19.2 Ultrasound Wave Properties, Propagation, Frequency, and Wavelength

Define the mechanical wave

Diagnostic ultrasound is a longitudinal mechanical pressure wave. Particles in the medium oscillate parallel to wave travel, creating compressions and rarefactions; matter does not travel from transducer to heart with the pulse. Ultrasound requires a medium and does not propagate through a vacuum. A piezoelectric element converts electrical energy into sound during transmission and returning pressure into electrical signal during reception. The system assigns echo location and brightness from return time and amplitude using simplified propagation assumptions.

The fundamental equation is c = fλ. In soft tissue, the system assumes c = 1,540 m/s. For a 5-MHz wave, λ = 1,540 m/s ÷ 5,000,000/s = 0.000308 m = 0.308 mm. Convert megahertz to hertz before dividing and meters to millimeters afterward. In one medium, changing transducer frequency changes wavelength, not propagation speed. At a boundary, transmitted frequency remains constant while speed and wavelength change with the new medium.

Frequency creates a penetration-resolution tradeoff. Higher frequency produces a shorter wavelength and can support shorter pulses and better spatial detail, but attenuation increases and penetration falls. Lower frequency penetrates farther at the expense of detail. Choose the highest frequency that still reaches the structure with adequate signal. This is an optimization choice, not a rule that higher frequency always improves the entire image.

Connect pulses, time, and imaging depth

Clinical imaging sends short pulses rather than continuous trains. Pulse duration is the time from the beginning to end of one pulse:

Pulse duration = number of cycles × period

Spatial pulse length, or SPL, is its physical length:

SPL = number of cycles × wavelength

Axial resolution is approximately SPL / 2 because two reflectors must be separated by half the pulse length along the beam to return distinguishable echoes. Fewer cycles, shorter wavelength, strong damping, and broad bandwidth shorten SPL. Lateral resolution depends mainly on beam width, and elevational resolution on slice thickness; neither is calculated from SPL alone. Focus narrows the beam near the region of interest, so lateral detail is best near the focal zone.

Pulse repetition period, or PRP, is time from the start of one pulse to the next. PRF = 1 / PRP and is expressed in hertz. The system must wait for deep echoes before sending the next pulse, so increasing imaging depth lengthens PRP and lowers maximum PRF. Duty factor is pulse duration / PRP and describes the fraction of time transmitting. Diagnostic pulsed imaging spends far more time listening than transmitting. Do not confuse operating frequency, cycles within each pulse, and PRF; each has different units and functions.

Predict propagation at tissue boundaries

Acoustic impedance is Z = density × propagation speed. A portion of a wave reflects when it meets an impedance difference; a larger mismatch generally returns a stronger echo. At a smooth specular surface, perpendicular incidence sends more reflection back to the transducer, while an oblique beam may reflect away. Small or rough structures scatter energy in many directions and allow interfaces such as myocardium to be seen from multiple windows. Gas and bone create large mismatches and strong attenuation, explaining the need for intercostal acoustic windows and gel to eliminate air at the skin.

Refraction changes propagation direction when a wave crosses an interface obliquely and sound speeds differ. This bending follows the speed relationship between media and can laterally misplace or duplicate a structure. Normal incidence avoids refraction. The scanner nevertheless assumes straight-line travel and a constant 1,540-m/s speed; violations produce predictable location errors discussed in the artifact section.

Attenuation is the progressive loss of wave intensity through absorption, reflection, and scattering. In soft tissue, a useful average attenuation coefficient is about 0.5 dB/cm/MHz for one-way travel. Thus higher frequency and longer path cause more loss. A pulse also attenuates returning to the transducer, so deep echoes experience two-way loss. Overall gain amplifies all received echoes; time-gain compensation selectively increases amplification with depth. Neither restores information that never returned, and excessive compensation adds noise or blooming.

Link wave physics to Doppler

The Doppler shift for reflected ultrasound is approximated by:

fD = 2f₀v cos θ / c

The factor 2 represents travel to and from moving blood; f₀ is transmitted frequency, v is velocity, θ is the beam-flow angle, and c is propagation speed. A parallel beam has cos 0° = 1 and yields the largest shift; at 90°, cos 90° = 0 and no Doppler shift is detected even though flow exists. Higher transmit frequency produces a larger shift for the same velocity but also increases attenuation and aliasing susceptibility in pulsed Doppler.

PW Doppler localizes range by pulse timing but samples at a finite PRF. CW Doppler continuously transmits and receives, measures high velocity without aliasing, and lacks precise range resolution. Color Doppler maps mean shifts over many sample volumes rather than displaying actual blood color. Before accepting any calculation, write known values with units, convert prefixes, choose the matching equation, and test whether the direction and magnitude are plausible. Unit discipline prevents a correct formula from producing a meaningless answer.

Frequency does not set soft-tissue speed

Within the same medium, the scanner's 1,540-m/s soft-tissue assumption remains constant. Raising frequency shortens wavelength and increases attenuation; it does not make the wave travel faster.