acoustic pulse into the liquid. After travers- 
ing the distance L at the speed of sound C, the 
pulse is received at the piezoelectric receiver 
and converted into an electrical pulse. This 
pulse is then amplified and used to trigger the 
pulse generator, causing the pulses to sing 
around with a pulse repetition frequency being 
a function of the speed of sound. 
The relation between speed of sound in the 
liquid and output frequency of the instrument 
is not quite linear because of the finite time 
delay introduced by the electronic circuitry 
and piezoelectric transducers. Referring to 
Fige 1, we have -- 
Period of pulses = T +t 
where T is the transit time in the liquid and 
t is the delay time in the electronics. The 
expression for the pulse repetition frequency 
is then -- 
fe 1 
T+ 
L 
Since T = ¢, where L is the path length and 
C is the speed of sound, we have -- 
al 
f= L or 
ay 
Cc 
f- \—z (2) 
ae 
tC 
The term L in equation (1) leads to nonlinear- 
ity in the relation between f and C and becomes 
less important as t becomes smaller with res- 
pect to T. Typical values for velocimeters 
constructed so far are C = 1500 m/sec, L = 0.1 
meters, and t = 0.6 microseconds so that the 
nonlinearity over small ranges in the speed of 
sound is small enough that the errors intro- 
duced by assuming a linear relation are within 
allowable limits. For example, if the speed 
of sound were to be measured over a range of 
190 to 1550 m/sec, the error introduced by 
assuming the linear relation is only +0.5 
meters per second. If, however, a larger range 
in the speed of sound is to be measured or the 
accuracy is to be improved, there are at least 
two methods of reducing the data. 
The first method is to construct a calibra- 
tion curve giving the relation between f and C, 
which is derived by measuring the output fre- 
187 
quency of the instrument when immersed in dis- 
tilled water at different wee ratares in which 
the speed of sound is known.’ Such a calibra- 
tion curve is shown in Fig. 2. 
The second method is to determine the values 
of L and t for each instrument such that the 
data can be reduced using the relation -- 
C= Lf 
1-tf 
For either of these methods to be valid un- 
der all oceanographic conditions it is necessary 
that the quantity t should not vary over the com- 
plete range of temperature and pressure encount- 
ered in the ocean, and quite elaborate test 
procedures are necessary to determine that this 
condition is fulfilled. The tests involve main- 
taining the transducers in a water bath in which 
temperature and pressure are constant while the 
electronic circuitry is subject to temperature 
and pressure changes over the range -5°C to 0°C 
and 0 = 20,000 psi, respectively. Any change in 
output frequency is then undesirable and must be 
attributed to changes in the electronic circuit- 
rye 
These tests have been carried out on the 
Lockheed velocimeter. It was found that the 
change in time delay in the electronic circuitry 
over the temperature range of -5°C to h0°C af- 
fected the speed-of-sound readings by less than 
+0.2 m/sec. The change in time delay in the 
circuitry over the pressure range O to 20,000 
psi affected the speed-of=-sound readings by less 
than +0.1 m/sec. 
Another factor which may cause the time de- 
lay in the electronics to vary is variations in 
the voltage from the power supply. Tests on 
several of these instruments have shown that a 
change in voltage of +0.1 volt causes the speed- 
of-sound reading to chanse by less than +0.2 
m/sec e 
INSTRUMENT DESIGN 
The general form of the instrument is shown 
in Fig. 3. The transducers are located in the 
square end plates, which are made of Invar, 
as are the three rods which establish the trans- 
ducer separation and which serve to protect 
the transducers from accidental damage. Use 
of Invar ensures that changes in path length 
due to temperature differences in the ocean 
are negligible (less than one part in 25,000). 
The transmit-and-receive trmsducers are 
