echos part 2

Reflected and Transmitted Energy

  • Reflected Energy (Echo):

    • Defined as the energy that is reflected back when sound interacts with an interface.

    • A certain percentage is reflected based on the acoustic impedance of the materials involved.

  • Transmitted Energy:

    • The remaining energy after reflection, which continues traveling through the material.

    • The sum of reflected and transmitted energy will always equal the incident energy.

  • Energy Conservation Principle:

    • Energy is neither created nor destroyed, leading to the equation:
      extIncidentEnergy=extReflectedEnergy+extTransmittedEnergyext{Incident Energy} = ext{Reflected Energy} + ext{Transmitted Energy}

Relationship between Reflection and Transmission

  • At each acoustic interface, energy behavior is governed by the acoustic impedance mismatch.

  • The total of reflected and transmitted energies must amount to 100%:

    • ext{Reflection} + ext{Transmission} = 100 ext{%}

  • Acoustic Impedance Mismatch:

    • The difference in acoustic impedance between two materials affects how much sound is reflected versus transmitted.

Examples of Acoustic Impedance Mismatch

Example 1

  • Materials: Z1 = 120, Z2 = 5

    • Mismatched Impedance: Yes

    • Incident Energy: 100%

    • Reflected Energy: 80%

    • Transmitted Energy: 20%

    • Key Mnemonic: "Large mismatch, large reflection"

Example 2

  • Impacts of Direction:

    • Regardless of the direction of the incident sound, if there is a large acoustic impedance mismatch, a large percentage will always reflect:

    • Reflected Energy: 80%

    • Transmitted Energy: 20%

Example 3

  • Mismatched Impedance small comparison:

    • Materials Similar: Slightly varied at Z1 = 120 and Z2 = some similar value

    • Incident Energy: 100%

    • Reflected Energy: 10% (small percentage)

    • Transmitted Energy: 90% (large percentage)

    • Key Mnemonic: "Small mismatch, small reflection"

Example 4

  • Similar to Example 3:

    • Small impedance mismatch:

    • Reflected Energy: Small percentage reflected from interface

    • Transmitted Energy: Large percentage transmitted

Acoustic Impedance Values

  • Standard Values:

    • For soft tissue: Approximately 1.63 x 10^6

    • Comparison with air:

    • Air's impedance: 0.004 x 10^6 (very low)

    • Significant differences lead to large reflection:

    • Example: Air reflects about 99.9% of sound energy.

Acoustic Interfaces

  • Interface Definition:

    • Refers to regions where there is an acoustic impedance mismatch.

  • Types of Interfaces:

    1. Specular Interfaces:

    • Characteristics:

      • Large and smooth (mirror-like quality).

      • Reflect a high percentage of sound energy due to being larger than 10 wavelengths.

    • Examples:

      • Diaphragm, organ capsules, vessel walls.

    • Properties:

      • Angle dependent for strong echoes; need to be perpendicular.

      • Frequency independent; strength of echo is not affected by frequency.

    1. Scattering Interfaces:

    • Characteristics:

      • Smaller or irregular surfaces compared to wavelength.

      • Scatter sound in all directions.

    • Examples:

      • Organ parenchyma, irregular fluids with particulates.

    • Properties:

      • Angle independent; echoes return regardless of approach angle.

      • Frequency dependent; higher frequency provides stronger echoes.

Comparison of Specular vs. Scattering Interfaces

  • Specular Interfaces:

    • Large, smooth, angle-dependent, frequency-independent, strong echoes (brighter).

  • Scattering Interfaces:

    • Small, irregular, angle-independent, frequency-dependent, weak echoes (darker).

  • Final Summary:

    • Echoes produced by acoustic interfaces must account for impedance mismatches.

    • Strong echoes come from large mismatches (higher reflection), while weak echoes stem from small mismatches (lower reflection).

Summary Principles

  • Key Mnemotics:

    1. "Large mismatch, large reflection".

    2. "Small mismatch, small reflection".

  • Importance of Angle:

    • Specular interfaces require perpendicular incidence for strong echoes, whereas scattering interfaces do not depend on angle.

  • Frequency Dependency:

    • Scattering echoes improve with increased frequency, while specular echoes remain stable across different frequencies.