Wave behaviour — OCR GCSE Physics

Wave motion is described by four linked quantities. Amplitude is the maximum displacement of a point from its rest position, measured in metres; a taller wave carries more energy. Wavelength is the distance between two matching points on consecutive waves, such as crest to crest, also in metres. Frequency is the number of complete waves passing a point each second, measured in hertz (Hz), so 5 Hz means five full oscillations per second. Period is the time for one complete wave to pass, measured in seconds, and it is the reciprocal of frequency: period = 1 ÷ frequency. A wave of frequency 4 Hz therefore has a period of 0.25 s. On a displacement–distance graph the amplitude is the height from the centre line and the wavelength is the crest-to-crest spacing; on a displacement–time graph the period is the time between matching points.

Wavelength and frequency describe two different features of a wave. Wavelength is the distance between two matching points on consecutive waves, such as from one crest to the next crest, or one compression to the next compression in a sound wave; it is measured in metres (m). Frequency is the number of complete waves passing a fixed point each second; it is measured in hertz (Hz), where 1 Hz means one wave per second. A high-frequency wave repeats often and has many cycles per second; a long-wavelength wave has crests far apart. The two are linked through wave speed by v = f × λ, so for a fixed speed a higher frequency means a shorter wavelength.

Wavelength, frequency and wave velocity are linked by one relationship: velocity equals frequency multiplied by wavelength (v = f × λ). Wavelength λ is the distance between two matching points on consecutive waves, measured in metres; frequency f is the number of complete waves passing a point each second, measured in hertz (Hz), where 1 Hz = 1 s⁻¹. Multiplying hertz by metres gives metres per second, so the units confirm the equation. A wave of frequency 50 Hz and wavelength 4 m travels at 50 × 4 = 200 m/s. For a fixed velocity, increasing frequency shortens wavelength and decreasing frequency lengthens it, because f and λ are inversely proportional when v is constant. Describe the relationship in words, then apply it by substituting two known quantities to find the third, rearranging to f = v ÷ λ or λ = v ÷ f as needed.

Applying the wave formulae means selecting v = f × λ and rearranging it to suit the quantity you need. Velocity v is in metres per second (m/s), frequency f in hertz (Hz, equivalent to s⁻¹) and wavelength λ in metres (m). To find velocity, multiply frequency by wavelength: 200 Hz × 1.5 m = 300 m/s. To find frequency, divide velocity by wavelength: 340 m/s ÷ 0.5 m = 680 Hz. To find wavelength, divide velocity by frequency: 3.0 × 10⁸ m/s ÷ 6.0 × 10¹⁴ Hz = 5.0 × 10⁻⁷ m. Convert prefixes first, so 2 kHz becomes 2000 Hz and 50 cm becomes 0.5 m, then substitute. Keep powers of ten in standard form and check that the answer's unit matches the quantity requested.

Both transverse and longitudinal waves carry energy away from a source, but they differ in how the particles or fields vibrate relative to the direction the wave travels. In a transverse wave the vibration is at right angles (perpendicular) to the direction of travel, so a wave on a rope moves along the rope while each point of the rope moves up and down. In a longitudinal wave the vibration is along the same line as the direction of travel, so in a sound wave the air particles oscillate back and forth parallel to the direction the sound moves, forming compressions and rarefactions. The key comparison is therefore the angle between vibration and travel: perpendicular for transverse, parallel for longitudinal.

This statement applies only to the physics separate science qualification, so treat it as separate-science content even though the row is tagged for both tiers. When a sound wave passes from one medium into another, its frequency stays the same because it is set by the source, but its velocity (speed) changes with the medium. Because velocity = frequency × wavelength, a change in velocity at constant frequency must be matched by a change in wavelength: if the sound speeds up, the wavelength increases; if it slows down, the wavelength decreases. For example, sound travels faster in steel than in air, so at the same frequency its wavelength is longer in steel. Use v = f × λ to show the relationship and keep frequency fixed when comparing media.

At a boundary between two materials, an incident wave can be reflected, transmitted or absorbed, and usually a mixture of all three happens. Reflection sends the wave back into the first material, as when ultrasound pulses bounce off the boundary between soft tissue and bone or off the seabed in sonar. Transmission lets the wave pass into the second material, often with a change of speed and direction, as sound travels from water into the hull of a boat. Absorption transfers the wave's energy to the material, usually warming it, as when ultrasound is absorbed by tissue. The proportions depend on the materials and the wave, which is why sonar relies on strong reflection at the water–seabed interface and why gel improves transmission between a transducer and skin.

Sound waves in air are pressure disturbances, and they can be converted into vibrations in solids and back again. In the ear, sound waves travel along the ear canal and strike the eardrum, a thin membrane that vibrates. These vibrations pass through the small bones of the middle ear, which amplify them, and reach the cochlea, where they are converted into electrical signals sent to the brain. A microphone works similarly: sound waves vibrate a diaphragm, and the movement is converted into an electrical signal. The reverse happens in a loudspeaker, where a vibrating cone in a solid structure pushes air to create sound waves. The key idea is that a wave in one medium causes a solid to vibrate, and that vibration can be turned back into a wave.

Many wave processes respond well only within a band of frequencies. A detector, a vibrating structure or a medium has a natural frequency or resonant range, and it responds strongly near that range but weakly far from it; a microphone, a loudspeaker cone or the basilar membrane inside the cochlea each behaves this way. Human hearing therefore works over a limited range, roughly 20 Hz to 20 kHz in a young adult, with greatest sensitivity in the mid-frequencies. Ageing stiffens and damages hair cells and the cochlea, so the upper limit falls, high frequencies are lost first, and the audible range narrows. This content appears only in the separate physics qualification and is Higher tier only.

Ripples on a water surface are used as a model of transverse waves: the water surface moves up and down while the ripple travels along, so the oscillation is perpendicular to the direction of travel. Sound in air is longitudinal: air particles vibrate back and forth along the direction the sound travels, forming compressions and rarefactions. To measure ripple speed, record the time for a ripple to travel a measured distance across a ripple tank and use speed = distance ÷ time, or use the wavelength and frequency. To measure the speed of sound in air, measure a known distance between two points, time a sound travelling between them with a stopwatch or data logger, and divide distance by time; a common method uses echoes or a clap timed against a distant reflection.

A wave transfers energy from one place to another without transferring the medium itself. For ripples on water, a floating object such as a cork bobs up and down as the ripple passes but stays in roughly the same place, so the water oscillates while the ripple pattern moves outward. For sound in air, a vibrating source pushes air molecules back and forth; each molecule oscillates about a fixed position and passes the disturbance to its neighbour, so a compression travels through the air while the air itself is not carried across the room. In both cases the evidence is that the medium oscillates locally while the wave pattern and its energy travel.