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Date	November 2018	Marks available	2	Reference code	18N.3.HL.TZ0.16
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Determine	Question number	16	Adapted from	N/A

Question

A beam of ultrasound of intensity I₀ enters a layer of muscle of thickness 4.1 cm.

The fraction of the intensity that is reflected at a boundary is

${\left( {\frac{{{Z_1} - {Z_2}}}{{{Z_1} + {Z_2}}}} \right)^2}$ ${\left( {\frac{{{Z_1} - {Z_2}}}{{{Z_1} + {Z_2}}}} \right)^2}$

where Z₁ and Z₂ are the acoustic impedances of the two media at the boundary. After travelling a distance x in a medium the intensity of ultrasound is reduced by a factor e^–μx where μ is the absorption coefficient.

The following data are available.

Acoustic impedance of muscle = 1.7 × 10⁶kg m^–2s^–1

Acoustic impedance of bone = 6.3 × 10⁶kg m^–2s^–1

Absorption coefficient of muscle = 23 m^–1

Determine, in terms of I₀, the intensity of ultrasound that is incident on the muscle–bone boundary.

[2]

Determine, in terms of I₀, the intensity of ultrasound that is reflected at the muscle–bone boundary.

[2]

Determine, in terms of I₀, the intensity of ultrasound that returns to the muscle–gel boundary.

[1]

Markscheme

I₀e^{−23 × 0.041}✔

= 0.39 I₀✔

R = « ${\left( {\frac{{6.3 \times {{10}^6} - 1.7 \times {{10}^6}}}{{6.3 \times {{10}^6} + 1.7 \times {{10}^6}}}} \right)^2}$ ${\left( {\frac{{6.3 \times {{10}^6} - 1.7 \times {{10}^6}}}{{6.3 \times {{10}^6} + 1.7 \times {{10}^6}}}} \right)^2}$ =» 0.33 ✔

so reflected intensity is 0.33 × 0.39I₀ = 0.13I₀✔

0.13I₀× 0.39 = 0.05I₀ ✔

Examiners report

[N/A]

Syllabus sections

Option C: Imaging » Option C: Imaging (Additional higher level option topics) » C.4 – Medical imaging (HL only)

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