Chapter 9 Sound Beam

The Shape of a Sound Beam

  • The width of a sound beam changes as sound travels.

    • At the starting point, the beam's width is equal to the transducer diameter.

    • The beam narrows progressively until it reaches its smallest diameter (the focus).

    • After the focus, the beam begins to expand or diverge.

Anatomy of a Sound Beam

Key Terms Describing Regions of a Sound Beam

  • Focus:

    • Definition: The location where the beam is at its narrowest.

    • For disc-shaped crystals, the width at the focus is half the width of the beam when it exits the transducer.

  • Near Zone (Fresnel Zone):

    • Definition: The region extending from the transducer to the focus.

    • Also referred to as focal length, near zone length, or focal depth.

  • Far Zone (Fraunhofer Zone):

    • Definition: The region from the focus extending deeper into the medium.

  • Focal Zone:

    • Definition: The area surrounding the focus, where the beam remains relatively narrow.

Focal Depth

  • The focal depth in a standard transducer is a fixed value.

  • Focal Depth is directly influenced by the following:

    • Transducer Diameter:

    • A wider crystal produces a deeper focus and vice versa (inversely proportional relationship).

    • Frequency of Sound:

    • A higher frequency results in a deeper focus, while a lower frequency leads to a shallower focus.

  • Formula for Focal Depth: Focal Depth=D2×F6\text{Focal Depth} = \frac{D^2 \times F}{6}

  • Modern ultrasound systems (phased array technology) allow for manipulation of focal depth.

Sound Beam Divergence

  • Various transducer characteristics affect the divergence of sound beams in the far field.

    • Transducer Diameter:

    • Smaller diameter crystals produce beams that diverge more.

    • Larger diameter crystals enhance lateral resolution in the far field.

    • Frequency of Sound:

    • Lower frequency sound beams diverge more in the far field.

    • Higher frequency sound beams lead to improved lateral resolution in the far field.

  • If the half-angle of divergence in the far field is represented by θ\theta, the relationship is described mathematically as: sin⁡(θ)=1.22λD\sin(\theta) = \frac{1.22 \lambda}{D}

  • Where:

λ\lambda = wavelength

  • DD = diameter of the transducer

Huygens’ Principle: Explaining the Sound Beam Shape

  • Huygens’ Principle elucidates the hourglass shape of a sound beam.

  • Each minute section of the surface of the PZT (Piezoelectric Transducer) acts as a tiny sound source, producing Huygens’ wavelets (V-shaped waves).

    • Huygens’ wavelets are characterized as V-shaped waves, synonymous with spherical waves or diffraction patterns.

  • The overall hourglass shape of a sound beam is a result of the constructive and destructive interference arising from