MECHANICAL PROPERTIES OF POLYMERS 157 



velocities'^ in plastics was the method of observing the focusing efTect 

 of a cylindrical lens made of the plastic. Sound waves can be made 

 visible by the Debye-Sears technique of using a sound wave as a phase 

 diffraction grating. Here light from a slit Si is made parallel by the 

 lens L2 and passes through the cell parallel to the wave fronts of the 

 sound waves as shown by Fig. 25. The compressed parts of the medium 

 retard the light waves more than the rarefied parts do and hence the 

 medium acts as a phase diffraction grating. If a second slit So is used 

 which is small enough to pass only the zero order, a light valve action 

 is obtained which modulates the light according to the sound wave 

 intensity. If now the lens Lj is used which focuses on the median plane 

 of the tank, a picture of the sound beam is obtained as shown on Fig. 26. 

 The bottom figure shows the focusing effect of a plastic and from the 

 focal distance d and the radius of curvature r of the lense, one can cal- 

 culate the velocity in a plastic compared to the velocity in the water 

 bv the formula 



Vv = 



-/(-S 



(11) 



This method gives velocities good to from 2 to 5 per cent depending on 

 the attenuation in the lens. 



G. W. Willard" has devised recently a more accurate method for 

 measuring sound velocities as shown schematically by Fig. 27. Here a 

 plastic to be measured is placed half way across the sound beam in the 

 liquid and light is sent along the wave front occurring in both the plastic 

 and the liquid. If the waves are in phase the retardation in the two light 

 gratings, corresponding to sound propagation in both media, add up 

 and for a slit selecting the zero order the darkest pattern occurs on the 

 photographic plate. If the two waves are just out of phase, the retarda- 

 tion is reversed in the two media and the lightest part occurs. With 

 this relation it can be shown^^ that the spacing d of light and dark lines 



'2 W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, 

 D. Van Nostrand, 1950, p. 404. It was used in this country by G. W. Willard as 

 early as 1940. It was also used in Germany by J. Schaefer "Eine Neue Method 

 Zur Messung der Ultraschallwellen in Festkorpern." Diss Strassburg, 1942. By 

 making the front surface part of a cylinder, Schaefer also measured the shear 

 velocity in a solid. 



13 G." W. Willard, /. Acous. Soc. Ayn., 23, Jan. 1951, pp. 83-94. The origin of 

 this multiple path interference method goes back to the work of R. Bar (Helvetia 

 Physica Physica Acta Bd 13 page 61 (1940)) who attached a piezoelectric crj^stal 

 to a bar with a 45° end section and set up transverse and longitudinal waves, in 

 the bar. These waves produced longitudinal waves in a surrounding liquid and 

 by observing the interference pattern between them, the longitudinal and shear 

 constants could be determined for an isotropic medium. Willard's method as 

 described above is much more direct and is capable of higher accuracies. 



