[boyle] COMPRESSIONAL WxWES IN METALS 297 



Taking the case of steel, and a frequency of 40,000 vibrations per 



27r 

 second, yfe^ = — = o.5 (about) , £ = 2 . 14 X lO^^, p = 7 . 85. If the velocity 

 \ 



is diminished by viscosity by as much as 5 per cent., which Mr. Lang's 



experiments show_ is probably an excessive estimate, n works out at 



a value of about 4X10^ in C.G.S. units, instead of an order of 10^ as 



in the experiments quoted. 



With this value of coefficient of viscosity the damping constant 

 would be, at a frequency of 40,000 vibrations per second, 4.2X10^. 

 Hence the damping factor would be g-^ -^xio^'^ and the time for the 



1 . 



vibration to be damped to~ " , i.e., about 1/3 of its initial value, would be 



2.4X10~^ sees. The vibrations are certainly more sustained than 

 this, and therefore the coefficient of viscosity lower still than the value 

 taken in this example. It is probable that the order of the coefficient 

 of viscosity, when determined, will not be greater than 10^. 



Although no numerical values for the viscosity in metals can as 

 yet be quoted it is possible, at least qualitatively, to get some idea 

 of how sustained the vibrations are by the following experiment. 

 The waves excited in the clamped rod can be detected by a micro- 

 phone, provided the microphone is connected into a "tuned" electric 

 circuit, and the received effect is made to produce a heterodyne 

 "beat" note with the continuous electric oscillations from an ionic 

 valve. The high frequency detected oscillations, or this "beat" 

 note, or both, can be amplified, and the resulting tone made plainly 

 audible by an ionic valve amplifier. In such a method it is best to 

 put the waves from the rod into a liquid, like water or oil, and detect 

 them with the microphone in the liquid, though the damping in this 

 case will be increased by greater radiation from the rod than when 

 the rod was emitting its note in air. 



The experiment in the present case was performed as follows : 



High frequency vibrations were produced in metal rods one inch 

 diameter, and of lengths varying from 50 to 6 cms. The rods were 

 clamped at the centre, the clamp being provided with a handle which 

 could be held in the hand. The rod was hit at one end with a light 

 hammer two cms. long, its other end being dipped into water or oil 

 contained in a small box. A small water-tight microphone, affected, 

 no doubt, only by the pressure of the sound waves in changing its 

 electrical resistance, was employed, and is illustrated in figure 1. 

 It consisted of two steel discs, each one cm. in diameter, and one mm. 

 thick, with heavy rims, about 0.3 cms. wide and 0.3 cms. thick. 



