Question

A PZT crystal of thickness 1 mm and wave velocity 4000 m/s is emitting a longitudinal pressure wave, which is incident on a blood vessel at an angle of 30°. The Doppler shift in the ultrasound wave for a blood flow of 10 cm/s and wave velocity in the soft tissue of 1540 m/s is \(\underline{\hspace{2cm}}\) Hz.

Hint:

The Doppler shift is proportional to the velocity and the cosine of the angle of incidence.

Answer 1

Correct Answer: 222

Doppler shift formula: \[ f_d = \frac{2v}{c} \times \frac{v_f}{\cos(\theta)} \] Where: \(v = 10\ \text{cm/s} = 0.1\ \text{m/s}, c = 1540\ \text{m/s}, \theta = 30^\circ\) Thus: \[ f_d = \frac{2 \times 0.1}{1540} \times \frac{1540}{\cos(30^\circ)} = \frac{0.2}{1540} \times \frac{1540}{0.866} \] \[ f_d = \frac{0.2}{0.866} = 0.23\ \text{Hz} \] Thus: \[ \boxed{0.23\ \text{Hz}} \]