158 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



is related to the wavelength in the hquid X^ and the wavelength in the 

 sohd Xs, by 



1 = - _ A 

 d Xf Xs 



(12) 



This corresponds to a velocity in the solid compared to a velocity in 

 the liquid given by 



Vs = 



Vt 



Vl/fd 



(13) 



where / is the frequenc3^ Fig. 28 shows a photograph of a series of lines 

 in a transparent plastic and a transparent plastic in the form of a wedge. 

 It is seen that beyond the edge of the plastic there is a dark interference 

 band for each one in the transparent plastic. This phenomenon is caused 

 by the refraction of the sound wave that has traversed the plastic and 

 the dark lines are lines of equal phase of the two waves in the liquid. 

 The angle of the dark lines is half the refraction angle. Hence the velocity 

 can also be determined by counting the number of dark bands in the 

 liquid beyond the plastic. This makes it possible to measure the veloci- 



i i i I I 



\2 



■*\. 



d-- 



PHOTOGRAPHIC PLATE 



Vl 



Xs 



-Ad 



Fig. 27 — Optical method for measuring sound velocities of plastics by com- 

 paring their velocity with that of a liquid such as water. 



