| Date | May 2017 | Marks available | 2 | Reference code | 17M.3.HL.TZ2.15 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Calculate | Question number | 15 | Adapted from | N/A |
Question
The density of muscle is 1075 kg m–3 and the speed of ultrasound in muscle is 1590 m s–1.
State a typical frequency used in medical ultrasound imaging.
Describe how an ultrasound transducer produces ultrasound.
Calculate the acoustic impedance Z of muscle.
Ultrasound of intensity 0.012 W\(\,\)cm–2 is incident on a water–muscle boundary. The acoustic impedance of water is 1.50 x 106 kg\(\,\)m–2\(\,\)s–1.
The fraction of the incident intensity that is reflected is given by
\(\frac{{{{\left( {{Z_2} - {Z_1}} \right)}^2}}}{{{{\left( {{Z_2} + {Z_1}} \right)}^2}}}\)
where Z1 and Z2 are the acoustic impedances of medium 1 and medium 2.
Calculate the intensity of the reflected signal.
Markscheme
accept any value between 1 MHz to 20 MHz
[1 mark]
an alternating electrical signal is applied to a crystal
crystal vibrates emitting sound
frequency of vibration of crystal is the same as the frequency of the ac
mention of piezoelectric effect/crystal
[3 marks]
Zmuscle = 1.71 x 106 «kgm–2\(\,\)s–1»
[1 mark]
«\(\frac{{{I_2}}}{{{I_1}}} = \frac{{{{\left( {{Z_2} - {Z_1}} \right)}^2}}}{{{{\left( {{Z_2} + {Z_1}} \right)}^2}}}\)» = 4.3 x 10–3
I2 = «0.012 x (4.3 x 10–3) =» 5.1 x 10–5 «W\(\,\)cm–2»
Allow ECF from (c)(i).
Allow ECF from MP1 to MP2.
[2 marks]
