Physics and Instrumentation
Wave fundamentals
Ultrasound is a mechanical, longitudinal wave. Frequency is determined by the transducer; propagation speed is determined by the medium (about 1540 m/s in soft tissue). Because wavelength = c/f, wavelength changes when the medium changes even though frequency does not. Higher frequency gives a shorter wavelength, better axial resolution, and poorer penetration.
Attenuation and interactions
Attenuation is absorption plus reflection plus scattering, roughly 0.5 dB/cm/MHz in soft tissue, so a 5 MHz beam loses about 2.5 dB per centimeter. Reflection requires an impedance mismatch at an interface near perpendicular to the beam; oblique incidence produces refraction that can displace structures on the image. Time-gain compensation amplifies later echoes to offset depth-dependent attenuation.
Resolution and frame rate
Axial resolution is approximately spatial pulse length divided by 2, and SPL = cycles per pulse × wavelength. Lateral resolution depends on beam width and is best at the focal zone; elevational resolution is slice thickness set by the transducer. Frame rate = PRF ÷ lines per frame, so increasing depth or line density lowers the frame rate.
Doppler
Doppler shift depends on velocity, beam angle, and transmitted frequency; at 90° no shift is detected. The Nyquist limit is PRF/2. Exceeding it causes aliasing, corrected by raising the PRF/scale, lowering transducer frequency, shifting the baseline, or switching to continuous wave.
Trap: assuming frequency changes with the medium, or that a higher-frequency probe penetrates better.
Rule of thumb: at 1 MHz in soft tissue, wavelength ≈ 1.5 mm and axial resolution ≈ 0.75 mm.