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Question 18N.3.HL.TZ0.b

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Date November 2018 Marks available [Maximum mark: 2] Reference code 18N.3.HL.TZ0.b
Level HL Paper 3 Time zone TZ0
Command term Determine Question number b Adapted from N/A
b.
[Maximum mark: 2]
18N.3.HL.TZ0.b

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

( Z 1 − Z 2 Z 1 + Z 2 ) 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 × 106 kg m–2 s–1

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

Absorption coefficient of muscle  = 23 m–1

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

[2]

Markscheme

R = « ( 6.3 × 10 6 − 1.7 × 10 6 6.3 × 10 6 + 1.7 × 10 6 ) 2 =» 0.33 ✔

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

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