Curriculum · Ultrasound Physics & Instrumentation

Acoustic Waves & Parameters

What sound is, the seven acoustic parameters, the wave equation c = fλ, propagation speed, acoustic impedance, and the decibel scale.

~35 min · level: foundation · SPI draft — pending clinical review

Learning objectives

Describe ultrasound as a longitudinal mechanical wave and list its acoustic variables.
Apply the wave equation c = fλ and explain why frequency and wavelength are inversely related in tissue.
State the soft-tissue propagation-speed convention (1540 m/s) and rank tissue speeds.
Define acoustic impedance (Z = ρc) and explain its role in reflection.
Use the decibel scale and the −3 dB / −6 dB anchors.

Ultrasound is a mechanical, longitudinal (compressional) pressure wave: particles of the medium oscillate parallel to the direction of energy travel, creating alternating compressions (high pressure/density) and rarefactions (low pressure/density). Because it is mechanical, it cannot travel through a vacuum — it requires a material medium. "Ultrasound" means a frequency above the audible range ( $> 20\text{ kHz}$ ); diagnostic imaging uses roughly 2–15 MHz (up to 50–70 MHz for intravascular and superficial probes).

Acoustic variables

The physical quantities that actually oscillate as the wave passes: pressure (Pa, often MPa for peaks), density (kg/m³), and particle motion (displacement / particle velocity). Note: particle velocity (how fast tissue molecules jiggle) is not the same as propagation speed (how fast the wave front advances).

Seven parameters describe a sound wave. A crucial registry distinction is what determines each — the source (transducer), the medium, or the operator:

Parameter	Symbol	Determined by	Operator-adjustable?
Frequency	$f$	Source (transducer)	No
Period	$T$	Source	No
Wavelength	$\lambda$	Source and medium	No
Propagation speed	$c$	Medium only	No
Amplitude	$A$	Source	Yes (output power)
Power	$P$	Source	Yes
Intensity	$I$	Source + focusing	Yes

The seven acoustic parameters and what controls them.

Frequency and period are reciprocals ( $f = 1/T$ ). The single most-tested relationship is the wave equation:

c = f\,\lambda \qquad\Longrightarrow\qquad \lambda = \frac{c}{f}

Propagation speed equals frequency times wavelength.

At the soft-tissue convention $c = 1540\text{ m/s} = 1.54\text{ mm/}\mu\text{s}$ , this gives the handy form $\lambda(\text{mm}) = 1.54 / f(\text{MHz})$ . Because $c$ is fixed by tissue, frequency and wavelength are inversely related: higher frequency → shorter wavelength → finer axial resolution, but more attenuation → shallower penetration. This single tradeoff governs probe selection.

Frequency	Wavelength (λ = 1.54/f)
2 MHz	0.77 mm
5 MHz	0.31 mm
10 MHz	0.15 mm
15 MHz	0.10 mm

Wavelength in soft tissue at common imaging frequencies.

Propagation speed depends on the medium's stiffness (bulk modulus $K$ , ↑ → faster) and density ( $\rho$ , ↑ → slower), with stiffness dominating in tissue: $c = (K/\rho)^{1/2}$ (equivalently $c^{2} = K/\rho$ ). Scanners assume a single value — 1540 m/s — for every tissue, which is the origin of the 13-µs-per-cm range rule and of speed-error artifacts.

Medium	Speed (m/s)	Note
Air / lung gas	~330	Slowest; huge impedance mismatch
Fat	~1450	Below 1540 → speed-error artifact
Soft tissue (avg)	1540	Assumed constant by the scanner
Blood / liver	~1560–1570
Muscle	~1580–1600
Bone (cortical)	~3500–4080	Fast; very high impedance

Standard textbook propagation speeds (memorize the ordering).

Acoustic impedance is the resistance a medium offers to sound, and it governs how much sound reflects at a boundary:

Z = \rho\,c \quad\text{(units: rayls, kg·m}^{-2}\text{s}^{-1}\text{; usually Mrayls)}

Acoustic impedance is density times propagation speed.

Returning echoes span an enormous range of intensities ( $\sim 10^7$ – $10^8$ ), so we use the logarithmic decibel:

\text{dB} = 10\,\log_{10}\!\left(\frac{I_2}{I_1}\right) = 20\,\log_{10}\!\left(\frac{A_2}{A_1}\right)

Decibels for intensity (×10) and amplitude/pressure (×20).

Worked example — wavelength and impedance

(a) A 7.5 MHz linear probe images soft tissue. What is the wavelength? (b) Why does almost no sound penetrate beyond a soft-tissue/air interface?

Solution.

(a) $\lambda = 1.54 / 7.5 = 0.205\text{ mm} \approx 0.21\text{ mm}$ . (b) The reflection at a boundary depends on the impedance mismatch. Tissue ( $\approx 1.63$ Mrayl) vs air ( $\approx 0.0004$ Mrayl) is a near-total mismatch, so $R \approx 99.9\%$ of the intensity reflects — virtually nothing transmits, producing shadowing. (This is quantified in Lesson 3.)

Key takeaways

Ultrasound is a mechanical longitudinal pressure wave (compressions and rarefactions) that cannot travel through a vacuum, with diagnostic imaging using roughly 2-15 MHz.
The wave equation c = f times lambda means that because speed is fixed by the medium, frequency and wavelength are inversely related: higher frequency gives shorter wavelength and finer axial resolution but more attenuation and shallower penetration.
Frequency, period, and wavelength are set by the source while propagation speed is set by the medium alone (c = square root of K/rho); only wavelength depends on both source and medium.
Scanners assume soft tissue speed of 1540 m/s (1.54 mm/microsec, so lambda in mm = 1.54/f in MHz), with the ordering air ~330 < fat ~1450 < tissue 1540 < blood/liver ~1560-1570 < muscle ~1580-1600 < bone ~3500-4080.
Acoustic impedance Z = rho times c is a frequency-independent property of the medium that governs reflection, and the dB anchors are -3 dB = intensity halved and -6 dB = amplitude halved (intensity to 25%).

Check your understanding

Registry-style items with worked rationales.

1Which acoustic parameter is determined solely by the medium through which sound travels?recall

2A transducer operates at 10 MHz. What is the wavelength in soft tissue?application

3Increasing transducer frequency will:analysis

4A −3 dB change corresponds to what change in intensity?application

Go deeper — trusted free resources

Hand-picked, verified links to authoritative open resources. Opens in a new tab.

Radiopaedia

Physical Principles of Ultrasound

Concise reference covering acoustic waves, frequency, wavelength, propagation speed, and how these parameters interact to form the foundation of ultrasound imaging.

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Radiopaedia

Acoustic Impedance

Focused article on acoustic impedance (Z = density x propagation speed) and why impedance mismatches at tissue interfaces drive reflection and image formation.

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StatPearls

Ultrasound Physics and Instrumentation

Comprehensive open-access chapter detailing propagation speed in soft tissue, the decibel scale as a logarithmic intensity ratio, attenuation, and core wave parameters.

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Radiopaedia

Ultrasound Frequencies

Explains the inverse frequency-wavelength relationship and the resolution-versus-penetration tradeoff that determines transducer frequency selection in practice.

Open →

References

Edelman SK. Understanding Ultrasound Physics. 4th ed. ESP Inc.; 2012.
Kremkau FW. Sonography Principles and Instruments. 9th ed. Elsevier; 2016.
Ultrasound Physics and Instrumentation. StatPearls, NCBI Bookshelf.
ARDMS Sonographic Principles & Instrumentation (SPI) examination outline.

Acoustic Waves & Parameters

Learning objectives

✅ Key takeaways

Check your understanding

📚 Go deeper — trusted free resources

References

Key takeaways

Go deeper — trusted free resources