Topic 6: Waves

Waves transfer energy and information from one place to another without transferring the matter they travel through. This topic covers how waves are described and measured, how they behave when they meet boundaries, and the family of electromagnetic waves that ranges from radio waves to gamma rays.

Transverse and longitudinal waves

All waves transfer energy without transferring matter. If you drop a stone in a pond, ripples spread outwards but a floating leaf only bobs up and down, it does not travel to the edge. There are two main types. In a transverse wave the oscillations are at right angles (perpendicular) to the direction the wave travels. Ripples on water and all electromagnetic waves are transverse. In a longitudinal wave the oscillations are along the same line as the direction of travel, creating regions where particles are squashed together (compressions) and pulled apart (rarefactions). Sound waves are longitudinal. Longitudinal waves need a medium of particles to travel through, which is why sound cannot pass through a vacuum, but transverse electromagnetic waves can travel through empty space.

Wave properties: amplitude, wavelength, frequency and period

Several quantities describe a wave. The amplitude is the maximum displacement of a point from its rest (undisturbed) position, measured in metres (m); a bigger amplitude means more energy is being transferred. The wavelength is the distance from one point on a wave to the same point on the next wave, for example crest to crest, measured in metres (m). The frequency is the number of complete waves passing a point each second, measured in hertz (Hz), where 1 Hz is one wave per second. The period is the time taken for one complete wave to pass a point, measured in seconds (s). Frequency and period are linked by the equation period = 1 / frequency, so a higher frequency means a shorter period.

The wave equation

The speed of a wave links its frequency and wavelength using the equation: wave speed = frequency x wavelength. In symbols v = f x lambda, where speed v is in metres per second (m/s), frequency f is in hertz (Hz) and wavelength lambda is in metres (m). Worked example: a sound wave has a frequency of 170 Hz and a wavelength of 2 m. Its speed is wave speed = 170 Hz x 2 m = 340 m/s, the typical speed of sound in air. The equation can be rearranged to find any missing quantity. To find frequency, use frequency = wave speed / wavelength. To find wavelength, use wavelength = wave speed / frequency. Always check that values are in standard units before substituting them in.

Reflection and refraction

When a wave hits a boundary between two materials, part of it can be reflected, transmitted or absorbed. Reflection is when a wave bounces off a surface. The angle of incidence (the angle between the incoming ray and the normal, an imaginary line at 90 degrees to the surface) always equals the angle of reflection. A smooth surface gives specular reflection, producing a clear image, while a rough surface gives diffuse reflection, scattering the light. Refraction is the change in direction of a wave when it passes from one medium into another at an angle, caused by a change in the wave speed. When a wave slows down, such as light entering glass from air, it bends towards the normal; when it speeds up, it bends away from the normal. If a wave meets the boundary along the normal it changes speed but does not change direction.

The electromagnetic spectrum and its uses

Electromagnetic (EM) waves form a continuous spectrum of transverse waves that all travel at the same speed through a vacuum, about 300,000,000 m/s. In order of increasing frequency and decreasing wavelength they are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Each group has uses based on its properties. Radio waves are used for television and radio broadcasting. Microwaves are used for cooking and satellite communications. Infrared is used in electric heaters, cooking and infrared cameras. Visible light is used for fibre optic communication and in cameras. Ultraviolet is used in energy-efficient lamps, security marking and tanning. X-rays are used for medical imaging of bones and airport security. Gamma rays are used to sterilise medical equipment and to treat cancer.

Properties and dangers of EM waves

EM waves are generated by changes in atoms and their nuclei, so they can have different effects when they reach the body. The waves with the highest frequencies carry the most energy and are the most hazardous. Ultraviolet waves can damage skin cells and cause premature ageing and skin cancer. X-rays and gamma rays are ionising radiation, meaning they can knock electrons from atoms and damage DNA, leading to cell mutation and cancer. The risk from a radiation source is measured using a quantity called the dose, given in sieverts (Sv), which considers both the amount of radiation absorbed and how harmful that type is. Radio waves at the low-frequency end carry little energy and are generally regarded as safe.

Lenses and ray diagrams (Higher Tier)

A lens refracts light to form an image, and its power depends on its shape. A convex (converging) lens is thicker in the middle and bends parallel rays of light inwards so they meet at a point called the principal focus; the distance from the lens to this point is the focal length. A concave (diverging) lens is thinner in the middle and spreads parallel rays outwards so they appear to come from a principal focus behind the lens. Ray diagrams predict where an image forms. A convex lens can produce a real image (where rays actually meet and which can be projected onto a screen) or, when the object is very close, a magnified virtual image, as in a magnifying glass. A concave lens always produces a virtual image that is upright and smaller than the object. Magnification = image height / object height, and it has no units.

Black-body radiation (Higher Tier)

All objects emit and absorb infrared radiation, and the hotter an object is, the more radiation it emits and the shorter the peak wavelength becomes. A perfect black body is an idealised object that absorbs all the radiation that lands on it and reflects none; it is also the best possible emitter. An object stays at a constant temperature when the amount of radiation it absorbs equals the amount it emits. If it absorbs more than it emits its temperature rises, and if it emits more than it absorbs its temperature falls. This balance helps explain the temperature of the Earth: incoming short-wavelength radiation from the Sun is absorbed, warming the surface, which then radiates longer-wavelength infrared back out, and changes to the atmosphere can disturb this balance.

Sound waves and ultrasound (Higher Tier)

Sound waves are longitudinal waves that travel as compressions and rarefactions through a medium such as air, water or solids; they travel faster in solids than in gases. When sound reaches the ear, the eardrum vibrates and these vibrations are passed to the inner ear. The normal range of human hearing is roughly 20 Hz to 20,000 Hz. Ultrasound is sound with a frequency above 20,000 Hz, higher than humans can hear. When ultrasound meets a boundary between two different media, part of it is reflected, and the time taken for the echo to return can be used to calculate distance using distance = speed x time. This is used in medical scans, such as imaging an unborn baby, and in industry to detect cracks inside materials. A related method, echo sounding, uses ultrasound to measure the depth of water or to detect objects under the sea.