HookHow a Glasgow professor learned to see an unborn baby with sound
In 1958, Ian Donald, a professor of obstetrics at the University of Glasgow, published a paper with an engineer, Tom Brown, describing something that had never been done to a patient before: using pulses of high-frequency sound to image the inside of a living human body. Donald had noticed that the industrial flaw-detectors used to find cracks in ship hulls and boiler plates worked on a simple idea — send a pulse of sound in, listen for the echo, and the time it takes tells you where the boundary is. He reasoned that a growing baby, a cyst and a tumour would each reflect sound differently. Within a few years the grainy ultrasound scan had transformed pregnancy care worldwide, and it did it without a single X-ray, because sound is a wave that reflects at a boundary and carries no ionising danger.
That is the whole of P6 in one story. A wave transfers energy, not matter, from one place to another; it has a speed, a wavelength and a frequency tied together by one equation; it reflects, refracts and is absorbed at boundaries; and different waves — sound, seismic waves, and the whole electromagnetic spectrum from radio to gamma — do different jobs for us precisely because of their different properties. This section builds from what a wave is, through the maths of wave speed, to ultrasound and seismology, the electromagnetic spectrum and its uses and dangers, lenses, colour and the infrared radiation that sets Earth's temperature.
ModelTransverse and longitudinal — two ways to carry energy
A wave is an oscillation that travels, carrying energy while the medium itself stays put. Drop a stone in a pond and the ripple races outward, but a floating leaf only bobs up and down — the water does not travel to the shore. That is the defining idea: waves transfer energy and information, not matter.
There are two kinds. In a transverse wave the oscillations are at right angles to the direction the wave travels — like the ripples on water, a wave on a rope, and all electromagnetic waves. In a longitudinal wave the oscillations are along the same line the wave travels, producing compressions (particles squeezed together) and rarefactions (particles spread apart) — like sound moving through air, or a pushed-and-pulled spring. Because a longitudinal wave needs particles to compress, sound cannot travel through a vacuum; a transverse electromagnetic wave can.
ModelWave properties and the equation that ties them together
Four measurements describe any wave. The amplitude is the maximum displacement from the rest position — it sets how much energy the wave carries. The wavelength (\(\lambda\)) is the distance for one complete cycle, crest to crest. The frequency (\(f\)) is the number of complete waves passing a point each second, in hertz (Hz). The period (\(T\)) is the time for one complete wave, and it is simply the reciprocal of frequency: \[T = \frac{1}{f}\]
The single most important relationship in the topic ties speed, frequency and wavelength: \[v = f\lambda\] with speed \(v\) in m/s, frequency in Hz and wavelength in metres. High frequency means short wavelength for a fixed speed, and vice versa — which is why a treble note has a shorter wavelength than a bass note in the same air. Get comfortable rearranging this equation both ways; most wave calculations in the paper are a disguised version of it.
A wave on a string has a frequency of \(25\ \text{Hz}\) and a wavelength of \(0.08\ \text{m}\). Find its speed and its period.
Wave speed: \[v = f\lambda = 25 \times 0.08 = 2\ \text{m/s}\] Period: \[T = \frac{1}{f} = \frac{1}{25} = 0.04\ \text{s}\] A common slip is to mix units — a wavelength given in centimetres must be converted to metres first, or the speed comes out a hundred times too large. Substitute in SI units every time and the answer's unit takes care of itself.
MechanismBoundaries, reflection and sound (physics only)
When a wave meets a boundary between two materials, three things can happen: it can be reflected, transmitted (passing through, often refracting) or absorbed (its energy transferred to the material). Which dominates depends on the wave and the two materials — a mirror reflects light, black cloth absorbs it, clear glass transmits it. Reflection obeys a simple rule you draw on a ray diagram: the angle of incidence equals the angle of reflection, both measured from the normal (the line at right angles to the surface).
Sound is a longitudinal wave, and the human ear detects frequencies from about 20 Hz to 20 kHz (Higher tier). Sound travels by making particles vibrate, so at a solid boundary the vibration can be passed on: sound reaching a solid can make the solid's particles oscillate, converting the wave and letting it travel on through the new material. This conversion at boundaries is exactly what lets a stethoscope, or Ian Donald's scanner, pick up echoes from structures deep inside the body.
CaseUltrasound, seismic waves and echo sounding (physics only, HT)
Ultrasound is sound above 20 kHz, beyond human hearing. Sent as a pulse into the body, it partly reflects at each boundary between tissues; timing the echoes and knowing the speed lets a scanner build an image — used for pregnancy scans and for detecting flaws in metal. Echo sounding uses the same principle in water, bouncing high-frequency sound off the seabed or a shoal of fish to measure depth or distance.
Seismic waves from earthquakes come in two types that between them revealed the structure of the Earth. P-waves are longitudinal and travel through both solids and liquids; S-waves are transverse and cannot pass through liquids. Because S-waves fail to reach the far side of the planet, leaving an 'S-wave shadow zone', geologists deduced that part of the Earth's core must be liquid — a stunning example of using waves to probe somewhere no one can ever go.
An ultrasound pulse is sent into the body and its echo returns \(0.00009\ \text{s}\) later. Ultrasound travels at \(1500\ \text{m/s}\) in soft tissue. How deep is the reflecting boundary?
The pulse travels to the boundary and back, so it covers twice the depth. Total distance: \[s = v \times t = 1500 \times 0.00009 = 0.135\ \text{m}\] That is the there-and-back distance, so the depth is half of it: \[\text{depth} = \frac{0.135}{2} = 0.0675\ \text{m} \approx 6.75\ \text{cm}\] Forgetting to halve — treating the echo time as a one-way trip — is the mistake that doubles the answer and loses the final mark.
ModelThe electromagnetic spectrum and refraction
Electromagnetic waves are transverse waves that all travel at the same speed in a vacuum — the speed of light, \(3 \times 10^{8}\ \text{m/s}\). They form a continuous spectrum, grouped by wavelength and frequency into seven bands. From longest wavelength (lowest frequency) to shortest: radio, microwave, infrared, visible light, ultraviolet, X-rays and gamma rays. Learn the order — a mnemonic helps — because uses and dangers both follow it, with energy rising towards the gamma end.
When an electromagnetic wave crosses from one medium into another it changes speed, and if it meets the boundary at an angle it also changes direction — refraction. A wave slowing down (say, light entering glass) bends towards the normal; speeding up, it bends away. At Higher tier this is shown with wave-front diagrams: the fronts bunch closer together and pivot as one end enters the slower medium first, the same way a line of marchers wheels when one flank hits mud. The change in speed is the cause; the change in direction is the visible effect.
MechanismMaking EM waves, their uses and their dangers
Electromagnetic waves are generated when charges accelerate or electrons drop between energy levels in atoms, and they are absorbed the same way. Radio waves are produced by oscillating charges in an aerial — an alternating current in the transmitter creates a radio wave, and when it hits a receiving aerial it induces an alternating current of the same frequency. Gamma rays, at the far end, come from changes in the nucleus of an atom, not its electrons.
Uses map onto properties. Radio waves carry television and radio broadcasts; microwaves cook food and carry satellite and phone signals; infrared is used in remote controls, heating and thermal imaging; visible light for seeing, photography and fibre-optic communication; ultraviolet in security marking, tanning and sterilising; X-rays and gamma rays in medical imaging and cancer treatment. But the high-frequency end is dangerous: ultraviolet can damage skin cells and cause skin cancer, while X-rays and gamma rays are ionising and can mutate DNA. Exposure is measured as a radiation dose in sieverts, weighing the amount and the harm — which is why radiographers stand behind shielding and limit each patient's exposure.
ModelLenses, colour and reflection (physics only)
A lens refracts light to form an image. A convex (converging) lens is thicker in the middle and brings parallel rays together at the principal focus; a concave (diverging) lens is thinner in the middle and spreads rays apart. Ray diagrams locate the image, and its size is captured by \[\text{magnification} = \frac{\text{image height}}{\text{object height}}\] a ratio with no units — a magnification of 3 means the image is three times as tall as the object.
The colour of an opaque object is the colour of light it reflects; the rest it absorbs. A red jumper looks red because it reflects red and absorbs the other colours; under pure blue light it would look black. A filter works by transmitting one colour and absorbing the rest. Reflection itself comes in two forms: specular reflection off a smooth surface (like a mirror) sends parallel rays off parallel, giving a clear image, while diffuse reflection off a rough surface scatters rays in all directions, which is why you can see a matt wall from any angle but it forms no image.
ModelInfrared, black bodies and Earth's temperature (physics only)
Every object emits and absorbs infrared radiation, and the hotter it is, the more it emits — a fact your body and every radiator obey. A surface that is a good absorber of infrared is also a good emitter: matt black surfaces absorb and emit best, shiny silver surfaces worst, which is why hot-water tanks are lagged and survival blankets are shiny.
A perfect black body is an idealised object that absorbs all the radiation falling on it and is also the best possible emitter. As its temperature rises it emits more radiation overall and at shorter wavelengths — heated metal glows first red, then white. This governs the temperature of the whole Earth. Our planet absorbs radiation from the Sun and emits infrared back to space; while the two rates are equal the temperature is steady. Anything that reduces the outgoing infrared — extra greenhouse gases absorbing it — tips the balance, and the Earth warms until the rates match again at a higher temperature. That energy-balance argument is the physics underneath climate change.
CaseMeasuring waves in the lab — the required practicals
Three required practicals turn this theory into measurement. In Required practical 8 you find the frequency, wavelength and speed of waves two ways: in a ripple tank, using a strobe or a ruler to measure the wavelength of water ripples and their frequency, then \(v = f\lambda\); and for waves on a string driven by a vibration generator, measuring the length of a standing wave to get the wavelength. The independent-versus-dependent thinking and the use of \(v = f\lambda\) are what examiners probe.
In Required practical 9 you investigate how light behaves at surfaces — the reflection of light off different surfaces, and its refraction as it passes into different substances such as a glass block — measuring angles from the normal with a protractor. In Required practical 10 a Leslie cube (a metal cube with matt black, matt white, shiny and dull faces filled with hot water) is used with an infrared detector to show that a matt black surface radiates far more infrared than a shiny one at the same temperature. Across all three, the marks come from a fair test: change one variable, keep the rest constant, and measure carefully from the correct reference line.
VocabularyKey terms the mark scheme pays for
TrapsMisconceptions that cost marks
ExamWhat examiners want
Nearly every wave calculation is \(v = f\lambda\) or \(T = \frac{1}{f}\) in disguise — identify which quantity is missing, rearrange, and always convert lengths to metres and times to seconds before substituting. In echo and ultrasound problems, decide first whether the distance is one-way or there-and-back; the pulse travels twice the depth, so halve after multiplying, or you will double every answer.
Learn the electromagnetic spectrum in order and pair each region with a use and, at the high-frequency end, a danger — examiners routinely ask you to justify a use 'in terms of a property of the wave', so link microwaves to their absorption by water, X-rays to their penetration, and so on. For refraction, always name the cause (a change of speed) and the effect (a change of direction), and state which way it bends relative to the normal.
On the required practicals, spell out the fair test: which variable you changed, which you measured, and which you kept constant, and measure all angles from the normal, not the surface. For infrared and black-body questions, remember a good absorber is a good emitter, and frame Earth's temperature as a balance between radiation absorbed and radiation emitted — that energy-balance sentence is the one that earns the top marks.