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Question 18N.3.HL.TZ0.16

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Date November 2018 Marks available [Maximum mark: 5] Reference code 18N.3.HL.TZ0.16
Level HL Paper 3 Time zone TZ0
Command term Determine Question number 16 Adapted from N/A
16.
[Maximum mark: 5]
18N.3.HL.TZ0.16

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

(a)

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

[2]

Markscheme

I0e−23 × 0.041 ✔

= 0.39 I0 ✔

(b)

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 ✔

(c)

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

[1]

Markscheme

0.13I0 × 0.39 = 0.05I0 ✔

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