Properties of Ultrasound

Sound is a mechanical wave — a travelling disturbance of pressure through a medium. Humans can detect sound frequencies roughly between 20 Hz and 20,000 Hz (20 kHz). Ultrasound is defined as any sound wave with a frequency above 20 kHz, placing it beyond the upper threshold of human hearing. The word comes from the Latin 'ultra', meaning beyond. Bats, dolphins, and dogs routinely use frequencies in this range for navigation and communication, giving us a clue that ultrasound is not exotic — it is simply sound at a pitch too high for our ears to register. Because ultrasound follows all the same physical laws as audible sound, it reflects, refracts, diffracts, and is absorbed by materials in predictable ways. However, its high frequency gives it two practical advantages: shorter wavelengths allow the imaging of finer details, and the waves can be tightly focused into narrow beams. Medical scanners typically operate between 1 MHz and 20 MHz; industrial flaw-detection equipment and sonar systems span a similarly wide range. Understanding why high frequency enables high resolution requires grasping the fundamental relationship between frequency, wavelength, and wave speed. Ultrasound is non-ionising — it carries no ionising radiation — making it far safer for repeated medical imaging than X-rays. It is also used in cleaning delicate instruments, welding plastics, measuring fluid flow, and detecting cracks in metal structures. Studying its properties is therefore both a rich exercise in wave physics and a window into some of the most important technologies in modern medicine and engineering.

Key takeaways
  • Frequency and the Hearing Threshold
  • The Wave Equation: Linking Speed, Frequency, and Wavelength
  • Reflection and Acoustic Impedance
  • Attenuation: Energy Loss with Distance
  • The Pulse-Echo Technique and Depth Calculation

Frequency and the Hearing Threshold

Frequency f is the number of complete oscillations per second, measured in hertz (Hz). Audible sound spans 20 Hz – 20 kHz. Ultrasound begins immediately above 20 kHz. A dog whistle at ~25 kHz is the simplest everyday example. Medical ultrasound probes typically emit 1–15 MHz — that is 1,000,000 to 15,000,000 oscillations every second. Infrasound, below 20 Hz, sits at the opposite end of the spectrum and is used by elephants and seismic monitoring stations.

The Wave Equation: Linking Speed, Frequency, and Wavelength

All sound waves, regardless of frequency, obey v = fλ, where v is wave speed, f is frequency, and λ is wavelength. The speed of sound depends on the medium, not the frequency. In soft tissue, v ≈ 1540 m/s; in air, v ≈ 343 m/s. Because v is fixed for a given medium, a higher frequency directly produces a shorter wavelength. At 1 MHz in tissue, λ ≈ 1.54 mm; at 10 MHz, λ ≈ 0.154 mm. Shorter wavelengths resolve smaller structures — this is why higher-frequency probes produce sharper images.

Reflection and Acoustic Impedance

When ultrasound strikes a boundary between two media, some energy is reflected and some is transmitted. The fraction reflected depends on the acoustic impedance mismatch between the media. Acoustic impedance Z = ρv, where ρ is density and v is wave speed. A large impedance mismatch (e.g. tissue–bone or tissue–air) causes strong reflection. This is why a gel is applied between an ultrasound probe and the skin — it eliminates the air gap, whose vastly different impedance would otherwise reflect nearly all the energy before it entered the body.

Attenuation: Energy Loss with Distance

As ultrasound travels through a medium it loses intensity through absorption (conversion to heat) and scattering. Attenuation increases with frequency: higher-frequency waves lose energy more rapidly, limiting their penetration depth. This is the fundamental trade-off in medical imaging. A 3 MHz probe penetrates 10–15 cm, suitable for abdominal scans, while a 15 MHz probe only reaches ~2 cm but resolves sub-millimetre features useful for imaging superficial structures such as tendons or thyroid glands.

The Pulse-Echo Technique and Depth Calculation

Medical and sonar systems emit a short pulse and measure the time t for the echo to return. Because the pulse travels to the reflector and back, the distance d to the reflector is d = vt/2. This is identical in principle to radar. The factor of 2 accounts for the round trip. By recording the amplitude and arrival time of each echo, a scanner builds up a cross-sectional image (B-mode scan) of internal structures, with brightness indicating reflectivity and position indicating depth.

The Key Equation

v=fλv = f\lambda
  • v — Wave speed (m s⁻¹): The speed at which the sound wave propagates through the medium; approximately 1540 m/s in soft tissue and 343 m/s in air at 20 °C.
  • f — Frequency (Hz (or MHz for ultrasound)): Number of complete wave cycles per second. For ultrasound, f > 20 000 Hz by definition.
  • \lambda — Wavelength (m): The distance between two successive points of the same phase (e.g. crest to crest). Shorter wavelength enables finer spatial resolution.

Worked Example

Problem. An ultrasound probe operating at 5.0 MHz is used to image a structure inside soft tissue. The speed of ultrasound in soft tissue is 1540 m/s. (a) Calculate the wavelength of the ultrasound in tissue. (b) An echo returns 78 μs after the pulse is emitted. Calculate the depth of the reflecting surface.

λ≈3.1×10−4 m;d=vt2≈6.0×10−2 m\lambda \approx 3.1 \times 10^{-4}\text{ m};\quad d = \frac{vt}{2} \approx 6.0 \times 10^{-2}\text{ m}

Answer. Wavelength ≈ 0.31 mm; depth of reflecting surface ≈ 6.0 cm

Figure
Diagram
The Sound Spectrum: Infrasound, Audible, UltrasoundInfrasound< 20 HzAudible Sound20 Hz – 20 kHzUltrasound> 20 kHz20 Hz20 kHzfPulse-Echo Depth MeasurementProbePulse →← EchoBoundary(reflector)d = vt / 2depth d
Origins · 1 minPaul Langevin and how this was discovered
PL
Paul Langevin
1872–1946 · French

Paul Langevin was a French physicist who, working during World War I, developed the first practical ultrasonic transducer. Using piezoelectric quartz crystals sandwiched between steel plates, he generated high-frequency sound waves in water and demonstrated that they could detect submerged objects — the foundation of SONAR. His work directly established that ultrasound follows the same wave physics as audible sound and can be used for pulse-echo ranging, a principle later adapted for medical imaging. Langevin noticed that fish near his underwater ultrasound transmitter were killed by the intense sound waves — an early, accidental discovery of ultrasound's ability to damage biological tissue at high intensities, which led to both safety protocols and the therapeutic application of focused ultrasound.

  • Wave Speed, Frequency and Wavelength — The wave equation v = fλ is the central mathematical tool for understanding why ultrasound frequency determines wavelength and hence imaging resolution.
  • Reflection of Waves — Ultrasound imaging relies entirely on the reflection of pulses at boundaries between media of different acoustic impedance.
  • Transverse and Longitudinal Waves — Ultrasound is a longitudinal mechanical wave; understanding how compressions and rarefactions travel through a medium underpins all ultrasound physics.
  • The Doppler Effect — Doppler ultrasound uses the shift in frequency of reflected waves to measure blood flow velocity, extending pulse-echo imaging into dynamic measurements.