Seven Parameters of Sound

Period and Frequency

• Seven sound-wave parameters (essential): $f$ (frequency), $T$ (period), $c$ (propagation speed), $\lambda$ (wavelength), amplitude, power, intensity.

• Five focus points to remember: definitions (and synonyms), units, symbols, formulas/relationships, and sonographer impact.

• Period and frequency are reciprocal:

  • $T = \frac{1}{f}$ and $f = \frac{1}{T}$.

• A cycle: one complete oscillation (rest → compress → rest → rarefaction → rest).

• Period units: typically microseconds in ultrasound (range ~$0.06-0.5\ \mu s$); frequency units: typically megahertz (MHz).

• Frequency in ultrasound: usually described as the transducer’s emitted frequency; actual frequency is largely determined by the transducer and machine bandwidth and is not freely adjustable by the sonographer.

• Important relationship with wavelength: $\lambda = \frac{c}{f}$.

• Soft-tissue speed (average speed of sound): $c \approx 1.54\ \text{mm/}\mu\text{s}$ or $c \approx 1540\ \text{m/s}$.

• For soft tissue, using MHz for frequency: $\lambda \approx \frac{1.54}{f\text{(MHz)}}\text{ mm}$.

• Higher frequency → shorter wavelength and better axial resolution but less penetration; lower frequency → longer wavelength with greater penetration but reduced detail.

• Propagation speed (c) basics:

  • c is the speed at which sound travels in a medium.

  • Directly related to stiffness; inversely related to density: stiffer media speed up; denser media slow down.

  • $c \propto \sqrt{\frac{\text{stiffness}}{\text{density}}}$.

• Media speeds (conceptual): air and lungs are slowest; bone is fastest; soft tissue is the standard reference (average soft-tissue speed used by ultrasound machines).

• Sonographer impact on period/frequency:

  • You cannot directly adjust period or the native frequency of the emitted wave.

  • Modern transducers have bandwidth; you can influence which echoes the system “listens for” by selecting a frequency range, but you are not changing the actual transducer’s innate frequency.

  • Choice of transducer frequency represents a balance: high frequency → better resolution, shallow penetration; low frequency → deeper penetration, lower resolution.

• Audible vs ultrasound reference:

  • Audible range: $20\ \text{Hz} \leq f \leq 20\ \text{kHz}$.

  • Ultrasound: f > 20\ \text{kHz}; diagnostic imaging typically uses $\approx 1-17\ \text{MHz}$.

• Quick calculation examples:

  • 2 cycles in 1 second: $f = \frac{2}{1\text{ s}} = 2\ \text{Hz};\ T = \frac{1}{2\ \text{Hz}} = 0.5\ \text{s}.$

  • 10 cycles in 1 microsecond: $f = \frac{10}{1\ \mu\text{s}} = 10\ \text{MHz};\ T = \frac{1}{10\ \text{MHz}} = 0.1\ \mu\text{s}.$

• Practice reminder: use complementary units (seconds with Hz, microseconds with MHz, milliseconds with kHz) when pairing period and frequency.

Wavelength and Propagation Speed

• Propagation speed (c): speed at which a sound wave travels through a medium.

• Units: $\text{m/s}$ or $\text{mm}/\mu\text{s}$.

• Soft tissue average: $c \approx 1.54\ \text{mm/}\mu\text{s}$ (≈ 1540 m/s).

• Medium effects:

  • Speed increases with stiffness (more bulk modulus).

  • Speed decreases with density (more dense media slow the wave).

  • Relationship: $c \propto \sqrt{\frac{\text{stiffness}}{\text{density}}}$

• Wavelength $\lambda$: distance that one cycle occupies in space.

• Wavelength units: typically millimeters (mm).

• Wavelength relation:

  • $\lambda = \frac{c}{f}$.

  • In soft tissue: $\lambda = \frac{1.54\ \text{mm/}\mu\text{s}}{f\text{(MHz)}}$ (mm).

• Soft-tissue wavelength ranges (example):

  • 8 MHz in soft tissue: $\lambda \approx 0.19\ \text{mm}$.

  • 3 MHz in soft tissue: $\lambda \approx 0.51\ \text{mm}$.

• Air vs soft tissue contrast:

  • In air, $c \approx 0.33\ \text{mm/}\mu\text{s}$ → much longer wavelengths at a given frequency.

• Practical implications:

  • Shorter wavelengths improve axial resolution; wavelengths are not independently adjustable since they depend on frequency and medium.

  • The frequency choice (via transducer/bandwidth) and the medium together determine the resulting wavelength.

• Memorized quick references (soft tissue):

  • 1 MHz: $T = 1\ \mu\text{s}$, $\lambda \approx 1.54\ \text{mm}$.

  • 2 MHz: $T = 0.5\ \mu\text{s}$, $\lambda \approx 0.77\ \text{mm}$.

• Example comparison (same time frame):

  • 8 MHz → shorter cycle length than 3 MHz (in soft tissue) within the same microsecond frame.

• Summary relation:

  • If frequency increases (within medium), wavelength decreases; if speed is higher, wavelengths are longer for the same frequency.

• Board/workbook note reference (conceptual): with known medium, you can derive period, frequency, and wavelength from a small set of data using these relationships.