Production & Use of Ultrasound (CIE A Level Physics)

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State the approximate value of the intensity reflection coefficient at the boundary between the two media when:

•    Z₁ is almost equal to Z₂

intensity reflection coefficient = ................................

•    Z₁ is very different from Z₂.

intensity reflection coefficient = ................................

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Ultrasound is thought to be more suitable than X-rays for scanning an unborn foetus.

Some values of linear attenuation coefficient of different media are shown in Table 1.1

Table 1.1

Fig. 1.1 shows a diagram of a piezoelectric transducer.

Fig. 1.1

With reference to Fig. 1.1:

Ultrasound is incident on a boundary between two materials. Some of the ultrasound is reflected at the boundary and the rest is transmitted across the boundary.

The acoustic impedance of air is 4.29 × 10² kg m^–2 s^–1

The acoustic impedance of coupling gel is 1.48 × 10⁶ kg m^–2 s^–1  

The acoustic impedance of skin is 1.65 × 10⁶ kg m^–2 s^–1

Calculate the percentage of the ultrasound which would be transmitted into the skin when incident on

Most modern ultrasound transducers are made from the piezoelectric material lead zirconate titanate (PZT).

Fig. 1.1 shows the effect on the structure of a crystal of PZT when an alternating potential difference is applied across it.

Fig. 1.1

An eye can be imaged using either an A-scan or a B-scan ultrasound. Fig. 1.2 shows the position of a piezoelectric transducer being used during an A-scan of an eye.

Fig. 1.2

Fig. 1.3 shows an ultrasound A-scan trace from the scan of an eye.

Fig. 1.3

The speed of ultrasound in the eye is 1520 m s^–1 and the speed of ultrasound in the lens is 1670 m s^–1.

Use Fig. 1.3 to calculate the thickness of

The graph in Fig. 1.4 shows the attenuation of the intensity of ultrasound at a frequency of 3 MHz with depth.

Fig. 1.4

When carrying out the scan, a gel is applied between the transducer and eye to enable 100% transmission of the ultrasound into the eye.

Use the information in Table 1.1 and the graph in Fig. 1.4 to calculate the ratio of the intensity of the reflections from A and B, by the time the pulses come back to the receiver.

Table 1.1

An ultrasound investigation was used to identify a small volume of an unknown substance in a patient. It is suspected that this substance is either a cyst or a tumour.

During the ultrasound investigation, an ultrasound pulse of frequency 5 MHz is passed through soft tissue and then into the small volume of the unknown substance.

The ratio of the reflected intensity to the incident intensity for the ultrasound pulse reflected at the boundary was found to be 7.54 × 10⁻⁵.

Table 1.1 shows some information about the density and speed of ultrasound in soft tissue, cysts and tumours.

Table 1.1

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Fig. 1.1 shows a beam of X-rays of energy 20 keV incident normally on some soft tissue which contains the cyst.

The cyst is located 2.1 cm from the surface of the soft tissue.

Fig. 1.1 (not to scale)

The attenuation constant of the soft tissue is 0.85 cm^–1 for X-rays. The incident intensity of the beam is 4.6 × 10³ W m^–2.

You may assume that the attenuating behaviour of X-rays in matter is the same as that of ultrasound in matter.

The X-ray beam is switched on for a time t.

Determine the energy of the X-ray beam incident on the front surface of the cyst each second. State any assumptions you make.

The ratio of the intensities of the emergent X-ray beams X and Y is determined to be

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