Ultrasound has a wide range of applications in both technology and medicine.
One well-known technological use is in sonar systems, such as depth sounding and fish finding. A ship emits ultrasound waves that travel through water, reflect off the seafloor, and return to a receiver. Using the relatively constant speed of sound in water, the distance to the ocean floor can be determined from the time delay $\Delta t$ between transmission and reception:
$$
\boxed{\Delta t = \frac{2\Delta s}{c}}
$$
This formula accounts for the two-way path (there and back).
Example: If sound travels at 1,500 m/s and the round-trip time is 0.2 s, the depth is 150 m.
In medical diagnostics, ultrasound is used for imaging organs, bones, and blood flow, often in real time. This method is called sonography.
Ultrasound is emitted using a piezoelectric crystal, which vibrates at high frequencies when driven by an alternating voltage. The same crystal also serves as a receiver: incoming sound waves make it vibrate, generating electrical signals.
To minimize signal loss at the skin–sensor interface, a gel (usually water-based) is applied to couple the ultrasound sensor to the body.
As ultrasound waves pass through the body, part of their intensity is reflected at boundaries between different tissue types. This reflected signal is used to generate images.
In the Amplitude Mode (A-Mode), the ultrasound sensor sends pulses and measures the time until echoes return. The signal is plotted as a function of time, revealing distance between tissue layers (from delay time) and tissue reflectivity (from echo height).
Reflectivity is also called echogenicity:
- High echogenicity: strong reflection (e.g., bone, air).
- Low echogenicity: weak reflection (e.g., fluid like urine).
Today, Brightness Mode (B-Mode) is more common. It scans over an area and reconstructs a 2D grayscale image:
- Brightness ∝ intensity of the reflected echo
- High frequencies (e.g. 40 MHz → λ ≈ 37.4 μm) improve resolution,
but also increase absorption, reducing penetration depth.
Thus, frequency must be optimized for each application.
In addition to static imaging, Doppler ultrasound (or Doppler sonography) measures motion, especially blood flow. It uses the Doppler effect to determine the velocity of moving tissue (typically blood cells).
Assume a blood cell moves away from the sensor:
- The moving object perceives a lower frequency from the transmitted wave:
$$
f_\mathrm{Q}' = f_\mathrm{S} \cdot \frac{c - v}{c}
$$
- It reflects the wave back, acting like a new moving source:
$$
f_\mathrm{S}' = f_\mathrm{Q}' \cdot \frac{c}{c + v} = f_\mathrm{S} \cdot \frac{c - v}{c + v}
$$
So the received frequency becomes:
$$
f_\mathrm{S}' = f_\mathrm{S} \cdot \frac{c - v}{c + v}
$$
The Doppler frequency shift is:
$$
\boxed{\Delta f = f_\mathrm{S}' - f_\mathrm{S} = f_\mathrm{S} \cdot \frac{2v}{v + c}}
$$
This frequency shift corresponds to a beat frequency (Schwebung) and can be measured electronically. The blood flow velocity is then calculated from $\Delta f$.
The Doppler signal typically originates from erythrocytes (red blood cells). Blockages (stenoses) in arteries can be identified by increased flow velocities.
In color Doppler imaging, velocities are color-coded (e.g., blue = moving away from sensor).
Example Problem
> How large is the expected frequency shift for blood moving at 10 cm/s, using a 10 MHz ultrasound probe? Assume $c = 1,500\,\text{m/s}$.
Solution:
$$
\Delta f = 10^7 \cdot \frac{2 \cdot 0.1}{1500 + 0.1} \approx 1.33\,\text{kHz}
$$