Topic C: Wave Motion

Wave Motion studies how energy is carried from place to place without the medium travelling with it. You will describe waves with frequency, wavelength and speed, follow how they reflect, refract and bend through lenses, see how they overlap to give diffraction and interference, place visible light within the electromagnetic spectrum, and apply these ideas to sound.

The nature and properties of waves

A wave is a disturbance that transfers energy from one place to another without transferring matter. In a transverse wave, such as light or a water wave, the particles vibrate at right angles to the direction the wave travels; in a longitudinal wave, such as sound, the particles vibrate back and forth along the direction of travel, forming compressions and rarefactions. Key quantities are the amplitude (maximum displacement, linked to energy), the wavelength (the distance for one complete cycle), the frequency f (cycles per second, in hertz) and the period T = 1 over f. The wave equation links them: v = f times wavelength. These ideas apply to every kind of wave.

Reflection

When a wave meets a boundary it can be reflected. For a flat surface the law of reflection states that the angle of incidence equals the angle of reflection, both measured from the normal, and the incident ray, reflected ray and normal lie in the same plane. A plane mirror forms an image that is upright, the same size as the object, laterally inverted, and virtual, appearing as far behind the mirror as the object is in front. Reflection of sound gives echoes, and reflection of water waves can be demonstrated in a ripple tank. The same rules apply to all waves, which is why mirrors and reflective coatings work consistently for light.

Refraction and lenses

Refraction is the change in direction of a wave when it passes from one medium to another because its speed changes. Light slows down on entering a denser medium and bends toward the normal; it speeds up and bends away from the normal on leaving. The refractive index n equals the speed of light in a vacuum divided by the speed in the medium, and Snell's law gives n1 sin(angle 1) = n2 sin(angle 2). When light travels from a dense to a less dense medium beyond the critical angle, total internal reflection occurs, which is the basis of optical fibres. A converging (convex) lens refracts parallel rays to a focus and can form real or virtual images, described by the lens formula 1 over v minus 1 over u equals 1 over f.

Diffraction and interference

Diffraction is the spreading of waves as they pass through a gap or around an obstacle, and it is most noticeable when the gap size is comparable to the wavelength. Interference occurs when two coherent waves overlap: where they meet in phase they add to give constructive interference (a louder sound or brighter fringe), and where they meet out of phase they cancel to give destructive interference. Young's double-slit experiment produces a pattern of bright and dark fringes and is strong evidence for the wave nature of light, with bright fringes where the path difference is a whole number of wavelengths. These effects confirm that light, sound and water all behave as waves.

Light and the electromagnetic spectrum

Visible light is one small part of the electromagnetic spectrum, a family of transverse waves that all travel through a vacuum at the same speed, about 3 x 10^8 metres per second. In order of increasing frequency and decreasing wavelength the spectrum runs: radio waves, microwaves, infra-red, visible light, ultraviolet, X-rays and gamma rays. Each region has characteristic uses and hazards, from radio communication and microwave cooking to medical X-ray imaging and the sterilising effect of gamma rays. White light can be split by a prism or diffraction grating into its colours because each wavelength refracts by a different amount, a process called dispersion.

Sound

Sound is a longitudinal wave produced by a vibrating source that travels through a material medium as compressions and rarefactions; it cannot travel through a vacuum. The speed of sound in air is roughly 340 metres per second and is faster in liquids and faster still in solids, because the particles are closer together and pass on the vibration more readily. The pitch of a sound depends on its frequency and the loudness depends on its amplitude. The human audible range is about 20 hertz to 20000 hertz; sound above this is ultrasound. Echoes, used in depth sounding and ultrasound scanning, arise from the reflection of sound at a boundary between different media.