AQA A-Level Physics: Medical Physics

Ultrasound is widely used for non-ionising medical imaging, for example to monitor a developing fetus. A typical obstetric scan uses a piezoelectric transducer placed against the skin, with a layer of water-based gel between the transducer and the body.

Describe and explain how an ultrasound pulse-echo scan produces an image of internal structures. In your answer you should refer to:

• how the transducer generates and detects the ultrasound pulses;
• why pulses are reflected at boundaries inside the body;
• why a coupling gel is placed between the transducer and the skin;
• the difference between an A-scan and a B-scan.

(6 marks)

The loudness of a sound is described by its intensity level $IL = 10\log\left(\dfrac{I}{I_0}\right)$IL=10log(I0​I​) measured in decibels (dB), where $I_0 = 1.0 \times 10^{-12}\ \text{W m}^{-2}$I0​=1.0×10−12 W m−2 is the threshold of hearing.

At a particular point in a workshop a single machine produces a sound of intensity $I = 6.5 \times 10^{-6}\ \text{W m}^{-2}$I=6.5×10−6 W m−2.

(a) Calculate the intensity level, in dB, of the sound from the single machine. (3 marks)

(b) A second, identical machine is switched on next to the first, so that the total sound intensity at the point doubles. Calculate the new intensity level in dB, and state the change in intensity level produced by adding the second machine. (3 marks)

A narrow parallel beam of X-rays of fixed energy is directed through increasing thicknesses of a soft tissue. The transmitted intensity $I$I is measured as a percentage of the incident intensity $I_0$I0​. The attenuation follows $I = I_0 e^{-\mu x}$I=I0​e−μx, where $\mu$μ is the linear attenuation (absorption) coefficient and $x$x is the thickness of tissue.

Thickness $x$x / mm	Transmitted intensity $I$I as % of $I_0$I0​
0	100
20	50
40	25
60	12.5

(a) Use the data to state the half-value thickness of this tissue, explaining how you obtained it from the table. (2 marks)

(b) Use a data point and the equation $I = I_0 e^{-\mu x}$I=I0​e−μx to calculate the linear attenuation coefficient $\mu$μ for this tissue. Give a suitable unit. (3 marks)

A patient is short-sighted (myopic). Their far point — the most distant object they can see clearly with the eye fully relaxed — is only 2.0 m from the eye. A person with normal vision has a far point at infinity.

The power of a thin lens in dioptres is $P = \dfrac{1}{f}$P=f1​, and the lens equation is $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$f1​=u1​+v1​, with distances in metres and the real-is-positive sign convention.

Determine the power, in dioptres, and the type (converging or diverging) of the thin spectacle lens needed to correct this patient's distance vision. Explain your reasoning, including why the chosen lens forms the correct image for a very distant object.

(5 marks)

During an ultrasound A-scan, a pulse is transmitted into soft tissue and the time for the echo from a particular boundary to return to the transducer is measured as $t = 5.2 \times 10^{-5}\ \text{s}$t=5.2×10−5 s. The speed of ultrasound in the tissue is $c = 1540\ \text{m s}^{-1}$c=1540 m s−1.

Calculate the depth of the reflecting boundary below the transducer, in cm. Explain why a factor of $\tfrac{1}{2}$21​ appears in your calculation.

(4 marks)

The response of the ear to sound is described using the quantities intensity and intensity level.

(a) Define what is meant by the intensity of a sound, and state its SI unit. (2 marks)

(b) State what is meant by the intensity level of a sound, and state the value of the reference intensity $I_0$I0​ (the threshold of hearing) used in its definition. (1 mark)