AQA A-Level Physics: Ultrasound in Medical Physics — mark scheme explained

The question

A sound wave travels from a material with acoustic impedance Z 1 = 1.5 × 10 6 rayls to another material with acoustic impedance Z 2 = 3.0 × 10 6 rayls. Calculate the intensity reflection coefficient (I r ). [Paraphrased for study — not reproduced from any exam paper.]

Mark scheme, decoded

What each mark is really for — in plain English — and the wording trap that loses it.

• S1

  Step 1: Identify the given values.

• S2

  Z 1 = 1.5 × 10 6 rayls

• S3

  Z 2 = 3.0 × 10 6 rayls

• S4

  Step 2: Use the formula for the intensity reflection coefficient.

• S5

  I r = (Z 2 - Z 1 ) 2 / (Z 2 + Z 1 ) 2

• S6

  Step 3: Substitute the values into the formula.

• S7

  I r = (3.0 × 10 6 - 1.5 × 10 6 ) 2 / (3.0 × 10 6 + 1.5 × 10 6 ) 2

• S8

  Step 4: Simplify the expression.

• S9

  I r = (1.5 × 10 6 ) 2 / (4.5 × 10 6 ) 2

• S10

  Step 5: Calculate the final value.

• S11

  I r = (2.25 × 10 12 ) / (20.25 × 10 12 )

• S12

  I r = 0.111

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   Step 1: Identify the given values.

2. S2

   Z 1 = 1.5 × 10 6 rayls

3. S3

   Z 2 = 3.0 × 10 6 rayls

4. S4

   Step 2: Use the formula for the intensity reflection coefficient.

5. S5

   I r = (Z 2 - Z 1 ) 2 / (Z 2 + Z 1 ) 2

6. S6

   Step 3: Substitute the values into the formula.

7. S7

   I r = (3.0 × 10 6 - 1.5 × 10 6 ) 2 / (3.0 × 10 6 + 1.5 × 10 6 ) 2

8. S8

   Step 4: Simplify the expression.

9. S9

   I r = (1.5 × 10 6 ) 2 / (4.5 × 10 6 ) 2

10. S10

    Step 5: Calculate the final value.

11. S11

    I r = (2.25 × 10 12 ) / (20.25 × 10 12 )

12. S12

    I r = 0.111

13. Final answer: 0.111

Common mistakes

• Confusing acoustic impedance (Z) with the speed of sound (c). — Remember that acoustic impedance (Z) is given by Z = ρc, where ρ is the density and c is the speed of sound. The speed of sound alone does not account for the material's resistance to sound propagation.
• Forgetting to square the impedance difference in the intensity reflection coefficient formula. — Always use the correct formula: I r = (Z 2 - Z 1 ) 2 / (Z 2 + Z 1 ) 2 . Ensure you square the difference in acoustic impedances.
• Misinterpreting A-scans and B-scans as the same type of image. — Remember that an A-scan is a one-dimensional display showing depth information, while a B-scan is a two-dimensional cross-sectional image created using multiple A-scans. Understand the unique features of each type of scan.
• Forgetting to consider both absorption and scattering in attenuation calculations. — Attenuation is the loss of energy due to both absorption and scattering. Ensure you account for both factors when discussing or calculating attenuation.
• Confusing the mechanical index (MI) with the thermal index (TI). — The mechanical index (MI) measures the potential for mechanical effects like cavitation, while the thermal index (TI) measures the potential for tissue heating. Ensure you understand and use the correct index for each context.
• Overlooking the operator dependence of ultrasound imaging in discussions of disadvantages. — Operator dependence is a significant disadvantage of ultrasound imaging. The quality of the image can vary based on the skill and experience of the operator. Always include this point when discussing the limitations of ultrasound.

Where the marks go

• Full worked solution (all marking points)4 marks

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