How Is the Doppler Effect Used in Medical Ultrasound and Radar? (HL)

At HL, the Doppler effect is used to determine velocity by measuring the frequency change of a wave reflected from a moving target. Medical ultrasound measures blood flow, while radar measures the speed of vehicles, aircraft, or weather systems.

The Reasoning and Mechanism

The Doppler effect is the change in observed frequency caused by relative motion between a source and an observer. In both applications, a transmitter sends waves toward a moving target, which reflects the waves back to a receiver.

The target first acts as a moving observer and then as a moving source. Therefore, the reflected wave undergoes two frequency changes, producing an approximate Doppler shift:

$$\Delta f \approx \frac{2f_0v\cos\theta}{u_{\text{w}}}$$

Here, $f_0$ is the transmitted frequency, $v$ is the target's speed, $\theta$ is the angle between its velocity and the wave beam, and $u_{\text{w}}$ is the wave speed. Motion toward the receiver increases frequency; motion away decreases it.

For ultrasound with $f_0=5.0\,\text{MHz}$, blood speed $v=0.30\,\text{m s}^{-1}$, , and sound speed :

$$\Delta f=\frac{2(5.0\times10^6)(0.30)}{1540}\approx1.9\times10^3\,\text{Hz}$$

The common misconception is that Doppler measurements give total speed automatically. They measure only the velocity component along the beam, $v\cos\theta$. If motion is perpendicular to the beam, $\theta=90^\circ$ and the shift is zero.

Exam Technique

For IB Physics C.5 HL, explain the two-stage reflection, state whether approach raises or lowers frequency, and include the angular component. In calculations, identify the correct wave speed: sound speed in tissue for ultrasound and $c$ for radar.