Good morning everybody I am Dr. Dudai Kumar Khan. Today I am going to give you a demonstration on the experiment to determine the wavelength and velocity of ultrasonic waves in a liquid by studying the diffraction through ultrasonic grating. Before I discuss the the experimental details of this particular experiment, let me first discuss what is ultrasonic waves and how it is generated and how the ultrasonic grating is formed with the help of ultrasonic waves. Soundwave which is capable of making sensation in our ear is having frequency in the range 20 Hz to 20 kHz.
And the soundwave which has the frequency above that, that is when the sound wave has the frequency in the range 20 kilohertz to 1 gigahertz, then it is called ultrasonic waves. This particular sound wave cannot make any sensation in our ear. But this particular ultrasonic wave or ultrasonic vibration has many applications.
the study of material solid liquid and gases and how this ultrasonic waves or ultrasonic vibrations are generated These are generated with the help of mechanical generation, with the help of thermal generation or piezoelectric generation etc. In this particular experiment, we are going to use piezoelectric generation of the ultrasonic waves. This piezoelectric crystals are basically these are the non centrosymmetric strong ferroelectric crystals it has a particular property if we apply some alternating voltage to the piezoelectric crystal it will generate a stream in the direction perpendicular to the direction of the alternative voltage and therefore there will be change in the dimension of the piezoelectric crystal.
It will expand and contract according to the frequency of the alternating voltage. And when the frequency of the alternating voltage becomes identical with the natural frequency of the piezoelectric crystal, then this variation of dimension becomes maximum. So it gives rise to a maximum. intense ultrasonic wave so we have to take a crystal and then it should have two terminals to send the Radio frequency signal to the crystal. When the voltage is applied in this direction, then the expansion and contraction will take place along this direction.
So it will expand and contract. Expand and contract. And the example of such type of crystal is the quartz, tourmaline etc.
Now I come to the generation of ultrasonic grating. How it is generated? if we keep a piezoelectric crystal like this inside a medium liquid or gas etc then because of application of the RF signal into the crystal it will expand and contract like this that way the medium We will have a compression and a reaffection periodically. Therefore, there will be a periodic density variation in the medium like this. So, there will be more dense region and less dense region.
So, this is the compression rare fraction. This will give rise to a periodic variation of density within the medium. And thus... The medium will behave like a ruled transmission gating and this is called the ultrasonic gating.
And the wavelength of this ultrasonic wave, lambda A, will have one compression and one rare fraction. This is identical with the plane transmission gating that will have opaque and transmission part. Therefore, As we calculate the grating element for plane transmission grating that is D is equal to A plus B where A is the length of the compression region and B is the length of the rarefaction region.
Therefore B this grating element is equal to A plus B. and this grating element is equal to the wavelength of the ultrasonic wave this is the acoustic wave that's why we label it lambda E and now if Light wave is allowed along this direction which is perpendicular to the direction of the ultrasonic rating. Then the light will pass through the medium and will give rise to diffraction phenomena. similar to diffraction which results from the plane transmission gating.
And on the screen we will see the diffraction pattern. like this. So it will have 0th order and above the 0th order it will have first order on both sides plus 1th order minus 1th order plus 2nd order minus 2nd order like this. Therefore if we compare the result with the condition of diffraction then the condition of diffraction for the nth order peak of the diffraction pattern d sine theta is equal to n lambda L where lambda L is the wavelength of the light pass through the ultrasonic grating. So d sin theta is equal to n lambda l where n is the order number and theta is the angle of diffraction like this.
As I showed you, this lambda A is equal to D. Therefore, we can replace D with lambda A. Then lambda A sine theta is equal to n lambda L and lambda A is equal to n lambda L by sine theta. This is the first working formula to find the wavelength of the ultrasonic waves.
As we know the frequency of the RF signal applied to the piezoelectric crystal, therefore we know the frequency of the ultrasonic wave because that RF signal frequency should match with the natural frequency of the crystal. So we know the frequency nu A of the ultrasonic wave and just now we have obtained the wavelength of the ultrasonic wave. Therefore the product of nu A and lambda A will give rise to the velocity of ultrasonic wave.
So this is another working formula. Now I come to the experimental arrangement of this particular experiment. This entire experimental arrangement is called, this is the optical diffraction method obtained by divine answers.
So the phenomena is called divisors effect. So what we do here, we have a liquid cell of rectangular cell. It's basically a tank.
rectangular tank we have which will have some liquid for our case we are going to use white kerosene then we will have a piezoelectric crystal attached near one of the wall and this crystal should remain immersed within the liquid. Then we have to connect the RF oscillator with the two electrodes we have attached with the crystal. Then we need a sodium vapor lamp set.
that should be collimated with the help of a collimator. So the wavelength of the light is lambda L and the entire arrangement is kept on a spectrometer. This liquid cell or liquid tank will be installed on the prism table and the sodium paper lamp will give rise to light that will be collimated with the help of collimator and then the diffraction pattern will be seen through the telescope.
So, to measure this theta to find the lambda e, that means the wavelength of the ultrasonic wave, this theta can be measured with the help of telescope and the two scales, vernier and main scales attached with the spectrometer. So, by measuring theta for various order of... diffraction peaks we can find lambda A for given lambda L So that way we can find the wavelength of the ultrasonic wave. And as we can read the frequency of the R-A oscillator from the display attached here with the signal generator, then we can calculate the velocity of the ultrasonic wave through this liquid using this formula. So now I am going to give you demonstration of the experiment so let's do the experiment this is my entire experimental setup for the optical diffraction method I have sodium vapor lamp here then a spectrometer this is collimator this is telescope For measurement I have the two scales, bhania and men's scale.
This circular scale is there. So I have two bhania scales A and B. Then I have the prism table and on top of the prism table I have the liquid tank.
Then I have the piezoelectric crystal here. This round shaped crystal is having two terminals for AC voltage to be applied and this has two connectors then I have to pour here the liquid here I am using white Kerosene for my experiment and for the RF signal I have the signal generator here RF oscillator that has a port here to change the frequency and it has output terminals then I have to connect two connector to supply the AC voltage to the piezoelectric crystal So now first I have to fit the crystal. Now there is one entrance slit at this end of the collimator and the light is coming.
through the collimator, going through the tank and then coming to the telescope. And if I look through the telescope, then what we find is the image of the entrance slit. That is a single line is visible here through the liquid tank. Now I have to pour the liquid inside the tank and make the piezoelectric crystal immersed in the liquid. So for that, pouring the liquid, I have to check whether the liquid level is sufficient to immerse the piezoelectric crystal what we find now again I have to check whether I am getting the same image of the slit.
After pouring the liquid in the tank, we again get the same image of the slit of the collimator. Now, I have to connect the RF oscillator with the piezoelectric crystal. I have to connect the RF oscillator with the piezoelectric crystal.
Now I have to switch on the RF oscillator. This pot is at minimum position. Now I have to increase the frequency of the RF oscillator and check when the frequency matches with the natural frequency of the crystal such that resonance occur and amplitude of oscillation becomes maximum and that gives rise to the ultrasonic grating. So I am now increasing the frequency of the Rx oscillator and keeping track whether the diffraction is taking place or not. So increasing.
there is no diffraction, there is no diffraction, there is no diffraction. Here it has started to come, the additional peaks apart from center maximum, 1, 1, plus 1 and minus 1. Peaks have started to come. So we are very close to the natural frequency of the crystal and that frequency is around 4 megahertz. I am getting the diffraction pattern.
So about the zeroth order maximum or principal maximum I am having two numbers of orders plus 1 plus 2 and minus 1 minus 2 about the 0th order peak. So to measure the angle of diffraction of plus 1th order plus second order I have to take the reading here in the vernier A and vernier B in the similar way as we take the reading for the plane diffraction rating. So we can get the order number and the angle of diffraction with the help of telescope.
And then if we put in the formula lambda E is equal to n lambda L by sin theta, we can calculate the wavelength of the ultrasonic waves. And to measure the velocity of the ultrasonic wave, The formula is Va is equal to mu A and lambda A as I showed you in the whiteboard. So this lambda A I can find the way I discussed just now and to get the frequency of the rf oscillator that is the resonance frequency of the crystal can be obtained from this scale.
which is nearly 4.3 megahertz for this particular crystal it comes around 5 megahertz or so. So knowing the frequency of oscillation and obtaining the wavelength of the ultrasonic wave we can find out the velocity of the ultrasonic wave through the kerosene. A few points I want to mention here to get best result out of this experiment we have to mount the piezoelectric crystal parallel to the wall of the liquid tank and we have to make sure that the wave is coming this way so, wave is propagating in the horizontal direction from this end to the other end of the liquid tank and we have to make sure that the wave is coming this way But the waves should not reflect back and should not form any standing wave pattern within the liquid. Then we won't get the proper result. And let me then get back to the white board once again.
So I have given you the demonstration how to determine the wavelength and velocity of ultrasonic waves in a liquid by studying the diffraction through ultrasonic grating and the experimental arrangement I had like this One point should be mentioned, the spectrometer should be labeled properly with the help of spirit level and the suster focusing etc. before doing the experiment. Now I come to the application of this experiment. Apart from obtaining the wavelength and the velocity of the ultrasonic wave, this particular experiment can be used to calculate the bulk modulus of the liquid used in this experiment such as the bulk modulus of the white kerosene can be obtained the formula is like this formula is bulk modulus rho V square, Vs square, where rho is the density of the liquid. And this experiment can also be used to find the adiabatic compressibility of the liquid used in the experiment. And that formula is adiabatic compressibility is equal to 1 by rho Vs coil.
So this is for the adiabatic compressibility and this is for bulk modulus K is equal to. So I hope you all will be able to perform the experiment in the laboratory. Thank you. Thank you for watching this video.
Have a nice day.