Attenuation and velocity of ultrasound in solid 5.1.6.08 Related Topics Propagation of ultrasonic waves, time of flight, sound velocity, damping of ultrasonic waves (scattering, reflection, absorption), transmission coefficient. Principle The damping of ultrasound in solid objects is determined for 2 (or optionally 3) different frequencies in the transmission mode. The resulting values are then compared to the corresponding literature values. In addition, the frequency dependence of the damping effect is analysed. Furthermore, the sound velocity in acrylic objects is determined for 2 (or optionally 3) different frequencies in the transmission mode. Equipment 1 Basic Set Ultrasonic echoscope 13921-99 1 Extension set: Shear waves 13921-03 1 Ultrasonic Probe 2 MHz 13921-05 1 Vernier calliper 03010-00 Optionally 2 Ultrasonic Probe 4 MHz 13921-02 Additionally needed PC with USB port, Windows XP or higher Caution! Pay attention to the special operation and safety instructions in the manual of ultrasonic echoscope. Fig. 1: Equipment for Attenuation and velocity of ultrasound in solid, experimental set-up www.phywe.com P5160800 PHYWE Systeme GmbH & Co. KG All rights reserved 1
5.1.6.08 Attenuation and velocity of ultrasound in solid Tasks 1. Measure the lengths of the three cylinders with the calliper. 2. Determine the amplitudes and times of flight of the ultrasonic transmission pulses for the three cylinders and the two (or three) ultrasonic probes. 3. Calculate the attenuation and sound velocity values. Set-up and procedure - Set the experiment up as shown in Fig. 1. - The lengths of the cylinders must be measured with a vernier calliper. - In order to determine the time of flight and attenuation in the transmission mode, proceed as follows: Connect the echoscope to the PC. Insert the probes into the probe holders and connect the two probes (of the same frequency) to the Probe connector (the switch must be set to Trans. ). Insert the cylinder into the holder block. Start with the shortest one. Connect the probes to a cylinder with the aid of a drop of ultrasonic gel. - Damping measurement: Set the software to HF+Amp representation. The gain and transmission values must be set so that the signals for the shortest cylinders are not overdriven but are still as high as possible. If this is the case, the amplitude measurement is possible with all of the frequencies, including in connection with the longest cylinder (Figures 2, 3, 5, 7, 8, 10, 12, 13, and 15). It must be ensured that the gain settings are always identical in order to be able to compare the various amplitude measurements. The measuring cursor for the amplitude determination is used to determine the amplitude of the transmission pulse at the three acrylic cylinders. If necessary, use the amplitude zoom function of the software in order to be able to analyse even small amplitudes with optimum precision (see Figure 15). The maximum amplitude, comprising a negative and positive HF peak (red signal) and also based on the A-scan (blue signal), will be determined. This is repeated for all of the frequencies that are used. Note: Amplitude measurements should always be viewed critically, since the amplitude of the echo is not only influenced by the frequency-dependent damping effect and by the reflection coefficient of the material, but also by the coupling quality and alignment of the probes. In addition, the resolution of the digitalisation process (time and dynamic range) plays an important role. This is why the maximum of the HF and amplitude signal should always be selected for damping measurements. - Sound velocity measurement: Set the gain, transmission power, and TGC so that the reception signal is slightly overdriven (Figures 2, 4, 6, 7, 9, 11, 12, 14, and 16). The time of flight up to the beginning of the signal can be read off directly with the aid of the measuring cursors. This must be performed with great care, since time-of-flight measurement errors have a strong effect on the accuracy of the final results. If necessary, use the time zoom function of the software in order to optimally determine the point of onset (see Figure 16). Perform the measurement with all of the three cylinders and with probes of the same frequency. Note: The time-of-flight or depth measurements of an echo should be performed at the beginning of the rising edge of the peaks in the amplitude signal (if necessary, use the time zoom function). Time-offlight measurements at the peak maximum can lead to incorrect results, since the peak shape can be influenced by the frequency-dependent damping effect. 2 PHYWE Systeme GmbH & Co. KG All rights reserved P5160800
Attenuation and velocity of ultrasound in solid 5.1.6.08 Software The measure Ultra Echo software records, displays, and evaluates the data that are transferred from the echoscope. After the start of the program, the measuring mode is active and the main screen A- Scan mode is displayed. All of the available actions and evaluations can be selected and started in this window. The upper part of the main screen shows the A-scan signal, the frequency of the connected transducer, and the operating mode (reflection/transmission). The current positions of the cursors (red and green line) are displayed at the bottom of the window. The cursors can be positioned by a mouse click. The time of flight is displayed under the cursor buttons. Note: Maintenance The ultrasonic cylinders and probes should be cleaned immediately after use with water or a standard detergent. Dried residues of ultrasonic gel are difficult to remove. If necessary, use a soft brush. Never use alcohol or liquids with solvents to clean the cylinders or probes. Deep surface scratches affect the coupling and can induce measurement errors. Fig. 2: 1 MHz probes, cylinder with approx. 40 mm, amplitude and time-of-flight measurement www.phywe.com P5160800 PHYWE Systeme GmbH & Co. KG All rights reserved 3
5.1.6.08 Attenuation and velocity of ultrasound in solid Fig. 3: 1 MHz probes, cylinder with approx. 80 mm, amplitude measurement Fig. 4: 1 MHz probes, cylinder with approx. 80 mm, time-of-flight measurement 4 PHYWE Systeme GmbH & Co. KG All rights reserved P5160800
Attenuation and velocity of ultrasound in solid 5.1.6.08 Fig. 5: 1 MHz probes, cylinder with approx. 120 mm, amplitude measurement Fig. 6: 1 MHz probes, cylinder with approx. 120 mm, time-of-flight measurement www.phywe.com P5160800 PHYWE Systeme GmbH & Co. KG All rights reserved 5
5.1.6.08 Attenuation and velocity of ultrasound in solid Fig. 7: 2 MHz probes, cylinder with approx. 40 mm, amplitude and time-of-flight measurement Fig. 8: 2 MHz probes, cylinder with approx. 80 mm, amplitude measurement 6 PHYWE Systeme GmbH & Co. KG All rights reserved P5160800
Attenuation and velocity of ultrasound in solid 5.1.6.08 Fig. 9: 2 MHz probes, cylinder with approx. 80 mm, time-of-flight measurement Fig. 10: 2 MHz probes, cylinder with approx. 120 mm, amplitude measurement www.phywe.com P5160800 PHYWE Systeme GmbH & Co. KG All rights reserved 7
5.1.6.08 Attenuation and velocity of ultrasound in solid Fig. 11: 2 MHz probes, cylinder with approx. 120 mm, time-of-flight measurement Fig. 12: 4 MHz probes, cylinder with approx. 40 mm, amplitude and time-of-flight measurement 8 PHYWE Systeme GmbH & Co. KG All rights reserved P5160800
Attenuation and velocity of ultrasound in solid 5.1.6.08 Fig. 13: 4 MHz probes, cylinder with approx. 80 mm, amplitude measurement Fig. 14: 4 MHz probes, cylinder with approx. 80 mm, time-of-flight measurement www.phywe.com P5160800 PHYWE Systeme GmbH & Co. KG All rights reserved 9
5.1.6.08 Attenuation and velocity of ultrasound in solid Fig. 15: 4 MHz probes, cylinder with approx. 120 mm, amplitude measurement with zoom ON Fig. 16: 4 MHz probes, cylinder with approx. 120 mm, time-of-flight measurement with zoom ON 10 PHYWE Systeme GmbH & Co. KG All rights reserved P5160800
Attenuation and velocity of ultrasound in solid 5.1.6.08 Theory and evaluation A sound wave that runs through a medium loses energy during various processes (scattering, absorption, and reflection). This is called attenuation. The intensity I of the wave follows the law of attenuation (1) I I s 0 e µ = where (I O ) is the initial intensity, (s) is the path length in the medium, and (µ) is the attenuation coefficient. By measuring two samples of the same material but of different lengths, the material-specific attenuation coefficient (µ) can be determined by (2) that follows from (1) through a rearrangement. Here, it is taken into account that the intensity (I) is proportional to the square of the amplitude (A²) and that the conversion into the commonly used unit db/cm results in (2) µ [ db / cm] µ [ db / cm] µ [1/ cm] or[ neper / cm] = = 20 Lg ( e) 8.686 µ = 2 8.686 (s A 2 Ln 1 s 2 ) A 1 A short mechanical wave is generated by a short voltage pulse that is applied to a piezoelectric ceramic. If this wave is coupled into a solid object, it propagates in a linear way and it will be reflected and transmitted on areas with acoustic impedance changes (boundaries). From the known distance (s) of a material between two ultrasonic probes and the measured time of flight (t), the sound velocity (c) can be determined for perpendicular sound incidence as follows: In the transmission mode: (3) c = s t The fact that nearly all of the ultrasonic probes have a protective layer on their active surface (ceramics) causes a measurement error concerning the sound velocity, since the time of flight through this layer is also measured. This means that the measured time of flight (t) includes the time of flight through the protective layers (t L1 and t 2L ) of the two probes and the time of flight through the sample (t s ). This error can be eliminated if the velocity of sound (c) is determined by calculating the difference of two measurements (t 1 and t 2 ) of two different sample lengths (s 1 and s 2 ) and by assuming that the protective layers of the two probes are identical (t L1 = t L2 = t L) : (4) c = ( s1 s2 ) ( s1 s2 ) = t t ( t + t ) ( t + t ) 1 2 S1 L S2 L = ( s s ) Results Measurement of the cylinder lengths with the vernier calliper (Table 1): t 1 S1 t 2 S2 Length [mm] Cylinder 1 39.75 Cylinder 2 79.50 Cylinder 3 118.95 www.phywe.com P5160800 PHYWE Systeme GmbH & Co. KG All rights reserved 11
5.1.6.08 Attenuation and velocity of ultrasound in solid Amplitudes measured for three cylinders with different frequencies (Table 2): Amplitude [mv] 1 MHz 2 MHz 4 MHz Cylinder 1 920 984 1,000 Cylinder 2 450 394 179 Cylinder 3 219 147 29 Times of flight measured for three cylinders with different frequencies (Table 3): Time of flight [µs] 1 MHz 2 MHz 4 MHz Cylinder 1 15.1 14.9 14.8 Cylinder 2 29.7 29.5 29.4 Cylinder 3 44.2 44.0 43.9 Evaluation of the damping effect The measured amplitudes values (Table 2) for each of the frequencies can be used to calculate the damping values µ in 1/cm based on (2). 1 MHz probe: s1 A1 s2 A2 µ [mm] [mv] [mm] [mv] [1/cm] 39.75 920 79.50 450 3.13 79.50 450 118.95 219 3.17 39.75 920 118.95 219 3.15 Mean 3.15 2 MHz probe: s1 A1 s2 A2 µ [mm] [mv] [mm] [mv] [1/cm] 39.75 984 79.50 394 4.00 79.50 394 118.95 147 4.34 39.75 984 118.95 147 4.17 Mean 4.17 4 MHz probe: s1 A1 s2 A2 µ [mm] [mv] [mm] [mv] [1/cm] 39.75 1000.0 79.50 179.0 7.52 79.50 179.0 118.95 29.0 8.01 39.75 1000.0 118.95 29.0 7.77 Mean 7.77 Figure 17 shows the attenuation coefficient as a function of the ultrasound frequency. 12 PHYWE Systeme GmbH & Co. KG All rights reserved P5160800
Attenuation and velocity of ultrasound in solid 5.1.6.08 9 8 attenuation coefficient 7 6 5 4 3 2 1 0 1 2 3 4 f requency [MHz] Fig. 17: Attenuation coefficient vs. ultrasound frequency The attenuation coefficient increases with an increasing frequency. The resulting approximate dependence is described in (5): (5) µ f n n = 1. 8 Sound velocity evaluation The measured values are used to calculate the sound velocity based on (3) (c1). In doing so, the time of flight through the adaptation layers must be taken into consideration, since it leads to an error concerning the calculated sound velocity. In order to eliminate this error, the sound velocity is determined based on (4) by a difference calculation of two measurements of the different sample lengths (c2). 1 MHz probe: s1 t1 s2 t2 c1 c2 [mm] [µs] [mm] [µs] [m/s] [m/s] 39.75 15.1 79.50 29.7 2,632 2,723 79.50 29.7 118.95 44.2 2,677 2,721 118.95 44.2 39.75 15.1 2,691 2,722 Mean 2,667 2,722 www.phywe.com P5160800 PHYWE Systeme GmbH & Co. KG All rights reserved 13
5.1.6.08 Attenuation and velocity of ultrasound in solid 1 MHz Probe Sound velocity [m/s] 2740 2720 2700 2680 2660 2640 c1 c2 2620 30,00 80,00 130,00 Thickness [mm] 2 MHz probe: s1 t1 s2 t2 c1 c2 [mm] [µs] [mm] [µs] [m/s] [m/s] 39.75 14.9 79.50 29.5 2,668 2,723 79.50 29.5 118.95 44.0 2,695 2,721 118.95 44.0 39.75 14.9 2,703 2,722 Mean 2,689 2,722 2740 2 MHz Probe Sound velocity [m/s] 2720 2700 2680 2660 2640 c1 c2 2620 30,00 80,00 130,00 Thickness [mm] 14 PHYWE Systeme GmbH & Co. KG All rights reserved P5160800
Attenuation and velocity of ultrasound in solid 5.1.6.08 4 MHz probe: s1 t1 s2 t2 c1 c2 [mm] [µs] [mm] [µs] [m/s] [m/s] 39.75 14.8 79.50 29.4 2,686 2,723 79.50 29.4 118.95 43.9 2,704 2,721 118.95 43.9 39.75 14.8 2,710 2,722 Mean 2,700 2,722 2740 4 MHz Probe 2720 Sound velocity [m/s] 2700 2680 2660 2640 c1 c2 2620 30,00 80,00 130,00 Thickness [mm] The thicker the adaptation layer is (and the smaller the frequency is), the greater the difference between c1 and c2 and, thereby, the error in the sound velocity determination. Literature value: longitudinal sound velocity in acrylic materials = 2,600-2,800 m/s. The measurement values concerning the sound velocity and attenuation coefficients in acrylic materials can vary strongly depending on the manufacturer and production method used. www.phywe.com P5160800 PHYWE Systeme GmbH & Co. KG All rights reserved 15
5.1.6.08 Attenuation and velocity of ultrasound in solid 16 PHYWE Systeme GmbH & Co. KG All rights reserved P5160800