The Doppler effect is used in modern ultrasound machines to image moving blood i

Question

The Doppler effect is used in modern ultrasound machines to image moving blood in arteries and veins. The largest speeds are around 30 cm/s going down to a few mm/s. In ultrasound textbooks the Doppler shift is taught as being twice the Doppler shift normally calculated for a moving observor. The argument that is presented for this is that the sound is reflecting off a moving particle. This argument is not strictly correct, but is a very good approximation as you will demonstrate below. Go by stages through the example to evaluate the claim made in standard ultrasound texts. To begin, determine the Doppler shift experienced by a moving blood cell in the path of a ultrasound transducer emitting a frequency of exactly 5 MHz. Suppose the blood cell moves toward the transducer at 18 cm/s. What frequency is received by the cell as a result of this motion? What is the shift in frequency (Delta f)? To keep track of the calculation you will need to keep all significant figures in this calculation (at least 7 digits). Now the cell re-emits (reflects) the sound back to the transducer. However, the cell is in motion as it does this and so needs to be treated as a moving source. In addition, it is reflecting the sound it percieves (as found in ) not the original tone. Determine the frequency detected by the transducer for the reflected sound. What is the overall shift in frequency (Delta f)? Ultrasound textbooks tell students to simply double the frequency shift (Delta f) found in to get the final frequency. Is that accurate? How close to correct is the recommendation from the ultrasound textbook?

Explanation / Answer

A) from gien data v=343m/s,v0=18cm/s=0.18m/s,vs=0,f=5mhz from doppler effect apparent frequency f1=f(v+v0/v)

f1=5(343+0.18)/343=5.0026239 Hz

doppler shift df=f1-f=0.0026239 Hz

B)now the cell is and it is treated as source then doppler shift df=2fv0/v

here v0=0.18m/s,v=343m/s,f=5 Mhz then df=2*5*0.18/343=0.0052478 Hz

c)yes it is accurate that is doppler shift frequency in second case that is calculated for moving observer is double than previous frequency

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