ELASTIC WAVES IN AMHERST SANDSTONE 13 
coils of wire are attached rigidly at either end, these coils being placed 
in a radial magnetic field. The coil at one end of the rod is connected 
to a calibrated variable-frequency oscillator, while that at the other 
end is connected through an amplifier to a rectifier and galvanometer. 
Suitable means are provided to measure and to adjust the current 
supplied by the oscillator to any desired value. The bar may thus be 
driven at any desired frequency and the amplitude of the motion at 
the further end of the bar is indicated by the magnitude of the galvan- 
ometer deflection. By holding the driving current constant while 
varying the oscillator frequency, a resonance curve may be drawn 
by plotting galvanometer deflection against the frequency of the 
driving current. In this manner the frequency corresponding with 
the natural frequency of the bar may be easily and accurately ob- 
tained.* Although the bar is capable of a number of modes of vibration 
this arrangement of apparatus allows the desired mode, in this case, 
the fundamental longitudinal vibration, to be easily distinguished. 
_ Having obtained the natural frequency of the bar, the velocity 
of elastic waves through it may be calculated at once by means of 
the relationship® 
v= 2fl 
where v is the velocity 
f is the natural frequency 
and l is the length of the bar. 
The velocity thus calculated is the so-called “‘bar velocity”’ which 
is in general lower than the “‘bulk velocity” obtained in field measure- 
ments. The ratio of these two velocities is a function of Poisson’s 
ratio for the material. In what follows the term velocity is used to 
denote the measured bar velocity, unless otherwise stated. 
To obtain quantitative data showing the effect of moisture upon 
the velocity of the sandstone, the percentage of water in the rock 
was varied, and the natural frequency corresponding to each moisture 
content was determined. The data obtained are shown graphically 
in Figure 4, in which the observed natural frequencies are plotted 
against total weight of the bar. The points on the curve were obtained 
in the order shown by the numeral opposite each. Point 1 was taken 
with the sample in an air-dry condition, that is, after it had been 
_ “Incalculating the natural frequency of the bar from the observed data, a correc- 
tion is made to take into account the effect of the mass of the coils attached to either 
end. In the present investigation this correction was negligible. 
® This relationship is strictly true only if the length of the bar is very large as com- 
pared with its other dimensions. In the case of short bars a correction must be applied. 
This correction is negligible for the bar used in this investigation. 
673 
