Ultrasound
Ultrasound is sound with a frequency above what we can hear (above 20 kHz; medical scanners use millions of hertz). A probe sends short pulses into the body. When a pulse reaches a boundary between two tissues, part of it is reflected back as an echo.
The scanner measures the time t for the echo to come back. The pulse travels there and back, so depth = speed × t ÷ 2. In soft tissue the speed is about 1 540 m/s. Many pulses build a moving picture.
Ultrasound is not ionising, so it is used for babies, the heart and the liver. It cannot go through bone or air well. More on this in Non-ionising imaging.
X-ray and CT
X-rays are very short waves of electromagnetic radiation, made when fast electrons hit a metal target in an X-ray tube. They pass through soft tissue easily, but bone absorbs more, so the film or detector behind the body shows bone as white.
A normal X-ray is a flat shadow. In a CT scan (computed tomography) the tube and detectors turn round the body. A computer joins the many views into cross-section slices and can stack them into a 3D picture. CT shows organs and small bleeds that a flat X-ray hides. Full detail is in X-ray imaging.
Radiation protection
X-rays are ionising radiation: they can damage cells. We use only as much as needed (the doctor decides if the benefit is bigger than the risk) and follow three rules:
- Time: the shorter the exposure, the smaller the dose.
- Distance: from a small source the dose falls as 1 ÷ distance². Double the distance, one-quarter of the dose.
- Shielding: lead aprons and walls stop most X-rays and gamma rays.
Staff wear a badge (dosimeter) that records the dose they receive. Pregnant women are scanned with extra care and often get ultrasound instead.
Try it
Echo at home: clap near a wall or a large building and listen for the echo. Move further away and notice the echo comes later.
Shadows: hold a toy in front of a torch with a hand behind it. A thick object makes a darker shadow, like bone on an X-ray film.
In the 3D: on Safety, slide the person away from the source. Check the dose number each time you double the distance.
Key formulas and definitions
- Depth = (speed × echo time) ÷ 2
- Speed of ultrasound in soft tissue ≈ 1 540 m/s
- Dose from a small source ∝ 1 / distance²
- Intensity after x of material: I = I₀ × (½)^(number of half-value layers)
Worked examples
1. An echo from an organ returns after 130 µs. Speed in tissue is 1 540 m/s. Find the depth.
Depth = 1 540 × 130 × 10⁻⁶ ÷ 2 = 0.2002 ÷ 2 ≈ 0.10 m = 10 cm.
2. The dose is 36 units at 1 m from a source. What is it at 3 m?
Dose ∝ 1/d². At 3 m it is 1/9 of the value: 36 ÷ 9 = 4 units.
3. A shield has a half-value layer of 2 mm lead for some X-rays. What fraction passes through 6 mm?
6 mm is 3 half-value layers. Fraction = (½)³ = 1/8 = 12.5%.
Common mistakes
- Forgetting to divide by 2 in the echo formula. The pulse goes there and back.
- Thinking ultrasound is a kind of radiation like X-rays. It is a sound wave and is not ionising.
- Saying the dose halves when the distance doubles. It falls to one-quarter (inverse square).
- Thinking CT is the same as MRI. CT uses X-rays; MRI uses magnets and radio waves.