Question

Question: A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is about 1540 m/s. What is the expected beat frequency if blood is flowing in large leg arteries at 3.0 cm/s directly away from the sound source?

Short answer

The expected beat frequency is $136.36\mathrm{m}/\mathrm{s}$.

Step-by-step solution

Concept.

When a source is emitting waves while moving, then the difference in frequency of can be observed at the source and observer.

Given data.

The frequency emitted by the device is $f=3.5\mathrm{H}\mathrm{z}$.

The speed of sound in human tissue is $v_s=1540\mathrm{m}/\mathrm{s}$.

The speed of blood in large leg arteries is $v_b=3.0\mathrm{c}\mathrm{m}/\mathrm{s}$.

Calculation.

The beat frequency can be calculated as,

$f_b=\frac{2f{v}_b}{v_s+v_b}$

Substitute the given values in above equation,

$\begin{array}{l}{f}_b=\frac{2\left(3.5\mathrm{M}\mathrm{H}\mathrm{z}\times \frac{{10}^6\mathrm{H}\mathrm{z}}{1\mathrm{M}\mathrm{H}\mathrm{z}}\right)\left(3.0\mathrm{c}\mathrm{m}/\mathrm{s}\times \frac{1\mathrm{m}/\mathrm{s}}{100\mathrm{c}\mathrm{m}/\mathrm{s}}\right)}{1540\mathrm{m}/\mathrm{s}+\left(3.0\mathrm{c}\mathrm{m}/\mathrm{s}\times \frac{1\mathrm{m}/\mathrm{s}}{100\mathrm{c}\mathrm{m}/\mathrm{s}}\right)}\\ f_b=136.36\mathrm{m}/\mathrm{s}\end{array}$

Thus, the expected beat frequency is $136.36\mathrm{m}/\mathrm{s}$.