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# Using ultrasounds to measure blood flow velocity

## Problem

Using the Doppler Effect, it is possible to measure motions within the body. The ultrasonic flow meter is a medical device that can approximate the velocity of blood flow in a particular vessel. The transducer of ultrasonic flow meter is composed of both a transmitter and a receiver component. Ultrasonic waves of a set frequency (start text, f, end text, start subscript, 0, end subscript) are emitted by the transmitter, which are then scattered by the moving red blood cells (RBCs) that they come in contact with. These scattered waves return to the receiver with a frequency altered by the Doppler Effect (f, prime). Figure 1 depicts how an ultrasonic flow meter functions.
Figure 1: Ultrasonic Flow Meter Measuring Blood Flow Velocity
The Doppler frequency,start text, f, end text, start subscript, D, o, p, p, l, e, r, end subscript, the difference between the received frequency,f, prime, and transmitted frequency, start text, f, end text, start subscript, 0, end subscript, can be estimated from the following equation:
start text, f, end text, start subscript, D, o, p, p, l, e, r, end subscript = start fraction, 2, start text, f, end text, start subscript, 0, end subscript, dot, start text, v, end text, start subscript, r, b, c, end subscript, dot, c, o, s, ϴ, divided by, c, end fraction
where v, start subscript, r, b, c, end subscript is velocity of the red blood cells, ϴ is the angle between the transmitted ultrasonic wave and the motion of RBCs, and c is the speed of sound moving through soft tissues which is approximately 1, point, 5, dot, space, 10, start superscript, 5, end superscript c, m, slash, s. Blood flow can be characterized as either laminar, plug, disturbed or turbulent. Laminar blood flow follows a parabolic pattern with the greatest flow velocities being greatest at the center of the vessel. Plug flow is seen in vessels with large diameter such as the aorta where the velocity of the flow is relatively uniform throughout the vessel. In a disturbed flow, RBCs no longer travels in straight lines; however, in general they continue to move in the forward direction. Turbulent flow is chaotic and random with RBCs flowing in all directions at varying velocities.
According to Figure 1, which of the following is a true statement regarding start text, f, end text, start subscript, 0, end subscript and f, prime when the angle ϴ is between 0 and 90 degrees (0 < ϴ < 90)?