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?

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

The frequency emitted by the device is \(f = 3.5\;{\rm{Hz}}\).

The speed of sound in human tissue is \({v_s} = 1540\;{\rm{m/s}}\).

The speed of blood in large leg arteries is \({v_b} = 3.0\;{\rm{cm/s}}\).

The beat frequency can be calculated as,

\({f_b} = \frac{{2f{v_b}}}{{{v_s} + {v_b}}}\)

Substitute the given values in above equation,

\(\begin{array}{l}{f_b} = \frac{{2\left( {3.5\;{\rm{MHz}} \times \frac{{{{10}^6}\;{\rm{Hz}}}}{{1\;{\rm{MHz}}}}} \right)\left( {3.0\;{\rm{cm/s}} \times \frac{{1\;{\rm{m/s}}}}{{100\;{\rm{cm/s}}}}} \right)}}{{1540\;{\rm{m/s}} + \left( {3.0\;{\rm{cm/s}} \times \frac{{1\;{\rm{m/s}}}}{{100\;{\rm{cm/s}}}}} \right)}}\\{f_b} = 136.36\;{\rm{m/s}}\end{array}\)

Thus, the expected beat frequency is \(136.36\;{\rm{m/s}}\).