Figure 7.1 Ultrasonic Interferometer Figure 7.2 Maxima and minima in the ammeter reading Department of Physical Sciences, Bannari Amman Institute of Technology, Sathyamangalam 58
Adiabatic Compressibility Ultrasonic Interferometer Expt. No.: Date: AIM To find the compressibility of the given liquid using ultrasonic interferometer GENERAL OBJECTIVE To study the compressibility of the liquid by measuring the wavelength and velocity of ultrasonic waves in the liquid using ultrasonic interferometer SPECIFIC OBJECTIVES 1. To generate high frequency ultrasonic waves in the liquid using piezoelectric oscillator 2. To form standing waves between quartz crystal and reflector plate 3. To measure the distance d between two successive maxima or minima 4. To find the wavelength and velocity of the ultrasonic waves in the liquid 5. To evaluate the compressibility of the liquid from the formula APPARATUS REQUIRED Ultrasonic interferometer Sample liquid (Water/Kerosene) High frequency generator FORMULA 1. Wavelength of the ultrasonic wave λ = 2d (m) 2. Velocity of ultrasonic waves in a given liquid ν = f λ (m/s) 3. Compressibility of the liquid 1 2 (m 2 /N) Department of Physical Sciences, Bannari Amman Institute of Technology, Sathyamangalam 59
TABLE I To calculate d Least Count (LC) Frequency of the ultrasonic waves = 0.01 mm = 2 10 6 Hz TR = PSR + (HSC LC) S. No. Order of maxima or minima Micrometer reading for n maximum deflections PSR (10-3 m) HSC (div) TR (10-3 m) (n+15) th reading n th reading) = 15 d (10-3 m) d (10-3 m) 1. n 2. n+5 3. n+10 4. n+15 5. n+20 6. n+25 7. n+30 8. n+35 9. n+40 10. n+45 11. n+50 Mean d =. x 10-3 m Department of Physical Sciences, Bannari Amman Institute of Technology, Sathyamangalam 60
Symbol Explanation Unit λ Wavelength of the stationary ultrasonic wave m d Distance between two successive maxima or minima m v Velocity of ultrasonic wave m/s f Frequency of the ultrasonic wave Hz ρ Density of the given liquid kg/m 3 β Adiabatic compressibility of the given liquid m 2 /N PREREQUISITE KNOWLEDGE 1. Ultrasonic waves Ultrasonic waves are the sound waves of frequency above audible range (i.e.) above 20000 Hz. 2. Properties of ultrasonic waves highly energetic travel through long distances undergo reflection, refraction and absorption similar to ordinary sound waves produce stationary wave pattern in liquids of suitable dimension and behave as an acoustical grating generate heat in materials for a longer time of exposure 3. Ultrasonic interferometer An ultrasonic interferometer is a simple and NDT device to determine the ultrasonic velocity in liquids with a high degree of accuracy. 4. Standing wave It is a wave in a medium in which each point on the axis of the wave has an associated constant amplitude. 5. Adiabatic compressibility Compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change. Department of Physical Sciences, Bannari Amman Institute of Technology, Sathyamangalam 61
CALCULATION 1. Wavelength of the ultrasonic wave λ = 2d (m) 2. Velocity of ultrasonic waves in a given liquid ν = f λ (m/s) 3. Compressibility of the liquid 1 2 (m 2 /N) Department of Physical Sciences, Bannari Amman Institute of Technology, Sathyamangalam 62
PROCEDURE 1. Ultrasonic interferometer is used to determine the velocity of ultrasonic waves in liquids. It consists of a high frequency generator and a measuring cell. 2. The high frequency generator is used to excite the quartz crystal fixed at the bottom of the measuring cell. The measuring cell is a double walled cell to maintain the temperature of the cell at a constant value. 3. The measuring cell is connected to a high frequency generator. The cell is filled with the given liquid and the frequency of the generator is set at a desired value. 4. Then ultrasonic waves are reflected back from the movable plate, and standing waves are formed between the quartz crystal and the reflector plate. 5. The micrometer screw is moved till the anode current reaches maximum. Microammeter readings are noted for n number of maxima / minima. 6. The distance d between two successive maxima and minima is obtained from the readings taken. 7. The wavelength of the ultrasound is calculated using the d value and hence the velocity of the ultrasonic wave can be calculated using the known frequency. 8. The compressibility of the given liquid is determined by knowing the density of the given liquid. Department of Physical Sciences, Bannari Amman Institute of Technology, Sathyamangalam 63
Department of Physical Sciences, Bannari Amman Institute of Technology, Sathyamangalam 64
RESULT 1. The wavelength of ultrasonic wave is λ =.. m 2. The velocity of ultrasonic waves in the given liquid =..m/s medium is ν 3. The adiabatic compressibility of the given liquid β =. m 2 /N APPLICATIONS Detection of flaws in metals, SONAR for detection of submarines, iceberg and other objects in ocean, soldering and metal cutting, diagnostics applications such as detection of tumors and defects in human body, ultrasonic cleaner and humidifier. VIVA VOCE QUESTIONS 1. Why ultrasonic waves are not audible to humans? 2. Are ultrasonic waves electromagnetic waves? Comment. 3. Define acoustic grating. 4. List two methods to produce ultrasonic waves. 5. Name two technological importance of measuring the velocity and adiabatic compressibility of liquids. STIMULATING QUESTIONS 1. How do bats locate the prey and objects? 2. Recognize how dolphins communicate with each other. 3. Can we calculate adiabatic compressibility for a solid? Department of Physical Sciences, Bannari Amman Institute of Technology, Sathyamangalam 65