Waves for detection and exploration (physics only) (HT only) — AQA GCSE Physics

Ultrasound is defined by frequency and nothing else: it is a longitudinal sound wave with a frequency above 20 000 Hz, so a human cannot hear it. Medical scanners typically use between 1 MHz and 15 MHz. The high frequency matters because, from the wave equation v = f λ, at a fixed speed a higher frequency means a shorter wavelength, and a shorter wavelength resolves smaller detail and reflects cleanly from small boundaries. In soft tissue the speed is about 1500 m/s, so a 3 MHz wave has a wavelength of about 0.5 mm. Ultrasound obeys all the usual wave rules: it needs a medium, it is reflected and refracted at boundaries, and it is absorbed as it travels, which is why deep structures give weaker echoes.

The key word is partially. When an ultrasound pulse reaches a boundary between two media, some of it is reflected back towards the probe and the rest carries on into the second medium. That is what makes scanning possible: the first boundary returns an echo but does not stop the pulse, so deeper boundaries return their own echoes a little later and each appears as a separate pulse on the detector trace. The greater the difference between the two media, the larger the fraction reflected, which is why a tissue to air or tissue to bone boundary reflects so strongly. It is also why coupling gel is smeared on the skin: it removes the air gap that would otherwise reflect almost the whole pulse at the surface.

The measurement is a timing. A short pulse is sent out, travels to the boundary, reflects and travels back, and the detector records the time t between transmission and echo. In that time the pulse has covered twice the depth, so the distance to the boundary is (v × t) / 2, where v is the speed of the wave in that medium. Forgetting the factor of two is the classic error because it doubles the answer. For a boundary 6 cm deep in tissue where the speed is 1500 m/s, the echo returns after 2 × 0.06 / 1500 = 8 × 10⁻⁵ s. If two echoes are recorded, the separation between the two boundaries comes from the difference in their times, using the same halving rule.

Because part of a pulse reflects at every boundary and the return time gives the depth, a scanner can build up a picture. In medicine ultrasound is used for prenatal scanning, for imaging soft tissue such as the heart and liver, and for breaking up kidney stones. It is chosen over X-rays for a foetus because it is not ionising, so it will not mutate genes. In industry the same method finds cracks, voids and corrosion inside castings, welds and pipes without cutting them open, which is why it is called non-destructive testing. The limits are real: ultrasound is almost completely reflected at a tissue to air or tissue to bone boundary, so it cannot image the lungs or see through the skull.

An earthquake happens when rock under stress suddenly slips along a fault, releasing stored energy. This sends mechanical waves out through the Earth in all directions from the focus, known as seismic waves. They are detected at the surface by seismometers. Two types travel through the body of the Earth: P-waves, which are longitudinal, and S-waves, which are transverse. P-waves are faster, so they arrive first. The gap between the two arrivals grows with distance, letting records from several stations locate the earthquake. While P-waves cross the whole planet, S-waves cannot travel through the liquid outer core, creating a shadow zone. This distinction provides crucial evidence for the Earth's internal liquid structure.

P-waves are longitudinal, which means the rock particles oscillate backwards and forwards parallel to the direction of energy transfer, squeezing and stretching the rock into compressions and rarefactions. That is the same motion as a sound wave in air, which is why P-waves are sometimes described as sound waves in rock. Because the material only has to resist being compressed, and both solids and liquids do resist compression, P-waves travel through solid rock and through the liquid outer core. They are the faster of the two body waves, which is why they are called primary waves and why they are always the first arrival on a seismogram. In the mantle their speed is several kilometres per second and it changes with depth.

The speed of a seismic wave depends on the properties of the material it is passing through, so when a P-wave crosses from the solid mantle into the liquid outer core its speed changes sharply. A change of speed at a boundary refracts the wave, bending its path, so P-waves do not travel in straight lines through the Earth; their paths curve as the speed changes gradually with depth and kink where it changes suddenly. The consequence is measurable at the surface: there is a band of the globe, roughly 105° to 140° away from the earthquake, where no direct P-waves arrive, called the P-wave shadow zone. Only a core of a particular size with a very different wave speed can produce a shadow of that width.

In an S-wave the rock particles oscillate at right angles, perpendicular, to the direction of energy transfer, so the rock is sheared from side to side rather than squeezed. That is the same geometry as a wave on a rope or a light wave. Shearing only works where the material resists a change of shape, which solids do and liquids do not, so S-waves travel through solid rock but stop dead at a liquid boundary. They are slower than P-waves, roughly half to two thirds of the P-wave speed in the same rock, which is why they arrive second and are called secondary waves. The delay between the P and the S arrival at a station grows steadily with distance from the earthquake.

Put the two behaviours together and the inside of the Earth can be mapped without anyone going there. S-waves are transverse and need a material that resists shearing, so they stop at the boundary of the liquid outer core; that leaves a huge S-wave shadow covering most of the far side of the globe, which is the evidence that the outer core is liquid. P-waves do cross the core but change speed as they enter it, so they refract and leave a narrower P-wave shadow zone. The angular width and position of each shadow is measured from seismometers worldwide, and the only structure that fits is a layered Earth: solid mantle, liquid outer core, and a solid inner core revealed by faint refracted P-wave arrivals inside the shadow.

Echo sounding is the same timing method as an ultrasound scan, carried out in water. A ship sends a short pulse of high frequency sound downwards, the pulse reflects from the sea bed, a shoal of fish or a wreck, and a detector on the hull records the time for the echo to return. Because the pulse travels down and back, the depth is (v × t) / 2 with v the speed of sound in sea water, about 1500 m/s. A pulse returning after 0.4 s therefore comes from a depth of 1500 × 0.4 / 2 = 300 m. High frequencies are used because the shorter wavelength reflects well from small objects and gives better resolution. Repeating the measurement along the ship track builds a profile of the sea bed.

This statement is about how science works, not only about the Earth. Nobody has ever seen the core; the model of a layered Earth was built because seismic records contained patterns the earlier models could not explain, in particular shadow zones where expected waves failed to arrive. When new evidence appears that the current model cannot account for, scientists change the model. That is what happened when the S-wave shadow forced the conclusion that the outer core is liquid, and again when faint P-wave arrivals inside the P shadow led to a solid inner core being proposed. Exam questions usually ask why scientists change a theory, and the expected answer is that new observations or evidence appear that the existing theory cannot explain.