Week 1 Sound Wave Parameters

Learning Objectives

  • Understand the key sound wave parameters relevant for ultrasound physics.

Key Sound Wave Parameters

  • Wavelength (λ):

    • Distance one cycle occupies (distance between 2 areas of maximal compression or rarefaction).

    • Unit: meters (m) or millimeters (mm).

    • MEASURE OF DISTANCE.

  • Period (T):

    • Time taken for one cycle occurred.

    • Unit: seconds or microseconds.

    • Inversely related to frequency.

    • MEASURE OF TIME.

  • Frequency (ƒ):

    • Number of cycles passing per unit time.

    • Measured in Hertz (Hz).

    • Higher frequency = shorter wavelength; Lower frequency = longer wavelength.

  • Speed of Propagation (Velocity) (c or v):

    • Speed at which the wave travels through a specific medium.

    • v = λ f

    • Units: m/s or mm/s.

    • Average speed in soft tissue: 1540 m/s or 1.54 mm/µs.

  • Amplitude (A):

    • Maximum variation from the mean value (baseline to peak or trough).

    • Represents strength of sound

  • Intensity (I):

    • Distribution of power (P) over a defined area.

    • Formula: I=PAreaI = \frac{P}{\text{Area}}

    • Intensity increases with decreased beam area due to focusing.

Wave Representation

  • Sound expressed as a sine wave depicting cycles of compression and rarefaction.

Importance of Frequency in Ultrasound

  • High Frequency (e.g., 17 MHz):

    • Short wavelength = better resolution = limited depth.

  • Low Frequency (e.g., 5 MHz):

    • Longer wavelength = lower resolution = better depth penetration.

Wavelength and Frequency Relationship

  • Wavelength (λ) is inversely proportional to frequency (ƒ):

    • λ=1ƒ\lambda=\frac{1}{ƒ}

    • High frequency results in a short wavelength, and low frequency results in a long wavelength.

Wave Equation

  • Using a transducer's frequency and soft tissue propagation speed to calculate wavelength:

    • λ=cƒ\lambda=\frac{c}{ƒ}

    • Given soft tissue velocity c = 1.54mm/us

Propagation Speed Dependencies

  • Propagation speed in a medium is influenced by:

    • Density (ρ): Mass per unit volume.

    • Stiffness (Bulk Modulus): Resists deformation under stress; critical for determining velocity.

  • Higher stiffness leads to higher propagation speeds than density increases alone.

Propagation Speeds in Various Tissues

  • Bone: 4080 m/s

  • Muscle: 1580 m/s

  • Liver: 1550 m/s

  • Soft Tissue (average): 1540 m/s

  • Kidney: 1560 m/s

  • Blood: 1570 m/s

  • Fat: 1450 m/s

  • Water: 1480 m/s

  • Air: 330 m/s

Power and Amplitude Relationship

  • Power (P): Energy expended per unit time, measured in Watts.

  • Relationship: Power is proportional to the square of amplitude: P∝A2P \propto A^2

    • Increasing transmit voltage enhances acoustic energy or power, resulting in stronger echoes and increased penetration but may also lead to bio-effects.

Analyzing Amplitude and Frequency

  • Amplitude relates to sound strength; Frequency relates to pitch.

    • Same frequency but different amplitudes create variations in perceived strength.

Conclusion

  • To summarize:

    • Understanding these parameters is essential for effective ultrasound imaging and diagnostics.

    • For deeper learning, references include Khan Academy and other physics resources available online.