The overall transmission coefficient αT,G between a transmitter of characteristic impedance R1 and a gas of impedance R2 separated by a matching layer of impedance R is given by eqn [16.40]. By differentiating [16.40] and setting the derivative equal to zero (or any other method), show that αT,G is a maximum when 
(a) Explain briefly the meaning of the following terms used in ultrasonics:
(i) Attenuation
(ii) Matching layer
(iii) Resonant stationary wave.
(b) An ultrasonic transmitter is in the form of a piezoelectric disc of diameter 1.0 cm and thickness 2.0 mm. The transmitter is to be used to launch 1 MHz pulses into biological tissue. Use the concepts of part
(a) and the data below to detail what modifications are made to the transmitter so it meets the following specification:
(i) Maximum power for pulse transmission from the front face into the tissue
(ii) Minimum power for pulse transmission from the rear face into the tissue.
