Chapter A, Problem A.5P

1. (20 pts) Plot the pulse and the FFT for a pulse with the following properties at x=0 and x=10 cm. f=2 MHz m=3 Ncyc=2, 6, 20 po 1 MPa (source pressure) x=10 cm (propagates in a Newtonian fluid for 10 cm as a plane wave-not a sound beam) a=0.5 dB/(MHz cm) Consider 3 types of waves: sine, square, and sawtooth. (square and sawtooth only for grad students) Observe your plots and draw some conclusions. Discuss any possible issues you encounter. 2. (20 pts) We have the following 3 ultrasonic transducers: a. Focused 1 MHz, 2.54 cm diameter, 5.08 cm focus b. Focused 3 MHz, 2.54 cm diameter, 5.08 cm focus c. Unfocused 0.1 MHz, 2.54 cm diameter The transducers are operating in water (c=1486 m/s). I. Plot the axial field for all transducers II. Plot the focal transverse field for the focused transducers and the transverse field at the Rayleigh distance (R_0) and at 2R_0 for the unfocused. III. Assume source pressure of 0.1 MPa, and find the acoustic pressure in MPa at the location (r=0, z=4.5…

Find the Q-points for the diodes in the circuit. Assume ideal diodes, and startwith the assumption that D is OFF, and D2 is ON for both circuits.

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5- Find the Eigenvalues and the corresponding Eigenvectors. [4 5 31 A=0 4 6 Lo 0 1

Find the Eigenvalues and the corresponding Eigenvectors. 4 2 -2 A = 2 5 0,2=4 -2 -2 0 3

1. Label the x, y, z coordinates for each frame. 2. Compute the homogeneous transformation matrices H between frames 0, 1, 2, and end- effector.

Find Eigenvalues and Eigenvectors for the following matrices: 1] [5-6 A = 1 1 0 L3 0 1

Use Gauss-Jordan Elimination method to solve the following system: 4x1+5x2 + x3 = 2 x1-2x2 3x3 = 7 - 3x1 x2 2x3 = 1. -

Find the Eigenvalues and the corresponding Eigenvectors. A = [³/2 9] 3.