The Doppler shift of ultrasonic waves can measure the speed of blood in an artery.If the frequency of the stationary source is 95.0 kHz and the reflected sound has a Doppler shift of 210 Hz,what is the blood flow speed? (The speed of sound inside the body is 1 500 m/s. )
A)1.0 m/s
B)1.7 m/s
C)3.3 m/s
D)3.9 m/s
E)6.5 m/s

Question

Quizplus · Accepted Answer

The Doppler shift formula for sound waves is $\Delta f = \frac{2fv}{v_s}$, where $\Delta f$ is the Doppler shift (210 Hz), $f$ is the frequency of the stationary source (95,000 Hz), $v$ is the speed of the object (blood flow speed, which we are solving for), and $v_s$ is the speed of sound in the medium (1,500 m/s). Rearranging the formula to solve for $v$, we get $v = \frac{\Delta f \cdot v_s}{2f}$. Substituting the given values, $v = \frac{210 \cdot 1500}{2 \cdot 95000}$, which calculates to approximately 1.7 m/s.

The Doppler Shift of Ultrasonic Waves Can Measure the Speed