ELASTIC CONSTANTS AND LOSSES IN NICKEL 



981 



The attenuation A (and hence the Q of the rod) was obtained by solving 

 the equation 



sinh Alo = 



(r — cosh AlQ)nirM( 



(13) 



in which r is the ratio of output with crystals together to output with 

 specimen attached, lo is the length of rod, Mc the mass of either crystal, 

 Mr the mass of the rod, and Qc the Q of the crystal as determined by reso- 

 nance response method. 



For this equation to apply accurately, the terminating impedance pre- 

 sented to the rod by the crystals at resonance must be small compared to 

 the characteristic impedance of the rod, and the Q of the rod should be > 10. 

 This method may be used even when the total loss in the rod is so high that 

 well defined resonances no longer exist. At the lower frequencies, however. 



Fig. 9 — Experimental arrangement for measuring the AE effect and associated loss in 

 a polycrystalline rod at low frequencies. 



a useful check may be made by the resonance response method of determin- 

 ing Q which involves determining the frequency separation A/ for two fre- 

 quencies 3 db from the maximum response frequency, and using the formula 



e = 



Jmax 



A/ 



(14) 



Correction for the mass and dissipation of the piezoelectric crystals must of 

 course be made. Both methods have been found to agree within about 10% 

 — the probable error to be expected. 



The Appendix lists formulae to be used when the resonance frequency of 

 the crystal driver differs from the frequency at which phase balance is ob- 

 tained. This condition of necessity occurred when the rods were subjected 

 to a magnetic field, which caused an increase in the velocity of propagation. 



Figure 10 shows a typical measurement of change in frequency and 

 change in decrement with magnetizing field excited in a solenoid surround- 



