Diffraction of light due to ultrasonic wave propagation in liquids

Size: px

Start display at page:

Download "Diffraction of light due to ultrasonic wave propagation in liquids"

Primrose Cobb
5 years ago
Views:

1 Diffraction of light de to ltrasonic wave propagation in liqids Introdction: Acostic waves in liqids case density changes with spacing determined by the freqency and the speed of the sond wave. For ltrasonic waves with freqencies in the MHz range, the spacing between the high and low density regions are similar to the spacing sed in diffraction gratings. Since these density changes in liqids will case changes in the index of refraction of the liqid, it can be shown that parallel light passed throgh the excited liqid will be diffracted mch as if it had passed throgh a grating. The experiment can serve as an indirect method of measring the velocity of sond in varios liqids. The phenomenon of interaction between light and sond waves in a liqid is called the Debye-Sears effect. Objective: 1. To stdy the diffraction of light de to propagation of ltrasonic wave in a liqid 2. To determine the speed of sond in varios liqids at room temperatre 3. To determine the compressibility of the given liqids. Apparats: 1. Radio freqency oscillator fitted with a freqency meter 2. Qartz crystal slab fitted with two leads 3. Spectrometer 4. Glass cell with sample liqid (kerosene/tolene/trpentine oil etc) 5. Sodim lamp 6. Spirit level. Theory and evalation: Diffraction phenomenon similar to those with ordinary rled grating is observed when Ultrasonic waves traverse throgh a liqid. The Ultrasonic waves passing throgh a liqid is an elastic wave in which compressions and rarefactions travel one behind the other spaced reglarly apart. The sccessive separations between two compressions or rarefactions are eqal to the wavelength of ltrasonic wave, λ in the liqid. De to Last pdated in Dec 2017 NISER Page 1

2 reflections at the sides of the tank or the container, a stationary wave pattern is obtained with nodes and antinodes at reglar intervals. We are ths dealing and hence having a periodically changing index of rarefactions which prodces diffraction of light according to the grating rle. If λ denotes the wavelength of sond in the liqid, λ the wavelength of incident light in air and θ n is angle of diffraction of n th order, then we have, d sinθ n = nλ In a transparent medim, variations in density correspond to variations in the index of refraction and therefore a monochromatic parallel light beam traveling perpendiclar to the sond direction is refracted as if it had passed throgh a diffraction grating of spacing d =λ, Where d is eqal to λ, ths- λ sinθ n = nλ If ν is the freqency of the crystal, the velocity of ltrasonic wave in the liqid is given by, = νλ Ths, by measring the angle of diffraction θ n, the order of diffraction n, the wavelength of light, the wavelength of ltrasonic wave in the liqid can be determined and then knowing the freqency of sond wave, its velocity can be obtained. Compressibility of liqid, K The speed of sond depends on both an inertial property of the medim (to store kinetic energy) and an elastic property (to store potential energy): = elastic property inertial property For a liqid medim, the blk modls E acconts for the extent to which an element from the medim changes in volme when a pressre is applied: B = p Last pdated in Dec 2017 NISER Page 2

3 Here / is the fractional change in volme prodced by change in pressre P. The sign of and P are always opposite. The nit of E is Pascal (Pa). Therefore, the speed of sond in liqid can be expressed as νλn = = sinθ E ρ E = 2 ρ = 1/ K Where, E = Blk modls of Elasticity ρ = Density of liqid. K= the compressibility of the liqid Figre 1: The schematic of the ltrasonic diffraction experiment Procedre: 1. Switch on the sodim vapor lamp (if it is not on) and wait for 15 mintes to get the intense light. 2. Check for basic adjstment of the spectrometer. If needed level it taking help of the spport manal for the spectrometer. 3. Place the glass cell containing the experimental liqid (i.e. kerosene oil or others) on the central part of the prism table. 4. Mont the transdcer (qartz crystal in its holder) and dip it exactly parallel in the liqid near a wall of the glass cell so that the ltrasonic waves prodced by the crystal travel in the liqid in a direction perpendiclar to that of the incident light. Connect the leads of the transdcer with the otpt terminals of the RF Oscillator. 5. See throgh the telescope eyepiece so that a sharp well defined image of the slit is seen in the field of view in the centre of the micrometer scale fitted in the eyepiece. Last pdated in Dec 2017 NISER Page 3

4 6. Now switch on the RF Oscillator. Adjst the freqency of the Oscillator to generate the ltrasonic wave (of the order of ~2MHz) so that it becomes eqal to the natral freqency of the crystal slab. At this stage resonance takes place and diffraction images of the slit will be seen in the telescope. Note the freqency of the RF Oscillator and maintain it constant throghot the experiment. 7. Using the vernier scale on the angle display window, measre the angles corresponding to m = 0, m = ±1 and m = ±2. Use the data to find ot the wavelength of the sodim light. Observations: Least Cont of Spectrometer = Freqency of ibrating crystal = Density of liqid = Table: (Make separate tables for different liqids) Order Left of Right of Central Central a a b b Set-I 2θ = (a b) 2θ = (a -b ) Average 2θ θ (m/s) Set-II Set-III Order (m/s) Mean Set-I Set-II Set-III (m/s) Sample reslt for trpentine oil is m/s Reported vale 1 of the mean velocity of ltrasonic wave in trpentine is 1240m/s at room temperatre. Last pdated in Dec 2017 NISER Page 4

5 Reslts and Discssion: 1. Report the mean velocity in each of the liqid. 2. Calclate the Blk modls of Elasticity and compressibility for each liqid 3. Estimate the experimental errors, both by relative error and propagation error. 4. Compare the reslts with data from the literatre. Precations: 1. Rotate the knob on the RF oscillator extremely slowly to vary the freqency. 2. This experiment reqires precision in taking readings, especially the mintes in the spectrometer scale. 3. The crystal shold be monted parallel to the side walls, otherwise a good standing wave pattern will not be obtained & hence diffraction grating will not be formed. As a reslt the higher orders may not be of eqal intensity on either side of maxima. Reference: 1. Note: 1. elocity of sond in liqids is temperatre dependent. 2. From this experiment we are determining the blk modls for adiabatic compression becase there is no energy exchanged with the region next to the sond wave. This shold be distingished from the isothermal blk modls. Last pdated in Dec 2017 NISER Page 5

L = 2 λ 2 = λ (1) In other words, the wavelength of the wave in question equals to the string length,

L = 2 λ 2 = λ (1) In other words, the wavelength of the wave in question equals to the string length, PHY 309 L. Soltions for Problem set # 6. Textbook problem Q.20 at the end of chapter 5: For any standing wave on a string, the distance between neighboring nodes is λ/2, one half of the wavelength. The