03A: Reflections

Perpendicular Incidence

• Sound beam travels perpendicular to boundary between two media 90 o Incident Angle Boundary between media 1 2 George David Associate Professor

Oblique Incidence

• Sound beam travel not perpendicular to boundary Oblique Incident Angle (not equal to 90 o ) Boundary between media 2 1 George David Associate Professor

Perpendicular Incidence

• What happens to sound at boundary?



reflected

» sound returns toward source 

transmitted

» sound continues in same direction 1 2 George David Associate Professor

Perpendicular Incidence

• Fraction of intensity reflected depends on acoustic impedances of two media Acoustic Impedance = Density X Speed of Sound 1 2 George David Associate Professor

An Aside about Reflections

• Echoes occur at interfaces between 2 media of different acoustic impedances  speed of sound X density Medium 1 Medium 2 George David Associate Professor

Intensity Reflection Coefficient (IRC) & Intensity Transmission Coefficient (ITC)

• IRC  Fraction of sound intensity reflected at interface  <1 • ITC  Fraction of sound intensity transmitted through interface  <1 Medium 1 IRC + ITC = 1 Medium 2

IRC Equation

For perpendicular incidence reflected intensity z 2 - z 1 IRC = ------------------------ = --------- incident intensity z 2 + z 1 2 • Z 1 is acoustic impedance of medium #1 • Z 2 is acoustic impedance of medium #2 Medium 1 Medium 2

Reflections

reflected intensity z 2 - z 1 Fraction Reflected = ------------------------ = --------- incident intensity z 2 + z 1 2 • Impedances equal  no reflection • Impedances similar  little reflected • Impedances very different  virtually all reflected George David Associate Professor

Why Use Gel?

reflected intensity z 2 - z 1 IRC = ------------------------ = --------- incident intensity z 2 + z 1 2 Air Soft Tissue Acoustic Impedance (rayls) 400 1,630,000 Fraction Reflected: 0.9995

• Acoustic Impedance of air & soft tissue very different • Without gel virtually no sound penetrates skin

Rayleigh Scattering

• redirection of sound in many directions • caused by rough surface with respect to wavelength of sound George David Associate Professor

Diffuse Scattering & Rough Surfaces

• heterogeneous media • cellular tissue • particle suspension  blood, for example

Scattering

• Occurs if  boundary not smooth • Roughness related to frequency  frequency changes wavelength » higher frequency shortens wavelength » shorter wavelength “roughens” surface

Specular Reflections

• Un-scattered sound  occurs with smooth boundaries • similar to light reflection from mirror  opposite of scatter from rough surface  wall is example of rough surface George David Associate Professor

Backscatter

• sound scattered back in the direction of source George David Associate Professor

Backscatter Comments

• Caused by  rough surfaces  heterogeneous media • Depends on scatterer’s  size  roughness  shape  orientation • Depends on sound frequency  affects wavelength George David Associate Professor

Backscatter Intensity

• normally << than specular reflections • angle dependance  specular reflection very angle dependent  backscatter not angle dependent » echo reception not dependent on incident angle • increasing frequency effectively roughens surface  higher frequency results in more backscatter George David Associate Professor