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Exercise:
For a Doppler sonography sound waves with a frequency of fO are coupled o the body. Calculate the speed of the blood flow if the frequency shift after reflexion on the blood cells is measured to be dfO. The propagation speed in blood is close to the one in water.

Solution:
Since the frequency shift is much smaller than the source frequency the approximation for the Doppler shift on reflection can be used: Delta f &cong ffracvv_S It follows for the speed of the blood flow v &cong vF vWtimesfracdftimesf v approx resultvP- Without the approximation the received frequency is given by f_R ffracv_S+vv_S-v and the frequency shift Delta f f_R-f fleftfracv_S+vv_S-v-right ffracv_S+v-v_S-vv_S-vffracvv_S-v Multiplying both sides by v_S-v leads to Delta fv_S-v f v which can be solved for v: v vexF vWtimesfracdff+df vex approx resultvexP- which is consistent with the approximation.
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Exercise:
For a Doppler sonography sound waves with a frequency of fO are coupled o the body. Calculate the speed of the blood flow if the frequency shift after reflexion on the blood cells is measured to be dfO. The propagation speed in blood is close to the one in water.

Solution:
Since the frequency shift is much smaller than the source frequency the approximation for the Doppler shift on reflection can be used: Delta f &cong ffracvv_S It follows for the speed of the blood flow v &cong vF vWtimesfracdftimesf v approx resultvP- Without the approximation the received frequency is given by f_R ffracv_S+vv_S-v and the frequency shift Delta f f_R-f fleftfracv_S+vv_S-v-right ffracv_S+v-v_S-vv_S-vffracvv_S-v Multiplying both sides by v_S-v leads to Delta fv_S-v f v which can be solved for v: v vexF vWtimesfracdff+df vex approx resultvexP- which is consistent with the approximation.
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Attributes & Decorations
Branches
Doppler Effect
Tags
doppler sonography, frequency shift, reflection, ultrasound
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration
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Link