A STUDY OF DIFFERENT ULTRASONIC STROBOSCOPES AND THEIR USEFULNESS FOR THE STUDY OF WAVE PROPAGATION AND ACOUSTIC BIREFRINGENCE by Walter L. Gessert AN ABSTRACT Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 1954 Approved Walter L. Gessert ABSTRACT The need for a stroboscope suitable for the study of Acoustic bi­ refringence in particular portions of a sound wave is stated, and the present situation of acoustic birefringence theories is given in summ­ ary. The theory for use of two sound waves for stroboscopic effects is discussed (1 ), and the results of experimental examination of some of these effects are shown, especially where a first sound wave is situat­ ed at a secondary light source. Simple pictures of some geometrical demonstrations are shown. The Rayleigh (2) phase shift by reflection of sound at a liquidliquid interface is studied showing good agreement with theory. The phase relationship in the field in the near-neighborhood of a long, narrow "piston-like" quartz transducer (3) is examined and shows that the apparent cylindrical waves from the edges of the quartz are out of phase with the plane waves by one-half wavelength. The phase change at the focus for a cylindrical wave (4) is mentioned and data given which is not in agreement with theoretical conclusions. A con­ clusion is written for the use of Bar's stroboscope. 1. R. Bar, Helv. Phys. Acta (8 ), 9_, 654,678 (1936). 2. Lord Rayleigh, The Theory of Sound, Second Edition, Macmillan (1896), Vol. II, PP. 84 (keprinted~T9Z9). 3. K. Osterhammel, Akust. Zeits., 6 _, 6 (1941). 4. F. Reiche, Ann. d. Phys.(4), 29, 65 (1909). A STUDY OF DIFFERENT ULTRASONIC STROBOSCOPES AND THEIR USEFULNESS FOR THE STUDY OF WAVE PROPAGATION AND ACOUSTIC BIREFRINGENCE BY Walter L. Gessert A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 1954 ProQuest Number: 10008462 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10008462 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 ACKNOWLEDGEMENTS The author wishes to take this opportunity to express his sincere gratitude to Dr. E. A. Hiedemann for suggesting the problems in acoustie birefringence and for his continuing interest and guidance in the results which have been achieved. Thanks are also due to Drs. R. D. Spence and F. Leitner for discussions on portions of the work on the diffraetion field and to Mr. M. A. Breazeale for the great assistance in the photo­ graphic work and in the adjustment of the optical equipment. Especially, the author acknowledges the financial assistance given under a U. S. Army Ordnance Contract without whieh the work could not have been acc­ omplished. TABLE OF CONTENTS INTRODUCTION Acoustic Birefringence Ultrasonic Stroboscopy THEORY Use of Two Sound Wares Phase Shift upon Reflection at a Liquid-Liquid Interface Diffraction Wavefield before a Beam Forming Quartz Phase Change at the Focus of a Cylindrical Lens EXPERIMENTAL APPARATUS Oscillator and Power Supply Optical Equipment Ultrasonic Equipment DISCUSSION Comparison of Two Velocities Tanlc^ in Direr gent Light Bar Stroboscope: T^ at D ' Raleigh Phase Shift Diffraction Field before a Beam-Forming Quartz Phase Change at the Focus of a Cylindrical Lens GENERAL CONCLUSIONS BIBLIOGRAPHY LIST OF FIGURES Figure page 1. Light Intensity Versus Square of Transducer Current. 5 2. Optical Arrangement. 9 3. Tank T-^ in Divergent Light. 4. Interference Points from Incident and Reflected Sound Beams. 5. Measurement of D and d. 11 14 15 . Drawing of Interference Points for Plane and Cylindrical Wares in Phase. 17 7. Drawing of Interference Points for Plane and Cylindrical Wares out of Phase by 180°. 18 6 8. Phase Change in the Region of the Focus for Spherical Wares (Reiche). 9. Circuit of Oscillator and Amplifiers. 20 22 10. Circuits of Power Supplies. 23 11. Impedance Matching Circuit. 24 12. Theoretical Curves for VelocityComparison. 28 13. Photographs of Fringes for CalculatingVelocity Differences. 14. Relationship between 15. Experimental Curve for d vs A . 35 16. Revised Optical Arrangement by Bar. 38 17. Broadening of Slit Image. 38 18. Photographs of Interference Points. 42 19. Sound Wares Focused by Cylindrical Plastic Lens. 43 20. Sound Diffraction Grating. 44 21. Diffraction Orders Brought to Focus by Lens. 45 andX^. 29 33 Figure Page 22. Experimental Curve for d\ vs 2 6 . 47 23. Evidence of Rayleigh Waves in l&ca Film. 50 24. Enlarged Image of the Neighborhood of a Long ThinQuartz. 52 25. Sound Wares Brought to a Focus by Cylindrical Lens. 55 INTRODUCTION It is not unusual for the thesis work to have been initiated with one purpose in view only to be changed, or narrowed down, to a purpose quite different from the original. The present work had as a main ob­ jective the experimental examination of the theoretical prediction* of three different theories for accidental acoustic birefringence. In the ©ourssof experiments to this end it was deemed necessary for reasons te be given below te use a stroboscope especially suited for this study. A form of stroboscope briefly mentioned by Bar (l) suggested it­ self as a likely method because of its promise of better light intensity than other stroboscopes furnish; but unfortunately Bar was unable to publish a critical discussion of the effectiveness of his stroboscope due to his untimely demise. Once work had been started en the method it was decided te limit the purpose of this thesis to an evaluation of the method and'to its use upon a number of problems for whieh it is well suited. In the course of the initial work upon the matter of birefringence in liquids a fair amount of experimental work had been completed; this work will be briefly summarized. Aeeustie Birefringence The fundamental relationship for dynamic (flow) birefringence (An) is that given by Maxwell (2): o5 (1) where a is refractive index, M is Maxwell 's constant, is the common shear viscosity and u is the x-eomp©nent of velocity; and is the velocity gradient perpendicular to the flow which is in the x direction. This relationship for flow is used by analogy in two of the three pre­ sent day theories for acoustic double-refraction. Stress Birefringence Theory of Lucas (3)(4)(5). This gives a macroscopic picture of an acoustic birefringence due to elastic deform­ ation in the liquid associated with a plane progressive wave. Lucas be­ gan with the Navier-Stokes equations for viscous liquids, obtained a velocity gradient from a wave equation for displacement, and arrived at the following: (2 ) in which u> is the circular frequency, I is sound intensity, ^ is the density, and V is the sound velocity. The Peterlin Theory. Peterlin (6 l further developed the success­ ful treatment of Peterlin-Stuart (7) for flow birefringence into a mic­ roscopic, orientation theory which postulates the kinematical effect upon assymetrical particles of any nature in the fluid. The optically anisotropic particles are oriented by the velocity gradient and tend to rotate with an irregular, but periodic motion, passing most slowly through the position in which the major axis is aligned with the direction of flow. The velocity gradient in this case is parallel to the flow. final result given by Peterlin is: (3) 2 The an expression quite similar to that of Lucas. Oka Particle-Orientation. acoustical double refraction. This is a second microscopic theory of It is due to Oka (8)(9) who based the orientation of optically anisotropic particles, and therefore the double refraction obtained upon the sound pressure. Here, as in the Peterlin theory, a colloidal suspension is intended. Symetrical particles which do not partake entirely of the motion of the suspending medium behave in a sound field like freely suspended Rayleigh disks. Depending upon whe­ ther they are more or less dense than the suspending medium they exper­ ience a torque tending to align them perpendicular or parallel to the direction of sound propagation (10). Oka makes use of an ideal special case which has been calculated by King (11), who assumed perfectly stiff, infinitely thin disks having a radius much smaller than the wave length of the sound. The resulting distribution functions and net birefringence equation for the system are lengthy, but the characteristics can be given briefly. The double refraction (An) is an inverse function of temp­ erature, no frequency dependence is indicated, and when the acoustic in­ tensity (I) is small, the double refraction is proportional to I. From a cursory examination of the Lucas and the Peterlin results it can be shown that both predict a light transmission through crossed nicol prisms which is proportional to sound intensity, whereas the KingOka theory predicts transmission proportional to square of the sound in­ tensity. The first two theories are given for plane-progressive waves while the Oka theory is set up for standing waves. Zvetkov, Mindlina and Makarov (12) working in certain vegetable oils found the birefringence (An) to be proportional to sound amptitude in agreement with the Lucas and Peterlin work. Bennett and Hall (13) also found this to be true for poly-alpha-methyl styrene, a Dow Chemical 3 Company Resin 276-V2 which is "primarily" composed of tri-polymer alphamethyl-styrene• In our laboratories an American Instrument Company photometer was used to obtain data for the curve for Castor Oil given in Figure 1. This curve shows that the light intensity through crossed nicols placed at 45° with the wave fronts of the sound is proportional to the square of the transducer current, and therefore proportional to the sound in­ tensity (14). Hall (15) obtained a similar curve for poly-alpha-methyl- styrene using the same equipment. Examination of such well defined liquids as the lower alcohols, nitrobenzene, cinnamic aldehyde, and B-phenylethyl alcohol which are re­ ported to be highly birefringent by Sadron (16) in dynamic double-refraction experiments produced no acoustic birefringence. This disagrees with the prediction of Lucas stress theory. Peterlin and Stuart (17) state in a footnote, page 103 j "Only the measurement of the amount and sign of the bire­ fringence can lead to a binding decision between the pre­ vious theories for molecular solutions." For this reason it was necessary to find an effective stroboscope which would permit the examination of the wave-field itself. In general the birefringence effects are weak so that the stroboscope must permit as much light as possible to pass through the polarizing prisms and liq­ uid. The Lucas-Peterlin theories predict a change in the sign of the double refraction, while the King-Oka theory predicts only a change in the amount. The Kerr cell was considered but was discarded because of the ser­ ious disadvantages listed by Goudet (18): 1. A stable high voltage field is required. o MS CURRENT D OF O +0o TRRNSDUCER o ■■'sh SQURRE h & \ o z CO _o \9 \cr INTENSITY & O Ui in VERSUS u O o P V 1 j§ LIGHT a in a .. J (6 ) and the observed intensity distribution l(x) after passage through both sound beams becomes: J M ^ -rf/- * cos trr . (6) This is in agreement with experimental evidence and one obtains the periodic intensity distribution which is characteristic of a stand­ ing wave in one tank wherein the distance between adjacent maxima is equal to a half-wavelength ^/z. • For parallel positioning of the sound beams no lines appear when both tanks contain the same liquid, i.e. the wavelengths of the sound in each tank are equal. But when the tanks contain liquids of different sound velocities then: (?) and Z 7T ( j / ~ $ ) ' X is the wavelength in T]_ and > (a) A in Tg* 10 The observed intensity distribution in this instance is: (9) where cos The separation between intensity maxima has become (l - cos V ) ( I- Vx') (10) This suggests the possible use as a method to measure the change of sound velocity relative to a normal value* Figure 3. Tank in Divergent Light. The case where tank T^ is placed in the space between D' and L 3 is treated in a similar fashion. The assumption is made that the dist­ ance the light travels through the first sound wave uj, is small com­ pared with the radius of curvature of the light beam; and one neglects the fact that only the paraxial light-rays pass through the sound waves perpendicularly. After the light has passed through the first sound wave ( uu, ): (11 ) If the diameter of the cone of light rays at u)f is d and behind L 3 is cd, then the amplification factor is c, and the wavelength A 11 at uU becomes A - C.A, after lens L 3 . j.' - / - s i n £77 Therefore becomes ': K Y (12) Thus, as in the previous case for both tanks in parallel light, with a different liquid in each tank the distance between maxima becomes: A As tank A (>~t) O-Vx) (IS) ' is moved toward D', (a)( approaches the secondary source and d goes to ?.ero, that is, the amplifying factor C —* *° and A -*■<*»; this then gives for i]_': which shows that the light intensity is independent of x, and is mod­ ulated with the period • After passage through the second progressive wave in tank Tg the intensity pattern becomes: (15) * the distance between maxima in the intensity pattern being _/l_ = A 12 Phase Shift upon Reflection at a Liquid-Liquid Interface Lord Rayleigh (34) has shown that for a sound wave incidentupon an interface between two liquids of velocities with densities ed wave; the *7r and and V 2 , anc* j** , there occurs a phase shift in the reflect­ phase shift is zero at the critical angle and increases to radians when the incident angle is increased to '7r/jS. . Rayleigh gives for the incident wave: (16) the interface lies at the x = 0 plane. And for the reflected wave: (17) where waves. 2 6 is the phase difference between the reflected and the incident It is given by: (18) The critical angle &/c is defined by: (19) There is also a refracted wave, or rather a disturbance, in the sec­ ond liquid which penetrates little more than a few wavelengths. Arons and Yennie (35) recently measured the phase distortion of acoustic pulses reflected obliquely from the ocean bottom and found good agreement be­ tween calculated and measured pulse shapes. Scheme for Measuring the Phase Shift The method for measurement of this phase shift in the present work is an outgrowth of a technique shown by Hiedemann and Bachem (36) for comparing the effectiveness of a stroboscope. In figure 4a there is shown a wave-train incident upon a reflecting surface at an angle and a wave-train which is in phase with the incident waves. beam, Figure 4. Interference points from incident and reflected sound (a) No phase shift, (b) phase shift of 180°. If this wave train is not illuminated stroboscopically the points of coincidence of the pressure nodes move parallel to the reflecting sur­ face and one sees a set of pseudo-stationary-waves, or combination waves, which appear to be emerging from the reflector with a phase velocity equal to V/cos The dots form a trace parallel to the reflector and move with a velocity v«. v/sin 0^. Illuminated stroboscopically the com­ 14 bination waves disappear and there appear only the points of coincidence. An analysis of the phase shift can be made by measurements of the spacings on a photograph according to the following sketches in figure 5. Figure 5. Measurement of D and d. From the drav/ing it can be seen that one need only measure the spacings D and d perpendicular to the interface and use the relationship • CO 22 -W N A A dc cc IT) o cn o tn < «■ UuU uuuuuuuu U > m is on u u J uuuu n m n m X O' I- r n i— UJ FIGURE 10«. L01/V VOLTR^E P O W E R SUPPLY PLUq > 5/25 HY, 250 Mfi. > U U l r 25,000 OHMS SO W. 81G PL&TE TPRNS, 115 V.RC. FIGURE 10 b. HIGH VOURGE POWER SUPPLY % QURRTZ LINK COIL FIGURE II. IM PEDRNCE MRTCRING CIRCUIT The use of separate drivers for the two tanks made it possible to op­ erate Tx and Tg independently, and to provide different sound intensit­ ies from the two quartz transducers. Optical Equipment The lenses are described elsewhere, and need no special comment here. The optical bench with associated riders, bilateral si its, and micrometer-screw traversing riders were manufactured by Spindler and Hoyer, Germany. The light source used was a high pressure mercury lamp A-H4; for certain portions of the experimental work, a Gaertner filter set L541 E was used to transmit the Green line of mercury 5461 A0 . Almost all of the photographs were taken with an Exacta model VX with lens removed. Other lenses of more suitable focal length were held in holders and mounted on riders. This camera had the advantages of a copious film supply to permit many exposures and a focal-plane shutter with speeds up to twelve seconds. Ultrasonic Equipment The transducers were in all cases x-cut quartzes of one half, three quarter, and one inch square. The beam patterns were produced by a special 71° x-cut quartz of one inch length. This quartz is used be­ cause the vibrating surface lies perpendicular to the direction of min­ imum Young's modulus, therefore the maximum amplitude is obtained. But most important, this cut of quartz has a more piston-like vibration than any other cut. This is the same type crystal used by Osterhammel (40) in his work. 25 DISCUSSION Comparison of Two Velocities In his discussion of the situation where both of the tanks are placed in collimated light and the progressive sound beams are parallel with each other and perpendicular to the light rays, Bar (1) suggested its use as a method for measuring, or for comparing two velocities of sound. The two velocities might be for two different liquids, or of the same liquid at different temperatures in each of the tanks. Another possibility is that for measuring diffusion rates of one liquid into an­ other, in which case the sound in Tg would be transmitted parallel to the diffusion layer. The velocity change across the boundary being a function of the diffusion at the boundary. Although the present method has not been cited as having been used before, Giacomini (33) has reported measurements made on a single liquid in which he employed two quartzes radiating progressive waves side by side in opposing directions. constant at In this case the value of -A- remains . Equation (10) from above was; A Substitution of in terms of frequency (10 ) A = and X ‘ - % into equation (10) gives -A- and the velocities v and v' in tanks T^ and Tg. (21) 26 This relationship is shown in the plot on Figure 12, where v* is taken equal to 1500 m/sec as a parameter; the graph is for A A v = v' - v. versus It shows clearly the sensitivity of this method for small velocity differences, and indicates the necessity for a longer wave-field. More exact measurements should be possible if the optics from a polariscope of the type for stress analysis in plastic models were used. A field of 17 centimeters could easily be obtained. Such a field would permit a distribution of the error, produced when selecting the center of an interference fringe, over many more fringes. The cal­ culations given in Table 1 make use of from three to twelve fringes in a field of 12.6 cm length. Figure 13 shows a series of photographs for a few common liquids at frequencies in the range 1-15 mc/sec. Unequal temperatures in the sound fields of one, or of both, tanks caused the curvature in the fringes of Figure 13(d). The defect can be avoided to a great degree by the use of stirring action in the liquids and with transducers which radiate a more homogeneous beam. The common technique for improving the homogeneity of a sound beam, that of placing a thin sheet of glass or metal into the sound path at an angle did not work well here, because in addition to the reflection out of the main beam of spurious rays, the thin sheet also caused attenuation of the sound and reduced thereby the contrast of the fringes. It should be noted that if the plate is flawless and homogeneous the attenuation can be neglected. Measurement from the photographs in Figure 13 are grouped together in Table 1. Assuming a greatest possible temperature error of 1% in each of the velocities and an error in the frequency measurement of a tenth of one 27 nr oo cc a Ui "oo UI _.o in o o o UJ _.o in o o o (a) Xylene-Acetone At = 160 m/sec 0 = 1.025 me/sec A m e a s . 9.51 mm (b) Xylene-CCl. A t = 394 m/sec 1.025 mc/sec Ameas.” 3.76 mm (e) m-xylenen-propyl alcohol A t = 116 m/see \) = 3.48 me/sec Ameas." 3.98 mm (d) m-xylenen-propyl alcohol A t = 117 m/seo \) = 8.87 mc/seo Ameas.” 1*646 mm Figure 13. Photographs of Fringes for Calculating Velocity Differences. 29 v o d V Jh b V‘. Ch *H •H a eo CO CO (J5 Cv3 CO 1 lO rH • to d S 1 s rH to ■ © Table « > o © w CO CM CO CM CO CM C1—1 1— 1 CO o to rH CO o CO rH LO o CO rH o CO rH 03 CD rH rH C— CO rH rH r-v « Si rH o X! I— 1 o X S -P X ■H e v_r rH d rH d © d © i— i r’i © d © .rH >3 rH 03 © 3 3 -p X •d o «d • cS 03 • CO CM CO rH i—1 u o i—t • 03 CM 03 CO CO -p © LO • CO CM o CO 1— 1 rH 1-1 V d LO • cc CM X i—1 o o X • o o <— ! >3 a o Si cl, i d « © 30 o o © d © i —i >3 X 1 6 rH >3 CL, o Si CLj i d • •a « d © rH >3 X 1 £ percent, the computed value of _/\_ The Measured values of -A. should be in error by less than 4%. will be expected to lie between b% for broad lines where only four fringes can be used and 1,0% when fringes are narrow and there are twenty fringes available. The measurements for in Table 1 were made rather coarsely on photographic enlargements by means of vernier calipers which could be read with an accuracy of a tenth of a millimeter. The frequencies given were taken from a General Radio s/Yave-meter, Model 566-A. A brass rod 12.71 mm diameter was placed in the field and photographed as a reference length for the calculation of A _ . The photographs and theoretical curves are sufficient to predict that, for a 20 mc/sec frequency, with two liquids having a ^ v of 20 m/sec and therefore a A. ~ of 126 mm width. mm, there will be 25 fringes in a field A large error of 10% in the selection of the center, or edges, of the first and last fringes would give only 0.4% error in ^ v, or 6 m/sec for v 1500 m/sec. The method would give greater accuracy for higher frequencies end for a longer wave-field, but each of these factors is limited. The upper frequency is determined by an available quartz transducer which can radiate the large sound intensities needed to produce fringes of sufficient contrast to be photographed. Quartz crystals of low fund­ amental frequency are durable when strongly excited but have increasingly small efficiencies at their harmonic frequencies; an x-cut quartz with fundamental at 30 mc/sec is extremely fragile. Further, with low power radiation and poor contrast in the fringes a longer exposure is necessary, consequently the temperature of the liquids would change. Since the co­ efficients for velocity change due to heating are likely to be difierent for the two liquids, there will result a variation of A 31 v. A serious application of this method would require an elaborate apparatus for temperature control. The liquids which are to be compared might limit one or both of the factors if either of them presented relaxation effects at the higher frequencies; such liquids as castor oil (44) would be troublesome by virtue of high absorption for sound at even moderate frequencies and relatively narrow optical fields. 32 Tank^ in Divergent Light That portion of Bar's paper in which the first tank Tj is placed between D' and Lg in Figure 2 has its principal value in the present work by being another test for the velocity comparison method. The in­ terference fringes seen in the field of tank Tg are the result of an op­ tical enlargement of the wavelength in fringe separation j\. approaches A, when . A, to A* with consequent change It is apparent from Figure 14 that is closest to Lg and therefore A, becomes in­ finitely large. The method for taking measurements can be explained by considering Figure 14 below. The distance d was measured by means of a simple meter- stick from the center of Lg toward D'; a meter-stick was sufficient for this because the lens Lg which was used had a focal length equal to 30 inches. This lens afforded a large range for the values of d, the dis­ tance of Tj from Lg. Figure 14. Relationship between A, and Equation (13) age in is: A, • where A is the distance between fringes, and c is an hmplification factor. Since L3 collimates the light from D», the distance fro* L3 to D' is equal to the focal length of L3 , and we can set: =L % ^ ( A = A \ C =■ these are conditions for A and A which fulfill equation (13). A relationship between d and c which will satisfy (22) is: • ~ (23) Substitution of equation (23) into (13) gives the following: A = A = L,X (24) which is the equation of an hyperbola if Lg and A are constants. Carbon tetrachloride was used in both tanks and the quartz trans­ ducers were excited at 3.0 mc/sec. Measurements of A were taken dir­ ectly from 2-y x 3|- film by means of a comparator whose accuracy was better than .001 mm. The measurement of A for d = 5.5o» had a possible error of 20$ because only three fringes were present on the film, but this point does fit well on the curve. That for d * 10 cm had eight fringes and a highest probable error of 2$. The errors for the larger values of d are approximately 1 - 5$ depending upon the number and sharp­ ness of the fringes. No stirring was used in T^ so that heating effects distorted portions of the field. The heating limited in some cases the number of fringes which could be used and lowered the expected accuracy. The data is plotted in Figure 15. Because this section of Bar's work 34 FIGURE 15. EXPERIMENTAL CURVE :o o < FOR cL V E R S U S ;o <; was of minor importance to the purpose of this thesis, it was not deemed necessary to seek greater accuracy. The data as plotted fit an hyperbola well* Although there appears to be no immediate use for the results of this work, it should be noted the Fox and Roch (32) have employed a lensless system wherein light from a thin incandescent filament is pass­ ed twice through a sound berm before it falls upon a photographic film. Simple measurements of line spacing on the film and of the distances in the optical system provide a measure of the sound wavelength for a cal­ culation of the velocity of sound* 36 Bar Stroboscope: at D' Credit is given to Bar (1) for this method of producing a strob­ oscopic light source; for, although Tawil (30) in 1930 was able to photograph a sound wave in air by passing light from a small source twice through the sound beam, it was Bar who gave the thorough discussion of the theory and used the first tank at D* in order to obtain an overall stroboscopioally illuminated field. It must be noted also that during the same year, 1936, but previous to Bar, Maercks (45) and Cermak and Schoeneck (31) used an arrangement whereby a light beam traversed two soundbearas. Lucas and Biquard (46) discovered a broadening of a narrow light beam as it passed through a sound field and explained it as being due to refraction. Recent work by Kolb and Loeber (47) and by Loeber and Hiedemann (48) has extended the explanation of the broadening of the narrow light beam. The latter authors have used the theoretical approach due to Wiener (49). Their explanation of the Lucas-Biquard effect is that the narrowbeam is deflected by a continuously varying index of refraction which is present in a half wavelength of sound. As the progressive sound wave moves past the narrow beam of light, both the gradient of index of re­ fraction and its sign change periodically. Thus the narrow light beam is deflected horizontally to each side of a normal zero position once during a period. Bar suggests the frequency limits of 1 mc/sec and 20 mc/sec when tank is at D'. The lower limit because the bending of light in the sound—field at this frequency would be small; the upper limit because sufficiently high sound intensities are difficult to attain above this 37 frequency. Contradictory to this lower limit is the fact that Loeber (50) obtained large deflections of a narrow bean at 400 kc/sec. Using a second optical arrangement given by Bar which is similar to Figure 16, a camera was placed at D Figure 16. at S2 was in focus* such that an image of the space Revised Optical Arrangement by B&r. The photographs in Figure 17 whow the slit image at S 2 for various sound intensities present in Tj. The greater de­ viation of the slit image with increase in sound intensity in T^ is ex­ pressed here as a broadening of the slit image. Figure 17. Broadening of Slit Image. A method for comparing the effectiveness of a stroboscope has been given by Hiedemann and Bachem (56). The duration of light during each cycle is given by comparing the length of a dot-trace with the distance between dot-centers. The ratio of dot length to separation of centers will give the fraction of the sound,period during which the light is transmitted through the combination waves. Pictures of these waves are shown in Figure 18; they were taken at two different frequencies, using the optical arrangements suggested by Bar. 38 It is difficult, as it is evident from Figure 18 (b), to obtain a field of light which is illuminated with an even intensity and with light of equal duration. Examples of this can be found also in Figures (19) and (20) showing sound xvaves through a lens and a diffraction grating. To use the optical arrangement in Figure (16) one first needs to adjust the sound beam until it is perpendicular to the axial rays of the cone of light at D' and until the wave-fronts are parallel to the slit S]_. If the latter adjustment were to be neglected, the different portions of the slit image at D 1 would not all be in the same phase. Slit S2 is then traversed until the best stroboscopically illuminat­ ed field is obtained. These adjustments can be made either with stand­ ing waves present in Tg or with the sound waves in T£ being reflected from the bottom of the tank, in which case psuedo-stationary waves will be formed, and the dot-pattern will appear as a measure of the strob­ oscopic action of T^. spacing will be in When stationary waves are used in T2 the fringe for non-stroboscopic light and A is well adjusted. when the quartz As the adjustment is improved, half of the fringes will disappear. Bar states that the cross section of the light beam at the focus (D') must be less than A . According to the findings of Loeber and Kolb (47) the cross section of the light beam should be less than for best results. Because the width of the transducer is a factor in determining the cross section of the light beam within the sound beam, tests were made using one inch, three quarter inch, and one half inch square quartzes and best results were attained using the one half inch square quartz. A one half inch quartz with one quarter inch electrodes produced less ill39 lamination, but no significant improvement in the stroboscopic action could be noted. A longer quartz (perhaps one inch) of only one half inch width should improve the light intensity without harm to the action of the cell. Again, a one inch square quartz with only a one-half inch electrode was applied with unsatisfactory results. The failure of narr­ ower electrodes may be attributed to unusual wave forms having been emitted, or to a sound beam which was wider than the electrode. Naturally, the focal lengths of the lenses used and their positions on the optical bench must be selected with care. Generally one seeks the lens components which by their positions and aperture will give the greatest amount of light and the narrowest beam-cone at D 1. Lz reason should be in its near position to For this , and lenses Lg and Lg should be of longest focal length consistant with a large aperture. An American Optical Company objective of 10 inch focal length and 2 inch diameter and an achromat of 19 inch focal length and two and five sixteenths inch diameter were used most often for Lg. A six and one half inch American Optical Company objective was used for Lg. The con- densor lens system C is that from a Spencer Projector when using 35 mm slides. Lg was an eight and one half inch achromat, or a three and one half inch, ■f /3.5, objective set from a surplus gunsight. Best action resulted when the light beam passed the face of the quartz at a distance of approximately two to four millimeters. When this proximity is used, stirring action is necessary in the stroboscopic cell T-^, since heat-schlieren will tend to reduce the shutter action of the sound waves. Stationary sound waves in Tj were used in a short series of test. It is possible to use this arrangement to effeot stroboscopic lighting, 40 but an additional adjustment is required. stand in tank The stationary waves must such that a sound pressure node is at D 1. Here too also would be found some of the difficulties mentioned by Goudet (18). The spacing between reflector and transducer must be adjusted, and heat­ ing in the liquid tends to change this adjustment. The use of progress­ ive waves is much more simple. Examination of Figure 18 (a) leads one to expect stroboscopic ill_7 umination with a period of 2.26 x 10 seconds and a duration of 4.77 x 10"® second. In Figure 18 (b) it is possible to estimate O'- 5.5 x 10~® second. Perhaps the one great advantage of this strob­ oscope is the increase in illumination. The best pictures shown by Hiedemann and Bachen (36) were taken with exposure times of ten to twenty seconds. In the present work exposure times of one-twenty - fifth of a second to four seconds were always sufficient. Figures 19 - 21 are given merely as examples of the effectiveness of the stroboscope. 41 a. 4.42 mc/sec b. Figure 18. 2 mc/eec Photographs of Interference Points 42 Figure 19. Sound Wares Focused by Cylindrical Plastic Lens. 43 Figure 20. Sound Diffraction Grating. 44 in*- :il|! Figure 21. Diffraction Orders Brought to Focus by a Lens. 45 Raleigh Phase Shift An interface between glycerin and carbon tetrachloride was chosen because of the extreme difference between their velocities, 1914 ny'sec and 923 */sec* respectively, at 25° C. This large difference gives a low critical angle: = S i n -1 — ~ 2.8° 30 V* (19) The advantage of a small critical angle is obvious upon inspection of the dotted theoretical curve for 2 t in Figure 22. The smaller critical angle permits a larger range of incident angles from 180°. & lt to Incident angles greater than 75° produce dots which are large and elongated; this reduces the accuracy of measurement to such an extent that no data was taken above 73°. Although the glycerin will float very nicely above the CC14 in the tank, it was impossible to work this simply because surface tension be­ tween the glycerin and CCl^ caused a meniscus at the tank wall to pull downward to such a depth that it was impossible to get an image of the interface between the two liquids. A square brass tank, 2 x 3 inches by 1 inch high, was made and a mica window was cemented to the bottom. The mica was a section which was peeled from a thick sheet until it was of uniform thickness. A thickness of 0.06 mm was though to be sufficiently thin to behave like a thin film. Assuming that the velocity of sound in mica to be 4000 m/sec the wavelength at 3.0 mc/sec would be A — 1.33 mm. The use of this tank with mica window made it possible to obtain a sharp image of both the reflecting layer and the dots formed by the waves. A sharp image of this boundary was most important for measurement of d , 46 180- / / 160- / / / / / $ Z' f 140} * / / v / « / / / o / 120 / Ze-PHFISE. SHIFT - / f / / / ♦ /♦ 100 - / / / / / ' * o * / / 80/ / / / <30/ i. 40} i ■RALEIQH PHASE SHIFT i i i / / 20 } * - 8 /2 /5 4 o - 7 /3 1 /5 4 ® 5 * -7 /3 0 /5 4 < i i 10° 20° FIGURE. 2 2 . 30° 40° , 50° , 60° 70° 80° J. 90° EXPERIMENTAL CURVE FOR