VELOCITY IN GRANITE AND LIMESTONE 113 
The frequency of the fork was maintained at 50 cycles per second 
within 0.03 per cent. The possible error in timing was therefore neglig- 
ible. 
Attention is directed to the fact that there are not as many sup- 
porting points on the time-distance graph of the transverse wave as 
there are on that of the longitudinal wave (Fig. 3). Due to the later 
arrival of the transverse energy in many cases there was interference 
between it and the longitudinal energy which made it difficult to pick 
corresponding points on successive traces. Consequently, only those 
traces were used where there appeared to be similar character. This 
is shown by the arrows on the transverse record of Figure 2. 
LABORATORY MEASUREMENTS 
Two samples of the granite were taken from this location for the 
purpose of making a laboratory determination of the velocity. 
These samples were cut into two rods with a square cross section 
of 1.125 inches and lengths of 11.3 inches and 9.0 inches. A thin piece 
of steel was cemented to one end of the rod, which was supported by 
a clamp at its center. A permanent magnet around which a coil was 
wound was placed in line with the bar and near the steel on the end 
of the rod. The rod was then struck lightly on the opposite end, pro- 
ducing longitudinal vibrations which generated an E. M. F. of the 
same frequency in the coil. This E. M. F. and an E. M. F. from a 
calibrated vacuum tube oscillator were then impressed on the input 
of an amplifier, the output of which was rectified and the resulting 
beat frequency recorded. Then, this beat frequency and the frequency 
of the oscillator being known, the resonant frequency of the granite 
rod was determined. Substituting this value in the following equation 
gave the longitudinal rod velocity of the granite. 
V=2fl 
Where V is the longitudinal rod velocity 
f is the natural frequency 
and Lis the length of the bar. 
Figure 4 shows specimens of records obtained by this method. 
The density of these granite samples was determined by weighing 
them in air and in water. Knowing the longitudinal wave velocity 
in the rod and the density of the material, the value of Young’s 
modulus may be found from the relationship 
E=pV? 
Where £ is Young’s modulus 
p is the density 
and V is the longitudinal rod velocity. 
635 
