Experiment 29Measurement of Sound VelocitybyUltrasonic Grating1Experiment29MeasurementofSoundVelocitybyUltrasonic GratingAcousto-optic effect refers to the phenomenon of diffraction when light passesthrough the medium disturbed by ultrasonic wave. This phenomenon is the result of theinteraction between light and sound wave in the medium. As the density of liquid ismodulated by ultrasonic wave, the uniform and transparent liquid becomes an"ultrasonic grating" with its refractive index changing periodically. When the lightbeam passes through the liquid, diffraction phenomenon happens, thus the propagationvelocity of sound wave in liguid can beaccuratelymeasured.As early as 1921, L.Brillouin predicted that high-frequency sound waves inliquids make the visible light diffract.Ten years later, acousto-optic diffraction wasobserved by P. J. W. Debye, F. W. Sears, R. Lucas and P. Biquard, respectively. After1960s, with the emergence of laser technology and the development of ultrasoundtechnology, the acousto-optic effect had been widely used. For example, acousto-opticmodulatoranddeflectorcanquicklyandeffectivelycontrolthefrequency,intensityanddirection of the laser beam. At present, acousto-optic effect is of great significance inthe applications such as laser technology, optical signal processing and integratedcommunication technology.Experimentalobjectives1. Understand the principle of acousto-optic diffraction2. Measure the sound velocity in liquid by ultrasonic gratingExperimental content1. Understand the experimental principle of acousto-optic effect2. Learn the method of measuring the sound velocity in liquid by using an ultrasonicgrating3. Learn the method of light alignment and the usage of the reading microscopesExperimentalinstrumentsUltrasonic signal source,low pressure sodium lamp,optical guide, optical slit, lensultrasonic pool,micrometer eyepiece and high-frequency wireExperimental principleUnder the action of alternating electric field from high frequency power supplypiezoelectric ceramic transducer (PZT) generates periodic compression and elongationvibration, which transmits in liquid to form ultrasonic wave.Ultrasonic wavecan bedivided intotravelling waveand standingwave.Whenultrasonic waves travel inliquidthe sound pressure makes the liquid molecules change periodically. The liquid will
Experiment 29 Measurement of Sound Velocity by Ultrasonic Grating 1 Experiment 29 Measurement of Sound Velocity by Ultrasonic Grating Acousto-optic effect refers to the phenomenon of diffraction when light passes through the medium disturbed by ultrasonic wave. This phenomenon is the result of the interaction between light and sound wave in the medium. As the density of liquid is modulated by ultrasonic wave, the uniform and transparent liquid becomes an "ultrasonic grating" with its refractive index changing periodically. When the light beam passes through the liquid, diffraction phenomenon happens, thus the propagation velocity of sound wave in liquid can be accurately measured. As early as 1921, L. Brillouin predicted that high-frequency sound waves in liquids make the visible light diffract. Ten years later, acousto-optic diffraction was observed by P. J. W. Debye, F. W. Sears, R. Lucas and P. Biquard, respectively. After 1960s, with the emergence of laser technology and the development of ultrasound technology, the acousto-optic effect had been widely used. For example, acousto-optic modulator and deflector can quickly and effectively control the frequency, intensity and direction of the laser beam. At present, acousto-optic effect is of great significance in the applications such as laser technology, optical signal processing and integrated communication technology. Experimental objectives 1. Understand the principle of acousto-optic diffraction 2. Measure the sound velocity in liquid by ultrasonic grating Experimental content 1. Understand the experimental principle of acousto-optic effect 2. Learn the method of measuring the sound velocity in liquid by using an ultrasonic grating 3. Learn the method of light alignment and the usage of the reading microscopes Experimental instruments Ultrasonic signal source, low pressure sodium lamp, optical guide, optical slit, lens, ultrasonic pool, micrometer eyepiece and high-frequency wire Experimental principle Under the action of alternating electric field from high frequency power supply, piezoelectric ceramic transducer (PZT) generates periodic compression and elongation vibration, which transmits in liquid to form ultrasonic wave. Ultrasonic wave can be divided into travelling wave and standing wave. When ultrasonic waves travel in liquid, the sound pressure makes the liquid molecules change periodically. The liquid will
Experiment 29Measurement of Sound VelocitybyUltrasonic Grating2compress and expand periodically,causing the density of the liquid change periodicallyin the direction of wave travelling,forming the so-called density wave.Periodicchanges inthedensity ofthe liquid leadtoperiodic changes intherefractive index ofit. Just like a phase grating, if parallel light pass through the liquid perpendicularly tothe direction of the ultrasonic wave travelling, it will be diffracted. The ultrasonic fielddiscussed above,causing the density of the liquid distributes hierarchically,is intheform of traveling wave.In this experiment,the ultrasonic wave travels in a pool withfinite size,forming a stable standing wave.Since the amplitude of the standing wavecan betwice as large as that of thetraveling wave,the changes of liquid density areintensifiedand it is easier to observe the stablephenomenonof diffraction.Theexperimental light path is shown in Figure. 29-1, where S is the light slit, Li and L2 arelenses.ultrasonicpoolLiPZTFigure 29-1Optical path of ultrasonic gratingIf the ultrasonic traveling wave propagates along the positive direction of the zaxis in theform of planewave,the waveequation can bewritten as:y= Amcos2元(二_三)(29-1)TaWhere,yrepresents thedisplacement ofeachparticlefrom its equilibriumpositionalong the Z axis direction, A represents the maximum displacement of the particle; Tsrepresents theperiod ofultrasonicwave,,is thewavelengthofultrasonicwave.Ifthe ultrasonic wave is reflected by the plane of the liquid groove perpendicular to the Zaxis, it will propagates backward. When the reflected plane is odd times the length of aquarter of the wavelength away from the wave source, the incident wave and thereflected wave are respectively:Ji= Amcos2元(元
Experiment 29 Measurement of Sound Velocity by Ultrasonic Grating 2 compress and expand periodically, causing the density of the liquid change periodically in the direction of wave travelling, forming the so-called density wave. Periodic changes in the density of the liquid lead to periodic changes in the refractive index of it. Just like a phase grating, if parallel light pass through the liquid perpendicularly to the direction of the ultrasonic wave travelling, it will be diffracted. The ultrasonic field discussed above, causing the density of the liquid distributes hierarchically, is in the form of traveling wave. In this experiment, the ultrasonic wave travels in a pool with finite size, forming a stable standing wave. Since the amplitude of the standing wave can be twice as large as that of the traveling wave, the changes of liquid density are intensified and it is easier to observe the stable phenomenon of diffraction. The experimental light path is shown in Figure. 29-1, where S is the light slit, L1 and L2 are lenses. If the ultrasonic traveling wave propagates along the positive direction of the Z axis in the form of plane wave, the wave equation can be written as: cos2 ( ) s s m z T t y A = − （29-1） Where, y represents the displacement of each particle from its equilibrium position along the Z axis direction; A represents the maximum displacement of the particle; Ts represents the period of ultrasonic wave; λs is the wavelength of ultrasonic wave. If the ultrasonic wave is reflected by the plane of the liquid groove perpendicular to the Z axis, it will propagates backward. When the reflected plane is odd times the length of a quarter of the wavelength away from the wave source, the incident wave and the reflected wave are respectively: cos2 ( ) 1 s s m z T t y A = − ultrasonic pool zz L1 L2 Φk ƒ S lk PZT Figure 29-1 Optical path of ultrasonic grating
Experiment 29 Measurement of Sound Velocity by Ultrasonic Grating32=Amcos2元(二+二)儿Add up the two equations above:y=)+号=24gcos2元元cos2元元(29-2)Ts1According to formula 29-2, the superposition result is standing wave, and theamplitude of each point along the Z direction is 2Am cos 2/2s. It is a function of Z,changing periodically with Z but not with time. Phase 2元t/T, is a function of time t,but do not changewith space.Forthe standing wave,at a certain time t, the particlesonboth sides of a certain nodesurgeto it,makingtheareanearthis nodebecomeadense area, while the areas near the two nodes adjacent to this one becomes a sparsearea of theparticles.andthedensityoftheliquidatantinodes remains unchanged.Afterhalf of a periodic, t+T/2, the particles on both sides of this node diffuse to the left andright, making the vicinity of the node become a sparse area of the particles, the vicinityof thetwo adjacent nodesbecomesa dense areaoftheparticles,and thedensityof theliquid at antinodes remains unchanged. Figure 29-2 shows the variation curves forstanding wave shape, liquid density distribution and refractive index at the twomoments t and t+T,/2. As can be seen from the figure, at a certain moment t, thedistance between two adjacent dense regions is As, which is the wavelength of thetravelling waves in liquid. For any two points with a distance As between them, thedensity and refractive index of the liquid are the same.As shown in Figure 29-1, it can be considered that the periodic distribution of thedensity and refractive index of the liquid in the process of the light passing through theultrasonic grating has no obvious change, since the light speed is much greater than thesound speed in liquid, that is, for the light wave, the ultrasonic grating can be regardedas static. Therefore, the position of the central principal maximum of the lightdiffraction can be determined by the grating equation,dsin=ka(k =0,±l,±2,..)(29-3)Where, is thek-order diffraction angle; is the wavelength oflight wave;, d= As, thatis, the wavelength of ultrasonic wave corresponds to the grating constant. Since theangle is small, one can think of it as:
Experiment 29 Measurement of Sound Velocity by Ultrasonic Grating 3 cos2 ( ) 2 s s m z T t y A = + Add up the two equations above: s s m T z t y y y A = 1 + 2 = 2 cos2 cos2 （29-2） According to formula 29-2, the superposition result is standing wave, and the amplitude of each point along the Z direction is 2𝐴𝑚 cos 2π⁄λs . It is a function of Z, changing periodically with Z but not with time. Phase 2πt/Ts is a function of time t, but do not change with space. For the standing wave, at a certain time t, the particles on both sides of a certain node surge to it, making the area near this node become a dense area; while the areas near the two nodes adjacent to this one becomes a sparse area of the particles, and the density of the liquid at antinodes remains unchanged. After half of a periodic, t+T/2, the particles on both sides of this node diffuse to the left and right, making the vicinity of the node become a sparse area of the particles, the vicinity of the two adjacent nodes becomes a dense area of the particles, and the density of the liquid at antinodes remains unchanged. Figure 29-2 shows the variation curves for standing wave shape, liquid density distribution and refractive index at the two moments t and t+Ts/2 . As can be seen from the figure, at a certain moment t, the distance between two adjacent dense regions is λs, which is the wavelength of the travelling waves in liquid. For any two points with a distance λs between them, the density and refractive index of the liquid are the same. As shown in Figure 29-1, it can be considered that the periodic distribution of the density and refractive index of the liquid in the process of the light passing through the ultrasonic grating has no obvious change, since the light speed is much greater than the sound speed in liquid, that is, for the light wave, the ultrasonic grating can be regarded as static. Therefore, the position of the central principal maximum of the light diffraction can be determined by the grating equation, d sink = k (k = 0,1,2, ) （29- 3） Where, Φk is the k-order diffraction angle; λ is the wavelength of light wave; d = λs, that is, the wavelength of ultrasonic wave corresponds to the grating constant. Since the angle is small, one can think of it as:
4Experiment29MeasurementofSoundVelocitybyUltrasonicGratingsin=(29-4)Where, lk is the distance between the zero-order and k-order spectral line for the lightdiffraction,andfisthefocal lengthof thelensL2.Sothewavelengthof theultrasonicwavecanbeexpressedask元kaf1,=-lksin pk(29-5)ThevelocityofultrasonicwaveinliquidiskifvV=A.V=Ik(29-6)Where, v is the vibration frequency of the ultrasonic signal source.sparsedensedensesparsedenseReflectSheetF2densedensesparsesparsesparseReflectn入Sheet1H7nmax4n.Figure 29-2Curves for the standing wave shape, liquid densityand refractive index intwo special moments.Experimentalprocedure1.PlacethedevicesasthelightpathinaccordancewithFigure29-1.Turnonthelow-pressure sodium lamp and adjust its position to make the light on the narrow slit
Experiment 29 Measurement of Sound Velocity by Ultrasonic Grating 4 f l k sin k = （29-4） Where, lk is the distance between the zero-order and k-order spectral line for the light diffraction, and f is the focal length of the lens L2. So the wavelength of the ultrasonic wave can be expressed as: k k s l k kf = = sin （29-5） The velocity of ultrasonic wave in liquid is： k s l k f V v = = （29-6） Where, ν is the vibration frequency of the ultrasonic signal source. Experimental procedure 1. Place the devices as the light path in accordance with Figure 29-1. Turn on the lowpressure sodium lamp and adjust its position to make the light on the narrow slit Reflect Sheet λs λs λs y λs dense dense sparse nmin nmax nmin nmax n0 n0 n n y dense sparse dense sparse sparse sparse dense Figure 29-2 Curves for the standing wave shape, liquid density and refractive index in two special moments. Reflect Sheet
5Experiment 29 Measurement of Sound Velocity byUltrasonic Gratinguniform and symmetrical, and possess suitable intensity.2.AdjustthepositionoftheslitandlensLtomakethecenternormaloftheslitcoincide with the optical axis of lens L (principal optic axis), and the distancebetweenthemisthefocal lengthoflensLi.Thefocal lengthof lens isrequiredtobemeasuredbyautocollimation3.Adjust the height of lens L2 and micrometer eyepiece to make their optical axiscoincide with the principal optic axis. Focus the eyepiece to see the crosshairclearly enough.4.The measured liquid (such as distilled water, ethanol or other liquids) is injectedinto a tank (ultrasonic pool). Put the tank on the fixed support and make the surfacesofthe tank basicallyperpendicular to theprincipal optic axis5.Connect oneend of the high-frequencywire to the bindingpost on the cover plateof the ultrasonic pool, and the other end to the output terminal of the ultrasonicsignal source.6.Adjust the position of micrometer eyepiece and lens La to make the diffractionpatterns in eyepiece clear enough.7.Move the ultrasonic pool forward and backward to observewhether the stripespacing changes or not. If so, change the position of lens L until the stripe spacingremains unchanged8.Adjust the frequency control knob on the ultrasonic signal source instrument tomake the signal frequency the same as the resonant frequency of the PzT. Andthen the quantities of the diffraction fringes will be significantly increased and thespectrum lines will be more bright.Rotate the ultrasonic pool slightlyto make theparallel light beam perpendicular to the pool, and observe the brightness andsymmetry of the diffraction spectral at the same time. Repeat the procedure aboveuntil you see the clear, symmetrical, stable diffraction patterns for three orders (k=±3)in eyepiece.9.Usethemicrometereyepieceto measureandrecord theposition ofeach spectralline.Rotate the microdrum of the micrometer eyepiece unidirectionally to eliminatethe idle error caused by the thread gap of the rotating components (for example, -3.....3.ExtendedcontentObserve and study the variation rules of the ultrasonic grating diffraction patternwhen the frequency of ultrasonic signal is changed
Experiment 29 Measurement of Sound Velocity by Ultrasonic Grating 5 uniform and symmetrical, and possess suitable intensity. 2. Adjust the position of the slit and lens L1 to make the center normal of the slit coincide with the optical axis of lens L1 (principal optic axis)，and the distance between them is the focal length of lens L1. The focal length of lens is required to be measured by autocollimation. 3. Adjust the height of lens L2 and micrometer eyepiece to make their optical axis coincide with the principal optic axis. Focus the eyepiece to see the crosshair clearly enough. 4. The measured liquid (such as distilled water, ethanol or other liquids) is injected into a tank (ultrasonic pool). Put the tank on the fixed support and make the surfaces of the tank basically perpendicular to the principal optic axis. 5. Connect one end of the high-frequency wire to the binding post on the cover plate of the ultrasonic pool, and the other end to the output terminal of the ultrasonic signal source. 6. Adjust the position of micrometer eyepiece and lens L2 to make the diffraction patterns in eyepiece clear enough. 7. Move the ultrasonic pool forward and backward to observe whether the stripe spacing changes or not. If so, change the position of lens L1 until the stripe spacing remains unchanged. 8. Adjust the frequency control knob on the ultrasonic signal source instrument to make the signal frequency the same as the resonant frequency of the PZT. And then the quantities of the diffraction fringes will be significantly increased and the spectrum lines will be more bright. Rotate the ultrasonic pool slightly to make the parallel light beam perpendicular to the pool, and observe the brightness and symmetry of the diffraction spectral at the same time. Repeat the procedure above until you see the clear, symmetrical, stable diffraction patterns for three orders (k = ±3) in eyepiece. 9. Use the micrometer eyepiece to measure and record the position of each spectral line. Rotate the microdrum of the micrometer eyepiece unidirectionally to eliminate the idle error caused by the thread gap of the rotating components (for example, - 3,., 0,., + 3). Extended content Observe and study the variation rules of the ultrasonic grating diffraction pattern when the frequency of ultrasonic signal is changed