Most of the measurements of velocity of ultrasonic waves in liquids since. methods is that progressive waves can be used. But there are a number of

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Ferdinand Garrett
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1 Experimental Methods chapter Introduction Most of the measurements of velocity of ultrasonic waves in liquids since 1932 have involved optical diffraction techniques. The advantage of these methods is that progressive waves can be used. But there are a number of limitations like streaming and sample heating for continuous wave methods. But it is possible with modem electronic equipments to measure with sufficient accuracy, the short time of passage of a pulse through a liquid to estimate its velocity, and the height of the echoes of the pulses can be used to measure ultrasonic attenuation. The notion that propagation of ultrasonic pulses through a medium can be made use of in the investigation of physical properties of the medium have fed to the development of various methods for measuring velocity and attenuation.

2 2.2 Pulse Technique The most widely used method for making ultrasonic measurements in liquids and solids is the pulse technique, introduced by Pellam and Galt in 1946 [I]. A pulse of sinusoidal voltage is applied to a piezo-electric transducer, which is kept in contact with the sample. The transducer converts the electrical pulse into an acoustical pulse that is transmitted in to the medium. Typically the voltage amplitude is between a few volts and a few hundred volts, the pulse widths between 1 and 10 ps, and the repetition rate between 100 and 1000 pulses per second. Frequencies from lmhz upwards are used. If the pulse width is 1 ps and the repetition rate is 100/sec, the canier signal will exist for only 0.01% of the time. Thus some of the disadvantages of continuous wave method such as streaming and sample heating are virtually eliminated. In the single transducer pulse technique the acoustic pulse is reflected back to the transducer, which then serves as the receiver. The reflector can be made of metal or quartz when the medium is a liquid and it is merely the sample face opposite the transducer for a solid sample. In either case it is imperative that the reflector should be accurately flat and parallel to the transducer face, conditions that became increasingly important with increasing frequency. Each time a pulse returns to the transducer, part of its energy is converted into an electrical signal, the rest being reflected. Repetition of this process leads to a series of detected echoes, each of which has made one more round trip through the sample than its predecessor. The attenuation and velocity of sound are determined from the echo amplitudes and transit times, respectively [2].

3 Two transducers are sometimes used, the receiving transducer replacing the reflector. This is particularly useful for highly attenuating samples where a short path length is needed and where difficulty is encountered in keeping the echoes separated from the applied signal. A block diagram of a typical pulse echo apparatus is shown in Figure 2.1 BLOCKING OSCILLATOR - PULSED OSCILLATOR 1 Transducer A SAMPLE SUPER HETERODYNE RECErn - EXPONENTIAC WAVEFORM GENERATOR - VIDEO MIXER = I ~ R ANDAMPLIFIER -@ I -! SWEEP AND DELAY CIRCUITS CRT Figure 2.1 A block diagram of pulse echo system The trigger activates the pulsed oscillator and the sweep of the cathode ray tube. The echo signal is amplified in a super heterodyne receiver, rectified and displayed on the CRT. To facilitate measurement, a calibrated exponential curve or variable amplitude comparison pulse is generally displayed simultaneously with the echo pattern and is positioned by a calibrated time delay. This is accomplished by activating the oscillating sweep, for example, 200 times per

4 second, while the pulsed oscillator and comparison pulse or exponential curve are activated on alternate triggers, each 100 times per second. A distinct advantage of the pulse technique is that the velocity and absorption can be measured simultaneously. Accurate velocity measurements require certain amount of care and sophistication. Velocity measurements with an accuracy to within slightly better than 1%, however, can be obtained by merely measuring the round-trip transit time with the time delay of the oscilloscope. This requires that the distance or the change of distance between the transducer and the reflector be known. Different pulse techniques like pulse superposition method, sing around technique, pulse echo overlap method, etc. are used to measure the velocity. Out of these techniques, pulse echo overlap method is the most accurate one Pulse echo overlap method The pulse echo overlap method is a versatile and highly accurate method for measuring the velocity of ultrasonic waves in materials. The absolute accuracy of this method arises from the fact that the method is capable of measuring accurately from any cycle of one echo to the corresponding cycle of the next echo. The pulse echo overlap method is able to handle diffraction phase corrections properly. So the absolute accuracy of the pulse echo overlap method may exceed the accuracy of most other methods even though the precision of some others may exceed that of the pulse overlap method. The pulse echo overlap method has four features that other methods generally do not possess simultaneously.

5 1. The pulse echo overlap method may operate either with the transducer bonded directly to the specimen or with a buffer rod interposed between the transducer and specimen. 2. The pulse echo overlap method may be operated with broadband pulses as well as rf bursts. On advantage of broadband pulse is that proper overlap can be set-up with broadband echoes unambiguously. 3. The pulse echo overlap method can be set-up to make through transmission measurements of the travel time on a single pass between two transducers. 4. The pulse echo overlap method can be adapted to measure group velocity as well as phase velocity by using the envelopes of moderately narrow band rf bursts. On the negative side, the pulse echo overlap method has never been automated, as its echoes are overlapped by the observer in 'scope time' and not in real time [3] MATEC ultrasonic velocity measuring system The MATEC ultrasonic measuring system (Matec Instruments, Inc., USA) consists of a Model 7700 pulse modulator and receiver with a 755 RF plug-in and the accessories-model 110 high-resolution frequency source, Model 122B decade divider and dual delay generator. For the measurement of ultrasonic velocity, a frequency counter (APLAB Model 1112) and an oscilloscope (PHILIPS PM 3206) are used. The Model 7700 provides a high power pulsed oscillator, repetition rate generator, modulator and IF amplifier in one complete package. Model 755 RF plug-in provides frequency coverage from 1 MHz to 20 MHz and

6 power output of up to 1000 watts RMS into 50 Ohms. The Model 122B decade divider and dual delay generator provides the necessary interfacing between the CW oscillator, Model 110 high-resolution frequency source (operating at that frequency whose period is equal to the reciprocal of the round trip time in the sample) and the modulator contained in the Model 7700 main frame. The system modulation mode of Model 7700 mainframe includes single pulse mode, which provides continuously variable pulse width from 0.3 to 100~s to 755 RF plug-in. Figure 2.2. The block diagram of the Matec pulse echo overlap system is shown in HIGH RESOLUTION Out to counter FREQUENCY FREQUENCY SOURCE COUNTER Sweap out - CW Input DECAY DIVIDERS AND DUAL DELAY GENERATOR Divided sync. out 50 ohm terminator Sync. in Intensification (Z axis) *El R. F. plug-in Video out vert in #I (Y-axis: WIDE BAND R.F. echoes out '#2 OSCILLOSCOPE PULSE MODULATOR AND RECEIVER Transducer u Liquid cell..... sample Figure 2.2 A block diagram of the Matec pulse echo overlap system Sync. In - (X-axis) 29

7 'The principle of measurement is to make the two signals of interest overlap on the oscilloscope by driving the x-axis with frequency whose period is the travel time between the signals of interest. Then one signal appears on one sweep of the oscilloscope and other signal appears on next sweep. The CW oscillator as showed in Figure 2.2 supplies the x-axis sweep frequency. For jitterfree overlap, signals of interest must be generating the repetition rate of the input pulse from the phase of CW voltage by a frequency divider. Division by a large integer (e.g. 1000) allows all echoes from one pulse to be attenuated before the next pulse is applied. The output of the frequency divider is a trigger signal synchronous with the phase of CW voltage. The trigger signal triggers the main pulsar, which pulses the transducer. A diode limiter circuit keeps the output pulse form overloading the amplifier. The main pulsar also triggers two intensifying pulses, which are applied to the CRT to intensify the trace. This feature is necessary to distinguish the two signals of interest from the rest of the echoes in the trace. In operation, the oscilloscope intensity is turned down so that only the two signals of interest (intensified by the two strobe pulses) are visible. The main pulse is delayed after the trigger from the frequency divider, in order to centre the pair of the received echoes on the oscilloscope face. The delay serves as a phase shifter to put the echoes at 0' on the phase of sine wave CW input. Also, the intensifying pulses are delayed to place them on the signals of interest. The pulses are of variable width to cover that Eraction of the signals desired. Overlap is achieved by adjusting CW frequency, such that its period is equal to the time between the signals of interest. The frequency counter counts the CW frequency and the reciprocal of this frequency is the time of travel of the pulse through the 30 \..

8 specimen. Alternatively, the frequency counter may be operated in the time mode to measure the period of the CW directly. In the present study, the measurement of velocity was done in the following way. The rf pulse from the Model 755 rf plug-in was applied to a PZT (lead zirconium titanate) transducer of frequency 2MHz. This transducer was bonded to the liquid cell, which contains the sample under study using a gel (sonotrac couplant, Mathbin scientifics) as the bonding material. The same transducer acted as the transmitter and receiver. The construction of the liquid cell is described in the Section 2.3. To make a measurement, the oscilloscope was set on the triggered mode of operation. The intensity of cathode ray tube was turned down so that only the intensified signals were visible and the main pulsar delay was adjusted so that those signals were in the centre of the screen. The CW frequency was then adjusted so that the two signals overlapped (Figure 2.3). Figure 2.3 Cycle-for-cycle overlap of echoes in pulse-echo- overlap method The CW frequency was counted using a frequency counter and the reciprocal of this frequency gave the time of travel (t) of the pulse through the 31

9 specimen. Since there were two interfaces in the liquid cell described in Section 2.3, the McSkimin At criterion was not valid [2]. The error due to phase matching can be avoided by proper rf tuning due to the large path length. The path length of the sample in the liquid cell is measured using a vernier calipers. Then the velocity is calculated using the formula 2 x path length Velocity = t-t, where t, is the travel time through the glass plate to which the transducer was bonded. t, was determined by assuming the ultrasonic velocity in the glass. The velocity measurements were accurate to + 0.2%. 2.3 Liquid Cell The liquid cell used in the present study consists of a glass tube 3.851~1 long and 2.5m in diameter with a side tube. The open ends are closed by means of two plane glass plates using araldite. The glass plates are exactly parallel to each other. The sample under study can be filled in the glass tube through the side tube. The transducer is bonded to one of the plane glass plates on the outer sides using a gel. Only a small quantity of the bonding material is used to obtain an intimate, acoustically transparent coupling of the transducer to the liquid cell. The transducer serves both as the transmitter of ultrasonic pulses into the sample and also as the receiver of the echoes. A heater coil is wound round the tube so that the sample can be heated to different temperature, each temperature being kept constant with an accuracy of +O.lOc with the help of a laboratory made

10 temperature controller [4]. The experiment in the present study was done at four different temperatures 30,40, 50 and 60'~. The highest temperature was limited to 60'~ to avoid the evaporation loses of the components in the mixture during the course of experiments. 2.4 Density Measurements Density of pure liquids and liquid mixtures were measured with the help of a loml pyknometer [5]. Masses were measured using a chemical balance with an accuracy of 1 mg. The thermal expansivity (P) of the liquids and liquid mixtures were calculated by the formula Mass expelled (2.2) = Mass remaining x Rise of temperature Knowing the density (pl) of the liquid mixture at temperature TI, the density of the liquid mixtures at different temperatures 30, 40, 50 and 60'~ were calculated by the formula. where p2 is the density of the liquid mixture corresponding to temperature T2. The density measurements had an accuracy of k 0.02%. 2.5 Viscosity Measurements For viscosity measurements a loml Ostwald viscometer was used. The viscosities of the liquids and their mixtures (ql) were calculated using the formula [6].

11 where 11, is the coefficient of viscosity of water, tl and t, is time of flow for the mixture and water respectively. The viscosity measurements were accurate within _+ 0.13%. Viscosity of the mixtures at different temperatures were determined by measuring the time of flow of the water and the mixture at different temperatures. Temperature being kept constant within +0.l0c using a laboratory made temperature controller [4]. 2.6 Absorption Measurements Absorption measurements were carried out using Matec ultrasonic velocity-measuring system using a suitably designed liquid cell. Absorption was measured by determining the height of echoes on a cathode ray oscilloscope. The transducer used to measure the absorption was a quartz crystal of fundamental frequency 2MHz. All measurements were done at the next harmonic frequency of 6MHz. The liquid cell was made to take care of various precautions in order to minimise errors enter in the measurement of ultrasonic absorption. The cell consists of cylindrical stainless steel vessel of length 6.5cm and imer diameter of 5cm. This cylindrical vessel was grooved in to a stainless steel base. '0' rings were used to prevent leakage of liquid. The transducer was fixed on the base with proper electrical contacts so that the sample liquid was in direct contact with the transducer. Thus transducer bonding was avoided and bond correction was completely eliminated.

12 The upper part of the cell consisted of a movable reflector attached to a micrometer screw with three levelling screws. By adjusting these levelling screws the reflector could be made parallel to the transducer. The reflector can be moved through a distance of 2.5cm. A thermometer and a stirrer could be inserted in to the liquid cell through holes provided at the top of the cell. Watching the echo pattern in the CRO can test the levelling of the reflector. The liquid in the cell was heated to different temperature by means of a heater coil wound over the cell. Absorption measurements were taken at four different temperatures 30,40,50 and 60'~. Initially the liquid was heated to 65'~ and all measurements were taken during the cooling process so that temperature gradients could be minimised. The temperature was measured with an accuracy of 1 c. To measure the absorption, the sample liquid mixture was filled in the liquid cell.the echo pattem was obtained in the CRO screen. The levelling screw of the reflector was adjusted so that the echo patterns became most symmetrical and the echoes were of maximum height there by ensuring the parallelism between the transducer and the reflector. The height of successive echo could be measured from the oscilloscope. Form the height of the echoes absorption was calculated. The following precautions were taken to minimise the error due to various factors such as refraction, diffraction etc at the surface of the reflector during absorption measurements.

13 1. The length of the liquid column used for measurement was chosen to he within the Fresnel region, i.e., with in a length of ~~/2h, where R is the radius of the quartz transducer and h is the wavelength of the ultrasonic waves with in the liquid. This is to minimise the diferaction effects [7]. In R the present case -- = 30m and the distance between transducer and 2a reflector was 5cm. 2. The reflector was adjusted such that its face was parallel to the transducer as accurately as possible, by ensuring that the height of the echo pattern on the CRO screen was a maximum in height and as symmetrical as possible. This was done by using the three levelling screws. 3. The reflector was polished so that it reflects the ultrasonic pulse efficiently. 4. One of the important errors that may occur is due to absorption (or transmission) of ultrasonic waves by the reflector. In order to overcome this readings were taken in for two distances between the reflector and transducer and the difference between the two readings was used for calculations. Let XI be the distance between the reflector and the transducer, and hl and h2 are the heights of the two consecutive echoes. Then

14 where 2aX1 corresponds to absorption of ultrasonic wave by the liquid of path length 2x1 and a, the absorption by the reflector. Let X2 be the distance between the transducer and the reflector in the second case. Then if h3 and h4 are heights of consecutive echo peaks then Taking logarithm in both sides in equations 2.1 and 2.2 h, In-=2aXl +a,... h2 (2.7) From equations 2.7 and 2.8 Thus the absorption per unit length of liquid could be determined after eliminating errors due to absorption by the reflector 5. To prevent temperature gradients with in the liquid mixture, it was kept under continuous stining.

15 References 1. J R Pellam and J K Cialt, J. Chem. Phys. 14, (1946) R T Beyer and S C Letcher, Physical Ultrasonic. Academic Press, New York (1 969). 3. E P Papadakis, Physical Acoustics, Vol. 12 (Eds. W P Mason and R N Thurston) Academic Press New York (1976). 4. L Godfrey and J Philip, J. Phys. E. Sci. Instru. 22, (1989) Vogel's Text Book of Practical Organic Chemistry, 41h Edn. Longman Group Ltd. Madras (1978). 6. J R Partington, An Advanced Treatise on Physical Chemistry Vol. 2, Longmans London (1951). 7. J M M Pinkerton, Proc. Phys. Soc. B 62, (1949) 286.

Design of Multi-Frequency Ultrasonic Pulse-Echo System

IOSR Journal of Applied Physics (IOSR-JAP) ISSN: 2278-4861. Volume 2, Issue 4 (Nov. - Dec. 2012), PP 35-39 Design of Multi-Frequency Ultrasonic Pulse-Echo System G.K.Singh 1, S.J.Sharma 2 and S.Rajagopalan