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Unformatted text preview: Theoretical Question 2 A Piezoelectric Crystal Resonator under an Alternating Voltage Consider a uniform rod of unstressed length and cross-sectional area A (Figure 2a). Its length changes by when equal and opposite forces of magnitude F are applied to its ends faces normally. The stress T on the end faces is defined to be F / A . The fractional change in its length, i.e., / , is called the strain S of the rod. In terms of stress and strain, Hookes law may be expressed as S Y T = or Y A F = (1) where Y is called the Youngs modulus of the rod material. Note that a compressive stress T corresponds to F < 0 and a decrease in length (i.e., < 0). Such a stress is thus negative in value and is related to the pressure p by T = p . For a uniform rod of density , the speed of propagation of longitudinal waves (i.e., sound speed) along the rod is given by / Y u = (2) The effect of damping and dissipation can be ignored in answering the following questions. Part A: mechanical properties A uniform rod of semi-infinite length, extending from x = 0 to (see Figure 2b), has a density . It is initially stationary and unstressed. A piston then steadily exerts a small pressure p on its left face at x = 0 for a very short time t , causing a pressure wave to propagate with speed u to the right. (a) If the piston causes the rods left face to move at a constant velocity v (Figure 2b), what are the strain S and pressure p at the left face during the time t ?...
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This note was uploaded on 11/08/2011 for the course PHYS 0000 taught by Professor Na during the Spring '11 term at Rensselaer Polytechnic Institute.
- Spring '11