m. i \. m. x. ‘ . 0" . .n .» .«J ‘ II t ., r. . c ' ’ -a- ‘h an. L- ;_,___4 _,__1' __ ' IHIllHiIHUII|||||lll||l||llllltlHlIllmlHllli ‘Iill [ 31293 01697848 This is to certify that the thesis entitled INVESTIGATION OF A METHOD OF SOUND PRESSURE MEASUREMENT WITH A MACH-ZEHNDER INTERFEROMETER presented by Robert: J. Clark has been accepted towards fulfillment of the requirements for Jfin—degree inm— 4&M Major professor Date August 114, 1952; 0-169 PLACE IN RETURN BOX to remove this checkout from your record. To AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. INVESTIGATION or A METHOD OF SOUND PRESSURE MEASUREMENT WITH A MACH- 23mm INTERFEROMETER by Robert J. Clark A,THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in.pertiel fulfillment of the requirements ‘ for the degree 0! MASTER OF SCIENCE Department or thaics and Astronomy 1952 /o Hf» 5’ L- ‘ ACKNOWLEDGMENT The author wishes to eXpress his sincere thanks to Dr. C. D. Hausa, under whose supervision and guidance this investigation was undertaken. and to Dr. G. S. Bennett for his help and interest throughout the project. Acknowledgment is also due to the entire group in the Physics and Mathematics Building basement of 1951-52 for hearing with the 125 Db. sound source. I‘, ‘fko CB?“ ‘ .. 1‘ a ~ ‘vv.0 t‘f" liXI"1_V’1\‘_5-.:: CHAPTER I II III IV TABLE OF CONTENTS INTRODUCTION AND PURPOSE INSTRUMENTATION~ . . . . Interferometer . . . . Detector . . . . . . . Optical System . . . . Light Source . . . . . SoundSource . . . . . CALCULATIONS AND RESULTS Dalculations a: Fringe Sound Pressure . . . . Results ....... SUMMARY . . . . . . . . BIBLIOGRAPHY . . . . . . APPENDIX........ PAGE 13 28 3O 31 32 52 36 43 47 FIGURE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 12. 13. 14. 15. LIST OF FIGURES SCHEMATIC OF THE APPARATUS . . . . . MACH-ZEHNDER INTERFEROMBTER . . . . PHOTO-TUBE . . . . . . . . . . . . . PHOTO-TUBE AND SELECTIVE AMPLIFIER . CIRCUIT DIAGRAM OP AMPLIFIERiAND PHOTO- TUEE . . . . . . . . . . . . . . . FREQUENCY RESPONSE CURVE AT CONSTANT SELECTIVITY. . . . . . . . . . . . AMPLIFICATION. . . . . . . . . . . . EFFECT OF SELECTIVITY WITH CONSTANT INPUT............... HIGH VOLTAGE REGULATOR AND FILAEENT CIRCUIT. . . . . . . . . . . . . . LIGHT AND SOUND SOURCE AND OPTICAL ’ SYSTEM . . .2. . . . . . . . . . . EXAMPLES OF SCOPE PATTERNS . . . . . EXAMPLES or SCOPE PATTERNS . . . . . EXAMPLES OF SCOPE PATTERNS . . . . . EXAMPLES OF SCOPE PATTERNS . . . . . SIGNAL OUTPUT AS A FUNCTION OF BLOWING PRESStJRE O O O O O O O O O O O O O 0 PAGE 15 15 17 2O 22 23 25 37 5? 58 4O 16. SIGNAL STRENGTH AS A FUNCTION OF FRINGEPATTERN. . . . . . . . 17. TOTALAPPARATUS..............44 18. LIGHT sOURCE CIRCUIT . . . . . . . . . . . . vi 0 O O C 42 good resolution. The averaging effects caused by the size of previously employed instruments and the effective distortion of the sound field from the presence of a detector in its path is eliminated. The purpose of this work was to ascertain that measurements of this type could be made and perhaps fur- ther developments in the method. The interferometer employed is that designed and constructed by lacy (2) in the Michigan State College Physics Laboratory. A general schematic diagram of the interferometer and the associated optical train follows: .5' " X5,“ «in 3., “IA ’1. f . ‘ §$j§lkm a" .l q" ':_ ‘ ‘ “T. ‘. . . ‘,-. "ICM‘V‘WWT @‘(W " ., 3‘, The interferometer consists of four glass plates whose planes are normal to a plane connecting their centers. Their mountings permit small adjustments of position.and crientation.from.their positions as shown. Plates 1 and 4 are plane parallels. half silvered or alumdnized ' mirrors, while plates 2 and 3 are plane front surface mirrors. Light from.source A rendered parallel by lens Ll travels to plate 1. The light beam is divided. part (I) is transmitted through plate 1 to plate 3 and then.re- flected to plate 4, while the other part (II) of the original beam is reflected to plate 2 and again reflected to plate 4. At plate 4 the reflected portion.of I and the transmitted portion of II are united.into a single beam. By proper adjustments of the plates one can observe directly with the eye. from.a position of the detector D, an interference pattern. The interference pattern is produced by slightly different optical path lengths of coherent rays.a A.point in the field is bright or dark fi Light producing a vertical fringe pattern can be thought of as coming from two separated horizontal images of the same point in.the real source. In a broad source the light may be thought of as coming from.many such points. Hew- ever. any particular pair Of virtual images that are chosen to be discussed are called coherent points, producing co- herent rays. 4 dependent upon whether the rays unite in or out of phase. It suffices to say that one can produce a pattern of alternate light and dark fringes which are perpendicular to a plane connecting the centers of the four glass plates. Furthermore , with a broad source of light and a circular aperture, this pattern can be localized in a plane normal to the light path at a designated place such as indicated in Figure l by I. A variation of the optical path of been I in the region of X will cause a variation in the fringe pattern. A sound wave propagated perpendicular to the light path will produce a time variation in pressure which is uniform along a line through I from plate 1 to plate 3. This local pressure change is accompanied by a density change which in turn varies the index of refraction that produces the Optical path variation and a subsequent shift in the interference pattern. The variation in fringe pattern is projected upon D by lens L2. L2 simultaneously serves the purpose of projecting an image of the slit S at the position I. This image causes no diffraction or distortion of the light beam within the interferometer proper or produces no dis- tortion in the sound wave. The slit is provided with an adjustable opening such that narrow sampling, of the order of .01 to .001 part of a wave length of the sound wave 5 may be obtained. The shift in the fringe pattern across the slit in its fixed poSition produces a light signal of periodic intensity variation. A photo-multiplier tube placed behind the slit receives the signal. The signal is amplified and the output observed with an oscilloscope or measured by a vacuum.tube voltmeter. The calibration of the instrument for absolute measurement lies beyond the scope of this report. but will be discussed briefly in the appendix. CHAPTER II INSTRUMENTATION Interferometer An.immediate problem to one unfamiliar with the interferometer is the obtaining of the desired fringe pattern. Each.plate has a rotational degree of freedom about a vertical axis passing through.its center and a rotational degree of freedom about a horizontal axis passing through its center. shown as H's and V's respec- tively in.Figure 2. In addition.plates 2 and 3 have trans- lational degrees of freedom.T. The translational motions are restricted to a horizontal plane such that the centers of the plates will move along straight lines connecting the centers of plates 4 and 1 respectively. The multiple degrees of freedom.allow a diversi- fied choice of patterns. auxiliary cells and compensation for such things as minute warping and temperature varia- tions. They also present a problem in the initial align- ment of the instrument to produce fringes. Ideally each controlled movement of a plate in one of its degrees of freedom would be independent of all other.movements. The construction of this instrument closely approximates the ideal case. e...“x. . "°'°-oe e --.o-ed.. t-‘tesebe "'ee..... ......... e e.......- m~" i fife _ LL .9. I Ate 'hti w—————— ~__..——.~... - _ . . m Nach-Zehnder Interferometer Figure 2. Price (5) reports a new auxiliary attachment for making the initial alignment of the instrument.b Pro- cedures for obtaining fringes are reported by Macy (2). Windkler (4). Winkler (5) and others. Following are some remarks intended to be supplementary and not a complete outline of the adjustment of the interferometer. The possible orientation of the sound source with the given.instrument and the method of detection, dictated that vertical localized fringes were to be used in this investigation. The desire for maximum.intensity contrast in the fringe pattern requires that one should work with or near the zero order fringe. the so called white light fringes. Briefly, this adjustment may be obtained as follows. The interferometer is illuminated with a monochromatic source of such.intensity that if L2 is removed, one may look with the naked eye directly into the interferometer from the position of D. It is assumed that proper initial adjustment of the instrument has been completed thereby aligning the feur plates into parallel planes. A.slight movement of any H adjustment, HS for instance, would then bring a vertical fringe pattern.into view. b Price's method untried by this author. 9 One can think of vertical fringes as being pro- duced by coherent points lying in horizontal planes. If the fringes are not vertical. and the controls are ideal. then proper adjustment of the individual V controls will produce vertical fringes. In actuality, small changes of the controls conform with the ideal case of independent adjustments but if large adjustments are to be made, then compensations with a plate's own conjugate controls must be made. _ In general an adjustment of plate 2 may be compen- sated by a corresponding adjustment of plate 3 while the fringes remain in the desired localization and vertical orientation. The same correspondence holds true between plates 1 and 4. It was found that after proper manipula- tion of V3 and V4, while compensated by V2 and V1, that a rotation of BS or H4 respectively, would allow the fringes to remain vertical. The establishment of this adjustment allows the operator to control his fringe pattern during Operation from plates 3 and 4 most easily. With the previous adjustments made one is now ready to examine the change of fringe locality and the number of fringes in view. Suppose the left and right orienta- tions of coherent points are such that a clockwise 34 rotation spreads the fringe pattern out, that is to say fewer fringes appear in the field. Furthermore. a shift 10 toward the source or toward the observer will simultaneously take place and. for the sake of the example, let it be toward the source. This movement may be checked by the parallax method of placing a fixed object in the vicinity of the fringes. As the eye is moved from side to side the fixed object will appear to move in a fixed relation- ship to the fringes only if it is at the same place in space as the fringes. The original number of fringes may now be restored without further change in the locality of fringes by the appropriate counter-clockwise movement of H5. The process is just reversed if the right-left sense is reversed. The above type of procedure is easily mastered by a few repeated and recorded trials of a beginning operator. The outline of a method for obtaining white light fringes follows. It is assumed that vertical fringes from a monochromatic source are in the view of the operator. H3 is turned in the direction that produces a broadening of the fringes. If the rotation is continued a curvature will appear in the nearly straight fringes, a position of parallelism of all the plates is passed through and beyond. The straight fringes will then reappear. The above process is the reversal of left to right or right to left of coherent points as the case may be. At the position of curvature or “flipping over" one can observe 11 a direction along which the center of curvature would seem to lie. One mirror can then be translated in a direction to equalize paths I and II such that the fringes appear to move across the field of view in the direction of the center of curvature. A white light should then be placed to illuminate either the upper or lower half of the field of view. As the zero order fringes approach, colored ’fringes will appear as extensions of the monochromatic fringes but in the white field of view. If one suspects that he has passed beyond the peeition of equal optical path length he may again try the center of curvature test. Observe carefully that the right-left orientation does not reverse during the process. The reversal may be detected since as one continues to translate in the same direction, the fringes in the field of view will appear to move in the opposite directiOn. ‘ The region of white light fringes is used for greater light intensity contrast, maximum.contrast being obtained when the coloring is symmetrically arrayed about the central black fringe. If this is not the case then the light rays in beams I and II are traveling through different thicknesses of glass. This is true because glass has a much different dispersive power than that of air. The pattern may be corrected by compensating rota- tions in the same direction of H1 and H4. H2 and H3 have 12 no effect because of the front surface reflection at plates 2 and 3. One may note in Figure 2 the sponge rubber supports underneath the tripod mount of the interferometer. This type of mount is one attempt to isolate the instrument in any manner possible from all mechanical shocks or vibrations. The sponge rubber in turn rests upon several layers of fiber blocks which are of the type used to damp sound waves. A discussion of the isolation of the sound field in a particular arm of the interferometer will be found in the appendix. Detector The normal fringe pattern has a spatial distribu- tion of light intensity that can be represented by a cosine squared curve. When the sound is on, the signal as seen from the photo-tube is the same as though the slit were moved back and forth across a small portion of the light intensity curve at the frequency of the sound wave. Suppose the fringe shift to be very small and the slit is arranged such that its relative central position is at the most nearly linear slope of the intensity curve. Further assume that the fringe shift is a sinusoidal func- tion of time, then relative motion between the two would generate a sinusoidal signal of light intensity for the tube. If a mercury arc, Operated by a 60 cycle alternat- 'ing voltage, is used as a light source, then the result- ing signal is not a simple sine wave, but rather an ampli- tude modulated sine wave because of the light variation. It is this type of signal which it is necessary to detect. The 931A photoomultiplier tube was chosen because of its good response to the proposed use of the mercury green line and for its availability. Other characteristics such as fatigue, amplification and voltage requirements, that were reported by Marshall, Coltman and Bennett (6). also by Kessler and‘Wolfe (7). indicated that this tube would be acceptable. 14 The tube was mounted as a unit with the adjustable bilateral slit (see Figure 3). The mounting is light tight. The upright barrel containing the tube is machined at the bottom.in a stepwise, slip fit fashion to set into its base; this preserves the light seal and allows the easy removal of the tube. It also permits a rotation of the slit about a vertical axis passing through the center of the tube. The slit proper is mounted on a short cylinder whose axis is normal to the main upright assembly. Again the connection is in the form of a machined slip fit with screw lock, which allows a fine adjustment of the slit jaws parallel to the fringes. The face of the slit holder is covered with a white screen. .A black scribe mark on.the screen indicates the position of the slit opening and allows a visual in- spection of the relative slit fringe position. The slit jaw length is approximately 15 mm. which corresponds to the height of the sensitive part of the photo-tube cathode. The opening is controlled by a fine micrometer screw, one complete turn of which provides an opening of 0.5 mm. A photograph of the slit and tube mounting is shown in Figure 4. Horizontal movement of the assembly by the micro- meter screw in.a direction normal to the light ray can be accomplished, while translational movement parallel to PhotoaTube ‘0 r Figure 3. {. Figure 4. Photo-Tube and Selective Amplifier 16 the light may be made along the optical bench. Various heights and angles may be readily obtained with the system of clamps and rods as shown. The entire photo-chassis is constructed of copper and aluminum providing an elec- trical shield which is adequately grounded to reduce stray signal pickup. In any photo-tube work there remains a great prob- lem of dark current or random noise (see appendix.) The random noise of a photo-multiplier appears well distri- buted over a large frequency range. It was therefore be- lieved that the amplification of the photo-tube signal should be restricted as closely as possible to the fre- quency of the signal. Since the work was to be carried out in the range of 5500 c/s. and up, one could place a high pass filter in the plate lead of the photo-tube (see diagram of circuit, Figure 5). The cut-off or critical frequency is calculated at about 1200 cycles. The pre- filter will then cut out the fundamental and first nine harmonics of the 120 cycle are noise and will damp the immediate harmonics above this frequency. ‘ The 'Selectoject' (8, 9) which is used by many radio amateurs to replace a variable crystal filter in phone work, etc., was used in the next stage of detection. While the circuit is most often used in rejecting a particular frequency, it is readily adaptable to the 17 .«d 0.... e -.J m museum .3 an.“ «a same .> So :..... :33 x03 2 2 .4 «See tax; am .3... magmas: on one: a. our on... n 3.. UN h n as m9: 2m 238333 5 mm 2.... .3 e... :.5 cos 2m .032 shear. mono. 3: . . (N :.. :3 Jazz an. n. t: 33038 zoo 2e: 233335 a... 5 1e: 93.3.3 4.5.. $.8an x one 5 ..q..3.:..5.7i,z: .43 on: a as. I. in 4 J - 0-. fi . -- , :I.. . oz .4“. .c e - v e V .. fl .. .. . Lea... .> ... . c a .o .o i .8 m. a 1 C H00 Av U. :3 H... 1.33.. a> "99243.... :... a1 a... «a: drum; 2394 H... 55 18 amplification of the same narrow band. Figure 4 shows the chassis containing the pro-filter and amplifier as connected to the photo-tube and slit assembly. This selective amplifier circuit was chosen to obtain amplifi- cation of the signal without including the amplification of all the random frequencies of the photo-tube noise. The amplifier is easily tuned to the frequency of the signal by a coarse frequency control, CFC indicated in the photograph. This control actuates R7 and RB (see Figure 5, wiring diagram) which are ganged rheostats that regulate the frequency of the feed-back signal which is to be in phase with the input signal, while others are fed back at 180° out of phase. R6 is a rheostat in.series with R7 and acts as a fine frequency control, FFC, such that very accurate matching between the sound frequency and the pass frequency of the amplifier can be made. 815 is a potentiometer that controls the amount of feed-back or sharpness of the pass band and is called selectivity S. Caution must be observed in the S adjustment since, if the feed-back becomes equal to or greater than the signal, oscillation will occur at the tuned frequency. Oscilla- tion.however is easily detected by the sharp increase in output signal. Isolation or matching of impedance between the photo-tube and the selective amplifier is accomplished 19 by the variable resistor R2, denoted as In on the photo- graph. While operating the system with the photo-tube as a signal source, the value of R2 should be near zero, however if one desires to check the amplifier with another source of input signal, there may be an adjustment nec- essary in order that the amplifier remain selective. The isolation is accomplished at the output end of the selec- tive amplifier by a standard stage of audio frequency amplification. R17 denoted as FAC, final amplification, controls the gain in this last stage. The tube sockets were mounted on a suSpended rubber sheet one-eighth inch in thickness providing a shock mounting to minimize the microphonic effect of the electron tubes. A common ground buss throughout, liberal wire shielding and a metal bottom for the chasSis were used to minimize stray signal. The performance of the amplifier is shown by the following curves. In Figure 6, curve A, the output is shown as a function of frequency, final amplification and selectivity being fixed but arbitrary. A 5 hy. choke was across the final output. The input voltage was a constant, from a Hewlett-Packard variable audio-oscillator, at 0.5 volts. The frequency of the amplifier was tuned at each point for a maximum signal. Curve B is the same as A except for a lower final gain but a slightly greater 20 331336 3338 as 3’30 sees—sex hoses—veh- .o 93»: {ea 5 962598 2 3 3 as 9 o e Leo . r17 5 '1 A allll 7] I Vi; . u 3 1T5 :ll 0 a on x // on _ L ill. 4.. i 0v . . . l - h. ! Ill-40m. r 00 sates u: sudsno 21 selectivity. Both remain fixed however throughout. Curve C is identical with B except that the choke was removed.c E is identical with A except that the selectivity was lowered. D shows the input voltage reduced to 0.5 volts, the selectivity is in the neighborhood of A but arbitrary, as is the final amplification. The five typical curves at constant selectivity all show an output voltage drop of about 6 Db. from 5 to 10 kc/s. Figure 7 shows the output as a function of input or amplification at frequencies at 6, 8 and 10 kc/s.t The final amplification was well below saturation. The selectivity was constant and just below the point of oscillation. The input signal strengths obtained from the photo-tube are in general well below 0.2 volts and therefore lie in.a region of constant amplification and relative signals may be compared most easily. Figure 8 gives an indication of the selectivity of the amplifier. Each curve was made at a constant 0.3 volt input. The amplifier was tuned to the frequency of the peak of the curve and held fixed for the readings of the particular curve. The frequency of the H. P. audio- oscillator was varied to obtain.the frequency readings and the output measured. Curves A, B, C and D with.peaks c 2.5 by was the final value decided upon. 838C393 .a. .93.. .38 5 :55 ‘0 ‘0 H. I --—.-—— ——.—4—-——‘- . -. .xlm." \ {on o." 8 at“ v! sudsno 23 use: 3338 5:. 3:333 no 88.3 .o 8.62. {on 5 goes.— "a 3 ca o o e o um v1 Mano 24 at 5, 6, 8 and 10 kc/s., were taken with the same settings of final amplification, impedence matching and selectivity. Curve E was obtained by increasing S only. Curve F was obtained by increasing 3 slightly more than for E. The sharp selectivity as shown reduces the interference of the random.noise so common in photo-tube work. A non. linear response was noted in Figure 6, however Figure 8 shows that by increasing the selectivity as the frequency is increased that a linear response in the range of 5 to 10 kc/s. can be obtained. The power supply for the amplifier was a commercial plate voltage supply unit. The regulation was checked and found to vary less than two volts in 310 for currents of 0 to 50 milli-amps. The plate voltage required for the amplifier was 250 volts and the total plate current was well below the 50 me. limit. The ripple factor was negligible. .The filaments were heated in series by a 24 volt battery. This method was used for convenience since a 24 volt supply was also needed in the light system. The high voltage needed for the 951A was obtained from.a commercial supply. The supply was well filtered but the regulation was below the standard required. A regulator for the high voltage was therefore included in the amplifier chassis. The wiring diagram (Figure 9) may be inspected for details of the regulator and filament EiIGH VLL-‘I‘AGP. REGULATOR 25 26 circuit. The filament power supply of the 6SJ7 in.the regulator circuit was provided by a separate transformer. This was felt to be a necessary protection.for the other tubes, in.the event that the 6SJ7 would somehow short out and place a high voltage on the amplifier tubes. R23 and 826 are rheostats that may be used as coarse and fine voltage controls, respectively, of the voltage that is applied across the photo-tube from cathode to plate. A milli-ammeter is in series with the line from the regulator to the photo-tube. One.milli-amp. corre- sponds to about 1200 volts. This voltage should not be exceeded to avoid harming the photo-tube. A value of 750 to 900 volts was found satisfactory to produce sufficient amplification of the signal and yet keep the noise level at a minimum. The micro-ammeter mounted in the amplifier measures the d.c. anode current of the photo-tube. The larger this current becomes the greater the fatigue of the tube and consequent loss of sensi- tivity. Therefore, the tube should be Operated at all times with the least current possible and still obtain the signal strength desired. Two-hundred and fifty micro-amps. is a maximum value of anode current quoted by the manufacturer. In measurement work one should try to keep the current well below 10 micro-amps. 27 There are four connections or plugs associated with the amplifier (see Figure 4). The first is a five plug connection carrying a negative 2000 volts on 1A, a positive 250 on lC with 13 as their common ground. 1D and 1E complete the 24 volt filament circuit. Plug 2.18 the connection between the amplifier and the photo-tube chassis. 2A is the regulated negative high voltage, 2D carries the signal, while 2C is the common ground. The third connection is provided for the signal output and black is the common ground, while the red terminal is a connection for the signal proper. vThe fourth plug must be connected to a 110 volt supply for the regulator tube filament power. The constancy Of the frequency of the sound source is critical because of the sharp selectivity Of the amplifier. This was checked continuously during measure- ments by applying the output of a microphone on the vertical input of an oscilloscope. The horizontal input of the oscilloscope was connected to a H. P. audio- oscillator and the lissajous figure was then observed. In this manner appropriate frequency adjustments of the sound could then be made. Optical System The optical system consists of two compound lenses L1 and L2, as shown in Figure 10, together with a mercury green filter placed as shown.in Figure 17. The lenses are high quality projection lenses; L1 has a focal length of approximately 25 cm. and L2 has a focal length.of about 20 cm. The lenses are mounted on ring stands for ease in adjustment and alignment. . Ll should be placed such that parallel or slightly convergent light enters the interferometer. The focus and height alignment Of the light source may be checked without disarrangement of the apparatus by Observing the image of the aperture on the room wall as it is reflected from the side Opposite the detector of plate 4. ,L2(re- posted for emphasis) simultaneously focuses the fringe pattern from x to the slit, and the slit to the position of X. The image of the slit acts as the limiting port- hole to sample a very small part of the sound wave at a time. Therefore, the fringes are localized atlx in order that L2 may play this double role. The position of L2 controls the magnification of the fringe pattern at the slit and the reduction of the slit image at X. The measure- ments taken were at approximately unit magnification. moumh___. H838 one mo...,............. newer. one woman. .04.. 33mg ‘. ‘. ‘t \- \ HM " ; Ni \ Light Source The light source was a 750 watt mercury vapor arc. The tube itself is about thirteen inches long and one and one-half inches in diameter, and contained within the up- right structure as shown in Figure 10. The upright is made in the form of a double walled chimney. A 24 volt d.c. exhaust fan is mounted at its tap and air is drawn from below and flows around the arc. Two flexible hoses carry the heat from the fan and it may be fed to the build- ing ventilating system. In the chimney are apertures of suitable size (10, ll, 5). shape and alignment to allow the light to pass to the interferometer. The design of the upright is such that different sized or shaped apertures can easily be in. corporated into the framework. The power is obtained from an ordinary 115 volt a.c. line, but the auto transformer can be adapted to work from a variety of the common line sources available. (See appen- dix, Figure 18, for a wiring diagram.) A selection switch enables one to use either 500, 625, or 750 watts at the operator's desire. Not shown in the photograph is a screen constructed of fiber squares the same as those upon.which the interfer- ometer rests. This screen.was used between the source and the interferometer to reduce temperature gradients within the interferometer which cause anomalous fringe shifts. Sound Source A Galton type of whistle was used for a sound source. The whistle was operated by a 45 lbs./sq. in. source of compressed air. It was mounted on an optical bench and is shown in position in Figure 10. The pressure at the whistle was adjustable by a standard welding regulator valve RG. A metal tank approximately three liters in volume was placed in the pressure line as a moisture col- lector. The frequency of the whistle was adjustable by a micrometer screw and has a range of about 5 to 15 kc/s. The sound level was checked by a General Radio Company Type 759 Sound Level Meter and found to have a maximum of approximately 125 Db. at about 8,000 c/s. Not shown in the photograph was a thin flexible plastic (opened refrigerator bag) screen placed between the whistle and the interferometer to reduce the cool air blast from entering the interferometer, thus causing temperature gradients as mentioned above. CHAPTER III CALCULATIONS AND RESULTS Calculations of Fringe Shift from Sound Pressure Calculations relating sound pressure of plane waves to fringe shifts are made by use of the Lorentz-Lorentz (12) formula for the relationship between the index of refraction n and density of the medium P . 2 (l) %i% . 3-5" const. n Since n = 1.0005 for air at room temperature; we can then write to a good approximation (2) (n - l) = CF where C is a new constant. By two assumptions, that air obeys the ideal gas law and that the transmission of sound in air is an adiabatic process, we have the well known relationship (5) 2° . const. ' p“? where p is the pressure and 3' is the ratio of the specific heat at constant pressure to specific heat at constant volume. By rewriting equation (2) we have (4) n-l-kp'x. 35 If we denote the extreme values of pressure along a given light path during a time interval, then the difference in index at corresponding times is found by equation (5) to be (5) n1 .. n2 - 15 (pl"‘- p2“) We now proceed in a manner similar to that of R. B. Kennard (15). From equation (4) (6) k= (n1 -1) pi and substituting into (5) p I (7) n1 - n2 :3 (n1 - l) (1 0(__1_) )0 . _ p2 Let L be the length of the light path, which is subjected to a uniform pressure change along its length (this assumes a plane sound wave). A0 is the wave length of the monochromatic light in a vacuum. The number of wave lengths N0 is given by . 0 X0 If we say that N1 and N2 correspond to n:L and 112 respectively, then (9) n1 ' El . NO ”2 9’1on 34 Let AN 2' NJ. - N2 and substitute equations (8) and (9) into (7) giving K (10) AN = (n:L - 1) XL- (1 -(El.\) . 0 P2 AN represents the number of fringe shifts expected as the pressure swings about the atmospheric pressure pa. Now let (11) P1 = pa -Ap ; p2 +013 where 1' Ap is the peak compressional and rarefactional pressure produced above and below Pa by the sound wave. lApl was found from the relationship (12) .33. + log 2.8 . 10"4 + 103 AP where Db is the decibel rating above the standard 2.8 . 10"4 dy./cm.2llevel. Following is a table prepared from typical values of sound levels ,' wave length of light and length of opti- cal path involved. pa - 1.015 . 106 dy./cm.2 n1 - l " 3 ° .10"4 L-ch. A0 - 5.46 . 10-5 cm. (10.1 - 1h?O 3 44' 55 IF=i.4 x m. 1-(£’_1.) . p2 (SN 100 8.4 - 10‘5 0.0085 120 7.72 . 10-4 0.0540 125 1.57 . 3.0"3 0.0803 130 2.45 - 10-3 0.108 It is apparent from the above table that high sound intensities are required to produce an appreciable fringe shift, Although.125 Db. in the audible range repre- sent a very high intensity (considered as equivalent to the sound level in an airplane engine test room). values of this magnitude are common in the ultrasonic range. Results Figures 11, 12, 15 and 14 are some typical pictures showing the signal obtained with the whistle radiating one arm of the interferometer. The photographs were made from the screen of the oscilloscope by a DuMont type 297 Oscillograph-Record camera. The top and middle print of Figure 11 was taken at 9 kc/s., a slit width of 0.12 mm. and with 40 and 20 lbs./sq. in. pressure on the whistle respectively, while the bottom print shows the noise level without the sound. Figure 12 is a similar series taken at 5.6 kc/s.. a slit width of 0.20 mm. and pressures at 40, 50 and 20 lbs./sq. in. reading from t0p to bottom. . Figure 15 indicates how the signal is modulated. The frequency of the signal was 5.6 kc/s. In the upper line the horizontal sweep was at one-half of the whistle frequency and internal synchronization was used. It shows a family of sine curves at the whistle frequency, the amplitudes of which vary due to the 120 cycle light source intensity variations. The bottom is a picture of the same signal but the horizontal sweep is set at 120 c/s. and the 60 cycle line signal was used for synchroni- zation. This may be thought of as the whistle frequency modulated by the light variation as in the ordinary type of amplitude modulation encountered in AM radio. 57 ma enamHm Heaven on do» eon» .na .am\.mna om use on .n¢ oesmmoaq waawoan .33 cm. macaw beam e\ox c.m monoaaehu AH Chandl 338 3 n3 lob .5 .uu\.3~ o e5 on .9 833.3 g .I 3. 53- and» w\ax a honourehu acheuudm oqoom no eoaanenu esofipwmom massage mzoaaa> .ea shaman .30 mm a aooaon .50 on n canoes .50 04 a no» and uvuodouohuou:« on magmas: ho oocdumwu «Samoyed ogoom ho moadadxm conueaseoa seamen .na seamed «\0 owe . eoaaon endow on a canons u\oa e.m - do» noose «duaouwuo: «\om 2.0 mucosaoau aoqwau 59 The three exposures of Figure 14 were taken at 9 kc/s. and at 15 lbs./sq. in. blowing pressure but the whistle was placed at 16, 56 and 56 cm. from the position of the slit image in a line perpendicular to the light beam. If one had a point sound source, emitting spheri- cal waves, then the exposures from top to bottom should show an amplitude decrease as the inverse of the distance from the light beam to the whistle. No particular effort was made in this investigation to obtain such a source or to damp the sound wave after its passing through the interferometer arm. It was observed with the sound level meter that a very small intensity decrease occurred in a distance of 40 cm. from the source as compared to readings taken at the source. The variation of output signal with whistle blow- ing pressure was further investigated. Plots were made while holding constant variables such as selectivity. amplification, photo-tube high voltage and slit width. Figure 15 shows four of these curves obtained at different sound frequencies, and the linear relationship (within anomalous fluctuations) between the output and pressure can be observed. The relative signal measurements were recorded from the oscilloscope face. 4O 0.53mi 93.8.3 no .3302 e no 2525 1.33 .3. one»: .5 2.2.2:. 5 .335. 05 ecu 93:93 05.0.3 _ . r14! - -2! i i n _ H x . m o.» . w . n x, I. ., an H e _, O O m x o i 1 iii 1-.-!!! ad m {on o e 0 {on e x I (on e.» o e {2. a.» I #1 on 41. Plots of the relative signal strength.as a function of slit position across the entire fringe pattern were made to determine if a maximum signal would be obtained if the slit was located in the region of the maximum slope of the light intensity curve of a single fringe and in the region of the greatest fringe contrast. One of these plots was made with the interferometer and associ- ated optical train producing ten dark fringes in a field 5 cm. wide at the detector. Figure 16 shows measurements taken across the central one-third of this pattern. This portion contained the zero order fringe and the strongest signals were produced in this portion of the pattern, while as in all such measurements taken, if the slit was located at the fringes nearer the edge of the pattern, a signal of lower amplitude was produced. It was also clearly seen that a maximum signal was obtained when the position of the slit was midway between a dark and a bright fringe, which is the theoretical position of maxi- mum light intensity slope. 42 cousenom manage seam oseaeaom on» no seasons. a no unease Aeneas .ea ensue. :8 5 53qu 093.6 no once IE 0.3". «e 693:9— ”.o sn.u - menu ea.» no.4 .n\ox 0.0 o 305 .I 03. u 533 and. 5.253... .353 .555: 3 neonate“. 53.335 053 lid:- ufi. lique- uo 1.3.33.— w:3923~d a news: 33.9.8 3.. man-«3:3 c.339— .3 n a uo 735-23 H9368 7 — — ands-Eco. ensues”:— uanwoua one 603043.33 0w < I'l ‘ fl: K .110“ m IQ” CHAPTER IV SUMMARY AND CONCLUSION Figure 17 presents a complete photograph of the apparatus used. The 750 watt mercury arc is at the ex- treme upper right. Its light is collimated by the lens L1 and illuminates the Mach-Zehnder interferometer. A fringe pattern is obtained and localized directly before the whistle. L2 projects the fringes through the green line filter F to the slit. A photo-tube is mounted directly behind the slit. The changing pressure associated with a sound produces a shift in the fringe pattern. The image of the slit in the interferometer samples a small portion of the sound wave that causes the shift. A light in- tensity variation thus produced is presented to the photo- tube: the output signal which is at the frequency of the whistle and is amplitude modulated by the alternating light source, isthen amplified by the selective ampli- fier. The amplifier together with a vacuum-tube volt- meter and oscilloscOpe, either of which can be used to measure the final signal strength, are shown in the lower part of the photograph. Included in the photograph is the sound frequency measuring equipment consisting of the micrOphone M and the second oscilloscope. .cu.--"' .. II ewe-e. .o-.o... I.IeIII-.Ie use... ."."¢IO-.o.o 0.0.0....- .ICCOOOCOIII I .. I eeeIIIIIO wool..- IIIIOIIOI IIIuo e I ......OIOIOOIOO 45 Figures ll, 12 and 15 show that the final signal observed was directly proportional to the pressure excit- ing the whistle. Signals were obtained in the continuous frequency range of from 5.5 to 10 kc/s. and from 5 to 45 lbs./sq. in. whistle blowing pressure. Results such as presented in Figure 16 show that two positions of minimum and two of maximum signal are observed as one locates the slit at different positions across one complete light-dark fringe. This was to be eXpected since the static fringe pattern intensity distri- bution is a cosine squared function and the signal may be thought of as being produced by a small periodic varia- tion along the light intensity distribution function, which contains two points of maximum lepe in one complete wave form. It is therefore shown by the qualitative results as presented in the previous pages that the method investi- gated, employing the Mach-Zehnder type of interferometer, can be used to measure quantitatively the absolute pressure in a sound field. It has the advantages of.non-distortion of the sound field and the measurement rests upon.well estab- lished pressure, density and index of refraction relation- ships. FUrthermore, the method has the advantage that a very small part of the sound field is sampled at a given time and therefore the method can even be extended to 46 measurements of sound pressures of the shorter ultrasonic waves and still be free from averaging effects. BIBLIOGRAPHY 1. Timbrell, V. Absolute Measurement of Sound Pressures at High Frequency. Nature. 167: 506-7, Feb. 24. 1951. 2. Macy, H. D. Design and Construction of a Mach Inter- ferometer. Unpublished M.S. Thesis, Library of Physics and Mathematics. Michi an State College, East Lansing, Michigan. (1949 22 pp. 5. Price, aw. Initial Adjustment of the Mach-Zehnder Interferometer. Review of Scientific Instruments. ‘4. Winckler, J. Mach Interferometer Applied to Studying an.Axia11y Symmetric Supersonic Air Jet. Review of Scientific Instruments. 19: 507-525, May. 1948. 5. Winkler, E. H. Analytical Studies of the Hach-Zehnder Interferometer. Naval Ordnance Laboratory Report No. 1077, Dec. 5, 1947. 6. Marshall, F., J. W. Coltman and A. I. Bennett. The Photo-Multiplier Radiation Detector. Review of Scientific Instruments. 19: 744-70, Nov. 19, 1948. 7. Kessler. K. 0.. and R. A. wolfe. Heasurement of the Intensity Ratios of Spectral Lines with Electron Multiplier Photo-Tubes. Joppp§l of the Optical Society of America. 57:5: 155- 45, March, 94 . 8. Villard. 0. 0., Jr. Selective A-F Amplifier. Electronics. p. 27, July, 1949. 9. Villard, O. G. Jr.. and D. K. weaver, Jr. The Selecto- Ject. QS . 55: 11-17, Nov.. 1949. 10. Bennett. F. D. Optimum Source Size for the Mach- Zehnder Interferometer. J0urpgl of Applied Physics. 22: 184-190, Feb., 1951. 11. Bennett, F. D. Effect of Size and Spectral Purity of Source on Fringe Pattern.of the Mach-Zehnder Interferometer. Journal of Applied Physics. 22: 776-779. June. 1951. 48 12. Lorentz. H. A. The Theor of‘Electron , G. E. Stechert and Company, New York (1909) Reprint 1923 . p. 1450 15. Kennard, R. B. Temperature Distribution and Heat Flux in Air by Interferometer. Chap. VIII - Special Applications and Methods. Tem erature. Its Measurement and Control in Science and In- dustry. Editors - American Institute of Physics Symposium held in New York, Nov.. 1959. Rein- hold Publishing Corp.. 550 W. 42nd. St., New York. .pp. 689-96. 14. McDonald, K. L.. and F. S. Harris, Jr. Diffraction . of Spherical Scalar waves by an.Infinite Half- Plane. Journal of the Optical Society of America. 42:5: 524-26, May. 1952. APPENDIX APPENDIX One of the next steps to be considered as a con- tinuation of this project would be the calibration of the instrument for absolute measurements.' Timbrell (1) uses a glass windowed cell in the arm of the interfer- ometer at a position X (see Figure l). The windows of . the cell must be parallel flats to prevent fringe dis- tortion and they must be compensated in the other arm II of the interferometer by an equal thickness of optically parallel glass to retain fringes of sharp contrast. The cell can be pressurized to a static value and, by means of a d.c. coupled amplifier, a calibration of the fringe shift with measurable pressures can be made. He also includes another set of windows that are part of a tube through which the sound may be propagated. This suitably constructed tube would allow one to propa- gate the beam (by machining a hole in the base of Macy's interferometer) in a direction perpendicular to the light beam and such that disturbance of the other arm of the interferometer would be minimized or eliminated. The second set of windows would again have to be compensated with glass in the undisturbed beam. This author would suggest trying to reduce the number of additional plates necessary, from eight to four, by the combination of the ii pressure cell and sound tube into one unit, or perhaps incorporate the compensating plates into a pressure tight calibrating cell. One might investigate a method of calibrating the instrument by plotting the light intensity distribution across the fringe pattern. then calibrate the intensity change required to give a certain signal output from the photo-tube. One could then find the amount of fringe shift causing the signal and thus the pressure change causing the shift. The instability of the signal output experienced in this preliminary work is believed to be caused by a combination.of the following factors. Disturbances of both arms of the interferometer by the sound, temperature gradients in the interferometer from the heat of the light source and from the cool air supplying the whistle and thus a fringe drift, variation in the illumination of the light source, and by dark current or random noise of the photo-tube. The first may be eliminated or reduced by con- struction of the sound tube described and placing it in a direction normal to the plane of the centers of the interferometer plates, such that its terminating end is highly sound absorbent. Temperature control could be more easily accomplished if the sound were thus confined. iii It would allow one to enclose the interferometer in a - Jacket such that a constant temperature could be main- tained by perhaps a flow of water about the Jacket. The degree of stability of the fringe pattern may be estab- lished by the superposition of two curves similar to that of Figure 16. Variations in the illumination of the light source could be reduced by the construction of a regulated voltage supply. McDonald and Harris (14) re- port the design of a refrigerated photo-tube mount that greatly reduces dark current and base leakage. If the sound tube is to be constructed. then the use of horizontal fringes will be necessary. Particular attention should then be given to the design of suitable shaped apertures for the best definition of fringes. One may consult Bennett (10, 11) or Winkler (5). Some con- fusion exists in Winkler's notation of the fringe orienta- tion angle ,0 but it is believed by this author that he is in agreement with Bennett. It is suggested that a careful study be made re- garding the ideal relationship of slit width to the width of the fringe pattern. If the anomalous fringe drift is reduced then it is believed that a much narrower slit opening could be used and the detection of smaller fringe shifts accomplished. iv The following hints are offered to anyone using the apparatus. Localize the fringes at the position of the sound wave in the interferometer by the parallax method, then place L2 in position such that the fringes are focused on the slit and the image of the slit is at the position of the real fringes. Next set the frequency of the selective amplifier at the frequency of the sound by a signal from the H. P. audio-oscillator that coincides with the micrOphone output of the sound source. Set the selectivity Just below the point of oscillation at this frequency, then one is ready to apply the high voltage to the photo-tube. Open the slit until a desired signal is obtained and yet keep the photo-tube anode current to a minimum. There is considerable backlash in the translating controls of the interferometer and Skewing of plates 2 and 5 results when the direction of thrust is reversed. It is convenient if one needs to move the central fringe across the field,to do it in the following manner. For example, make all movements to the right with the proper rotztion of T2, and all movements of the central fringe to the left with T5. These adjustments can be reversed after some length of time if the light paths become too long or too short, as the case may be. v There were pronounced anomalous fringe shifts ob- served at about 8.4 kc/s. This phenomenon is observed with the naked eye and is believed to be a resonant mechanical vibration of one of the interferometer plates at this particular wave length. As a matter of interest the original detection of the sound pressure varying the fringe pattern was seen by the naked eye in the following manner. The central fringe with chromatic light was obtained; the fringe pattern was then broadened until approximately two dis- torted fringes covered the entire field of view. This pattern gave a maze of color combinations intricately entwined. One could then observe particularly narrow bands of prominent colors. Upon introduction of the sound beam into one arm of the interferometer the parti- cular color noted would change shades due to the fringe shift. I A circuit diagram.f0110ws of the light source, to- gether with.the measured values of the variable reactor. It is the variable reactor that enables one to readily select different light intensities. ’hl ' --‘8 Figure 18* L1 - 0.145 hy. L2 - 0.161 hy. L5 - 0.177 hy. t4 - 0.195 hy. L5 - 0.215 hy. If the transformer is operated on a line voltage of 115 volts with the input connected across 110-115 as shown, then the power dissipated in the mercury arc: ;\ - Reactance Powegf \I“ .1 L5 ‘ 500 watts\ ‘\\ ~_ ‘5; L4 625 watts “““““ iv'\i 750 181313 . to ES HICHIGQN STRTE UNIV. LIBRQRIES lllllllllllIlllllHlIlllllllillfl||||lIll|||l||l||||1lllllllll|| 31293016978482