# 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:

• 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

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

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

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

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

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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