A very precise technique for measuring ultrasonic attenuation in a liquid is illustrated in the figure below. The water and the sample liquid are separated by a thin membrane whose attenuation is negligible. Two ultrasound transducers are mounted on a movable carriage with a fixed known distance d between them. Suppose the attenuation coefficient of water is given by water. The attenuation coefficient of the sample, sample, can be readily calculated by observing the change in received pressure signal after a displacement of the carriage, say, to the right, by d. Derive an expression for sample, in terms of known parameters, water,d,d, and the measured pressure signals P1 and P2 before and after carriage displacement