Final answer:
The velocity of the blood, calculated using the Doppler effect and frequency shift, is approximately 19.25 cm/s, which makes the closest option (c) 22.5 cm/s.
Step-by-step explanation:
The question involves the application of the Doppler effect in ultrasound to determine the velocity of moving blood. The diagnostic ultrasound echo is reflected from moving blood causing a frequency shift that is used to calculate the velocity. Given that the return frequency is 500 Hz higher than the original frequency of 2.00 MHz, we can use the Doppler equation for frequency shift to find the blood velocity:
Δf = f' - f = (2v / c) × f
Where Δf is the change in frequency (500 Hz), f is the original frequency (2.00 MHz), v is the velocity of blood, and c is the speed of sound in tissue (assumed to be 1540 m/s).
Let's rearrange the equation and solve for v:
v = (c × Δf) / (2 × f)
v = (1540 m/s × 500 Hz) / (2 × 2.00 MHz)
v = (1540 m/s × 500 Hz) / (2 × 2,000,000 Hz)
v = (1540 × 500) / (2 × 2,000,000)
v = 770,000 / 4,000,000
v = 0.1925 m/s
Converting to cm/s:
v = 0.1925 m/s × 100 cm/m
v = 19.25 cm/s
So the closest answer from the options would be (c) 22.5 cm/s.