Interaction of Sound & Media and Range Equation

Flashcards covering sound attenuation, decibel notation, components of attenuation (reflection, scattering, absorption), acoustic impedance, incidence, refraction, and range equation concepts as described in Edelman's Physics.

Attenuation

The gradual loss of sound wave strength (intensity, power, and amplitude) as it travels through tissue, measured in decibels ($dB$).

Decibel Notation ($dB$)

A relative measurement based on a logarithmic scale that compares a new intensity to the original intensity.

Logarithm

A value telling us how many times $10$ is multiplied by itself; used in ultrasound because intensity changes over extremely large ranges.

$$+3\,dB$$

A change in decibels indicating that the intensity has doubled ($Intensity \times 2$).

$$-3\,dB$$

A change in decibels indicating that the intensity has been reduced to one-half

$$+10\,dB$$

A change in decibels indicating that the intensity is ten times larger ($Intensity \times 10$).

$$-10\,dB$$

A change in decibels indicating that the intensity has dropped to one-tenth of its original value

Reflection

A component of attenuation where sound encounters a boundary between two tissues and part of the wave returns to the transducer.

Specular Reflection

Occurs at smooth, flat boundaries (like vessel walls or the diaphragm) where echoes return in a single organized direction.

Diffuse Reflection (Backscatter)

Occurs when sound strikes an irregular or rough surface, scattering echoes in many directions.

Scattering

The disorganized and chaotic redirection of sound in many directions, occurring when the reflecting surface is small (equal to or smaller than the wavelength).

Rayleigh Scattering

A special type of omnidirectional scattering that occurs when the scatterer is much smaller than the wavelength; it is directly related to frequency raised to the fourth power ($\propto Frequency^4$).

Absorption

The largest contributor to attenuation, where sound energy is converted into heat; it is highest in bone and directly related to frequency.

Attenuation Coefficient

The amount of sound energy lost per centimeter traveled ($dB/cm$); in soft tissue, it is approximately $\frac{Frequency\,(MHz)}{2}$.

Half-Value Layer Thickness (HVL)

The distance sound travels before its intensity is reduced by $50\%$ ($3\,dB$); also known as penetration depth or half-boundary layer.

Acoustic Impedance (Z)

The resistance a medium offers to the transmission of sound, calculated as $Z = \text{Density} \times \text{Propagation Speed}$.

Rayls

The unit of measurement for acoustic impedance ($Z$).

Normal Incidence

Occurs when a sound beam strikes a boundary at exactly $90^{\circ}$; also called perpendicular, orthogonal, or right-angle incidence.

Oblique Incidence

Occurs when a sound beam strikes a boundary at any angle other than $90^{\circ}$; may be acute or obtuse.

Intensity Reflection Coefficient (IRC)

The percentage of the incident intensity that is reflected at a boundary.

Intensity Transmission Coefficient (ITC)

The percentage of the incident intensity that is transmitted across a boundary.

Refraction

Transmission with a bend; occurs only with oblique incidence and different propagation speeds between two media.

Snell's Law

The mathematical description of refraction used to determine the angle of the transmitted beam based on propagation speeds.

Time of Flight

The go-return time or round trip time needed for a pulse to travel to a reflector and back to the transducer.

$$13\text{-Microsecond Rule}$$

In soft tissue, every $13\,\mu s$ of go-return time corresponds to $1\,cm$ of reflector depth.

Pulse Repetition Period (PRP)

The time from the beginning of one pulse to the beginning of the next, directly related to the maximum imaging depth.

Pulse Repetition Frequency (PRF)

The number of pulses the transducer sends each second, inversely related to imaging depth ($PRF\,(Hz) = \frac{77,000\,cm/s}{\text{imaging depth}\,(cm)}$ ) .