determine the unknowns ¢, and 7 in Eq. (1). It is 
also possible to determine t, by measuring f for two diffexent known values of 
1. This method is both more cumbersome and less accurate; the length / in Eq. 
(1) is only an effective length and is difficult to define in an absolute sense, 
especially in the case where the receiving transducer is not accurately parallel 
to a wavefront. 
5.3. APPARATUS 
5.3.1. The Transducers and the Path 
An external view of the velocimeter is presentedin Fig. 5.2. The structure on 
top is a protecting plate for the sound head; when it is removed, the essential 
parts are as shown in Fig. 5.3. The inner structures are the transducer mounts; 
on the left-hand mount the transducer is visible; the reflectors are on the peri- 
phery. The sound ray traverses a zigzag path about 20 cm long. The transducer 
mounts are fixed in their geometrically correct positions, but the reflectors are 
adjustable. The proper adjustment is made by trial while observing waveforms 
on an oscilloscope; once it is attained, the reflectors are locked in place with 
the cap screws shown. For some applications the reflectors should also be pinned. 
Good results have been obtained with both x-cut quartz and with ceramic 
transducers. The latter are now preferred because they operate in conjunction 
with simpler electronic circuits. The transducers are made as thin as is con- 
sistent with ease of handling; thicknesses from 0.2to 1 mm are satisfactory, the 
best value depending on the type of mount. 
Mounts of the type shown in Fig. 5.3 have become more or less standard. 
With these are used transducers of barium-calcium-lead titanate (Bag.g9 Cao.12 
Pbp,og TiO3), a material not overly sensitive to temperature, devised some years 
ago by W.P. Mason of the Bell Telephone Laboratories. The discs are 1.25 cm in 
diameter and 0.66 mm thick, corresponding to a fundamental thickness resonance 
of about 3.6 Mc, with surfaces flat and parallel to about 25 ». The electrodes 
are composed of fired-on silver-ceramic paste; the outer (ground) electrode 
covers the entire area and the inner (hot) electrode is about 6 mm in diameter 
and has two #30 silver-plated copper wires attached to it with 63-33-4 tin-lead- 
