(Solved): An ultrasound signal with frequency \( 5.3 \mathrm{MHz}(5300000 \mathrm{~Hz}) \) propagates in fat ...

An ultrasound signal with frequency \( 5.3 \mathrm{MHz}(5300000 \mathrm{~Hz}) \) propagates in fat within a patient's body and reaches the surface of the kidney. Some portion of the ultrasound reflects at the interface between the fat and the kidney, and the other portion transmits into the kidney. The density and the acoustic impedance of the fat are \( 920 \mathrm{~kg} / \mathrm{m}^{3} \) and \( 1330000 \mathrm{~kg} / \mathrm{m}^{2} \) s, respectively. The density and the acoustic impedance of the kidney are \( 1040 \mathrm{~kg} / \mathrm{m}^{3} \) and 1620000 \( \mathrm{kg} / \mathrm{m}^{2} \mathrm{~s} \), respectively. (a) What is the speed of the ultrasound in the fat and the kidney? ( 2 pt) (b) What is the wavelength of the ultrasound in the fat and the kidney? (2 pt) [hint the frequency of ultrasound remains the same no matter what medium it propagates in.] (c) What proportion of the ultrasound energy is reflected at the interface between the fat and the kidney? (2 pt) The same frequency of ultrasound \( (5.3 \mathrm{MHz}) \) is used for Doppler ultrasound to measure the velocity of a blood flow in an artery within the patient's body. There are two stages in this process: the first stage is when the ultrasound propagates from the transducer to the flow of blood, and the second stage is when the ultrasound reflects from the flow of blood and returns to the detector in the transducer. We will see how much the frequency changes at each stage because of the Doppler effect. In the following two questions, assume that the speed of the ultrasound in the patient body is \( 1540 \mathrm{~m} / \mathrm{s} \) and that the blood flows toward the transducer at a speed of \( 0.95 \mathrm{~m} / \mathrm{s} \). (d) For the first stage, treating the transducer as a stationary sound source and the flowing blood as a moving observer, find the apparent frequency of the ultrasound that the flowing blood receives. Round your answer to the nearest whole number, (2 pt) (c) For the second stage, when the ultrasound reflects off the flowing blood, the blood can be seen as a moving ultrasound source that emits the ultrasound with the frequency wo found in part (d). Treating the flowing blood as a moving sound source and the transducer as a stationary observer, find the apparent frequency of the ultrasound that the transducer receives. Round your answer to the nearest whole number. (2 pt)