(Solved): Correct Answers are (a) 0.46 mm. (b) 0.95V0. (c) V = V0e^-2ad, where a is the attenuation const ...

Correct Answers are (a) 0.46 mm. (b) 0.95V0. (c) V = V0e^-2ad, where a is the attenuation constant. (d) t = 2d/vc [s]

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7.9 Pulse-echo ultrasonic testing. In a pulse-echo ultrasound test, the transmitter serves as the receiver during the time the pulse is off. The transmitter sends a pulse of width $\Delta t$, at the end of which it is ready to receive. The test is applied to measure the thickness of a copper slab by detecting the reflected pulse from the far surface (Figure 7.50). The properties of copper are as follows: speed of propagation $4600\mathrm{m}/\mathrm{s}$, attenuation constant $0.45\mathrm{dB}/\mathrm{cm}$, acoustic impedance $42.5\times 10^6\mathrm{kg}/{\mathrm{m}}^2/\mathrm{s}$. The pulse generated during transmission is $200\mathrm{ns}$ wide. a. What is the thinnest slab that can be tested using the pulse-echo method described here and what is the maximum frequency of a train of pulses intended to repeat the process indefinitely? FIGURE 7.50 Pulse-echo testing of materials. 7.10 I Problems 393 b. Calculate the amplitude of the reflected pulse received by the transducer for the conditions in (a), given an amplitude of the transmitted wave, $V_0$. Note: The application of a pulse to an ultrasonic transducer generates a series of sinusoidal waveforms as the transducer oscillates at its resonant frequency. However, for simplicity we will assume here that the pulse propagates and reflects as a pulse. c. Find a relation between the thickness of the slab and the amplitude of the reflected pulse. d. Find a relation between the thickness of slab and the time it takes to receive the pulse.