Physical Principles and Instrumentation
Wave math you must own
Diagnostic ultrasound is a mechanical, longitudinal wave. Average soft-tissue propagation speed is 1540 m/s (1.54 mm/µs). Wavelength λ = c/f and period T = 1/f: higher frequency means shorter wavelength, shorter period, and less penetration. Attenuation in soft tissue is roughly 0.5 dB/cm/MHz, so a 5 MHz beam loses about 2.5 dB per centimeter and 5 MHz reaches roughly half as deep as 2.5 MHz.
Decibels and intensity
Intensity is power per unit area (W/cm²) and is proportional to amplitude squared. A 3 dB change doubles or halves intensity (1.41× pressure); 10 dB is a tenfold intensity change; 20 dB is a tenfold amplitude change. Match the descriptor to the question: SPTA is the spatial peak, temporal average intensity used in thermal bioeffects discussions, while SPPA describes peak pressure.
Pulses and resolution
Spatial pulse length = λ × number of cycles in the pulse, and axial resolution = SPL/2. Lateral resolution is beam width, narrowest at the focal zone. Frame rate = PRF ÷ lines per frame, so depth, line density, and color box size all trade against temporal resolution. Duty factor = pulse duration × PRF.
Traps
Mixing up axial (SPL-determined) and lateral (beam-width) resolution; assuming TGC changes frequency; believing write zoom improves resolution (it enlarges stored pixels, while read zoom re-scans with finer line spacing); forgetting harmonics improve lateral resolution at the cost of penetration.
Worked example
5 MHz, 3-cycle pulse: λ = 1.54/5 = 0.308 mm; SPL = 3 × 0.308 = 0.92 mm; axial resolution = 0.46 mm.