CIE A Level Physics (9702) 2019-2021

Revision Notes

19.3.3 Intensity Reflection Coefficient

Intensity Reflection Coefficient

  • The intensity reflection coefficient α is defined as:

The ratio of the intensity of the reflected wave relative to the incident (transmitted) wave

  • This can be calculated using the fraction:

Intensity Reflection Coefficient equation 1

  • Where:
    • α = intensity reflection coefficient
    • IR = intensity of the reflected wave (W m-2)
    • I0 = intensity of the incident wave (W m-2)
    • Z1 = acoustic impedance of one material (kg m-2 s-1)
    • Z2 = acoustic impedance of a second material (kg m-2 s-1)
  • This equation will be provided on the datasheet for your exam
  • This ratio shows:
    • If there is a large difference between the impedance of the two materials, then most of the energy will be reflected
    • If the impedance is the same, then there will be no reflection

Coupling Medium

  • When ultrasound is used in medical imaging, a coupler is needed between the transducer and the body
  • The soft tissues of the body are much denser than air
  • If air is present between the transducer and the body, then almost all the ultrasound energy will be reflected
  • The coupling gel is placed between the transducer and the body, as skin and the coupling gel have a similar density, so little ultrasound is reflected
    • This is an example of impedance matching

Worked example: Intensity reflection coefficient

Intensity_Reflection_Coefficient_Worked_Example_-_Intensity_Reflection_Coefficient_Question, downloadable AS & A Level Physics revision notes

Part (a)

Incident intensity = Transmitted intensity + Reflected intensity

I = IT + IR

Part (b)(i)

Step 1:            Write down the equation for intensity reflection coefficient α

Intensity Reflection Coefficient Worked Example equation 1

Step 2:            Write down the acoustic impedances for gel and soft tissue

Gel, Z1 = 1.5 × 106 kg m-2 s-1

Soft tissue, Z2 = 1.6 × 106 kg m-2 s-1

Step 3:            Calculate the intensity reflection coefficient

 Intensity Reflection Coefficient Worked Example equation 2

This result means that only 0.1% of the incident intensity will be reflected, with the remaining being transmitted

 

Part (b)(ii)

Step 1:            Write down the acoustic impedances for air and soft tissue

Air, Z1 = 4.3 × 102 kg m-2 s-1

Soft tissue, Z2 = 1.6 × 106 kg m-2 s-1

Step 2:            Calculate the intensity reflection coefficient

Intensity Reflection Coefficient Worked Example equation 3

This result means that 100% of the incident intensity will be reflected, with none being transmitted

Part (c)

    • At the air-soft tissue boundary, the intensity reflection coefficient is α ≈ 1
      • Therefore, without gel, there is almost complete reflection – no ultrasound is transmitted through the skin
    • At the gel-soft tissue boundary, the intensity reflection coefficient is α = 0.001
      • Therefore, the gel enables almost complete transmission of the ultrasound through the skin, with very little reflection

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