Ch.6 Class Interaction between Sound and Media notes

Interaction between Sound and Media

Sound and Media

• Sound interacts with the media it travels through.

• Different types of media exist within the human body.

• When sound encounters a boundary, reflection occurs.

Attenuation

• As sound travels, it weakens, a phenomenon known as attenuation.

• The received sound requires amplification by the system.

• A transducer converts received sound into electricity.

Measuring Attenuation and Amplification

• Decibels are used to measure and report changes in sound intensity.

• Decibels are based on logarithms.

Logarithms

• The logarithm of a number indicates the power to which 10 must be raised to equal that number.

  • Example:

    • 10 * 10 = 100, so the log of 100 is 2.

    • 10 * 10 * 10 = 1000, so the log of 1000 is 3.

• A logarithmic increase of 2 signifies that the signal is 100 times stronger than the original signal.

Decibels

• Decibels quantify the strength of sound waves and brightness.

• Decibel notation is logarithmic and represents relative changes.

• Decibel measurements require two intensities for comparison.

• Positive decibels indicate an increase in signal strength, while negative decibels indicate a decrease.

Decibels and Intensities

• Key decibel values:

  • 3 dB: Double.

  • 10 dB: Ten times greater.

  • -3 dB: Half.

  • -10 dB: One-tenth.

Attenuation

• Attenuation refers to the weakening of sound as it travels through a medium, which involves a decrease in power, amplitude, and intensity.

• Attenuation is determined by distance and sound frequency, with both being directly related to it.

• Attenuation is reported in decibels as a relative change.

Reflection

• Reflection occurs when some of the wave's energy is sent back to the sound source, weakening the transmitted wave.

• Specular reflection happens when sound hits a smooth boundary and reflects in one direction, similar to light hitting a mirror.

• Diffuse reflection or backscatter occurs when sound hits irregular surfaces.

Scattering

• Scattering involves the random redirection of sound in multiple directions, occurring when sound hits a small interface.

• Higher frequency sound beams scatter more than low-frequency sound waves.

• Rayleigh scattering is a specific type of scattering that occurs when the structure is smaller than the beam's wavelength.

Rayleigh Scattering Continued

• Higher frequency waves scatter more.

• Rayleigh Scattering Formula:

  • Rayleigh Scattering = F^4

• When frequency doubles, Rayleigh scattering is squared.

Absorption

• Most attenuation is due to absorption, which is the conversion of ultrasound into another form of energy.

• Higher frequency waves are absorbed more than lower frequency waves.

• Sound traveling through bone undergoes extensive absorption.

Attenuation Coefficient

• Attenuation coefficient is the number of decibels of attenuation that occur when sound travels 1 cm (dB/cm).

• Formula for total attenuation:

  • Total attenuation (dB) = AC (dB/cm) * Distance (cm)

Attenuation Coefficient in Soft Tissue

• Attenuation coefficient and sound frequency are directly related.

• AC is approximately equal to ½ of the frequency.

Half Value Layer Thickness

• Half Value Layer Thickness is the distance that sound travels in tissue that reduces its intensity to one half of its original value.

• Determined by frequency and medium.

Impedance

• Impedance is the acoustic resistance to sound as it travels through the medium.

• Calculated as:

  • density (medium) * propagation speed = impedance (rayls)

• Reflection depends on the differences in impedances of two media at a boundary.

Incidence

• Incidence is the angle at which a wave strikes a boundary, and this determines the behavior of the pulse.

• Normal Incidence: 90-degree angle (right, perpendicular).

• Oblique incidence: Any angle other than 90 degrees (obtuse or acute).

Intensity and Incidence

• Incident Intensity: The intensity of the sound BEFORE it strikes the boundary.

• Reflected Intensity: The intensity of the sound that RETURNS after hitting the boundary.

• Transmitted Intensity: The intensity of the sound that CONTINUES forward after striking the boundary.

• Relationship:

  • Incident Intensity = reflected intensity + transmitted intensity

Intensity Reflection Coefficient/ Intensity Transmission Coefficient

• IRC (Intensity Reflection Coefficient): Percentage of intensity that reflects when a sound beam strikes a boundary.

• ITC (Intensity Transmission Coefficient): Percentage of intensity that goes forward when a sound beam strikes a boundary.

Reflection with Normal Incidence

• Sound strikes the boundary at a 90-degree angle.

• Media must have different impedances to send back a reflection.

• IRC is related to the difference in impedances between tissues.

Transmission with Normal Incidence

• If incidence is normal and impedance is the same, all intensity will be transmitted with a soft tissue/ soft tissue boundary.

Reflection and Transmission with Oblique Incidence

• Reflection: Unpredictable.

• Mediums of the same impedance may still reflect.

• Transmission at oblique incidence may not occur; refraction may occur.

Refraction

• Refraction is transmission with a bend; it is the bending or changing direction of sound when traveling from one medium to another.

• Occurs with oblique incidence and different propagation speeds.

Snell’s Law

• Snell’s Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and equal to the ratio of the speeds of the two media.

  • \frac{Sin (transmit angle)}{Sin (incident angle)} = \frac{speed \space medium \space 1}{ speed \space medium \space 2}

Refraction and Speeds

• Relationship between speeds and angles:

  • Speed 2 = Speed 1: No refraction, TA = IA.

  • Speed 2 > Speed 1: TA > IA.

  • Speed 2 < Speed 1: TA < IA.

Reflection, transmission and refraction

• Event and Requirement:

  • Reflection with Normal Incidence: Requires different impedances.

  • Reflection with Oblique Incidence: Unpredictable.

  • Transmission: Depends on conservation of energy.

  • Refraction: Oblique incidence and different propagation speeds.

References

• Edelman, S. (2007). Understanding Ultrasound Physics.