A wave transfers energy without transferring matter. This topic covers the two types of wave, the equation relating speed, frequency and wavelength, and what happens when a wave meets a boundary.
In a transverse wave the oscillations are at right angles to the direction of energy transfer, as in ripples on water and all electromagnetic waves.
In a longitudinal wave the oscillations are along the direction of energy transfer, producing compressions and rarefactions. Sound is the usual example. In both cases the medium itself is not carried along: a floating cork bobs up and down as a ripple passes, it does not travel with it.
Amplitude is the maximum displacement from the rest position, and it is linked to the energy the wave carries. Wavelength is the distance from one point on a wave to the same point on the next. Frequency is the number of waves passing a point each second, in hertz.
Period is the time for one complete wave: \(T = \frac{1}{f}\).
Wave speed, frequency and wavelength are linked by \(v = f\lambda\), with speed in m/s, frequency in Hz and wavelength in m.
At a fixed speed, frequency and wavelength are inversely proportional: double the frequency and the wavelength halves.
At a boundary a wave may be reflected, absorbed or transmitted. In reflection the angle of incidence equals the angle of reflection, both measured from the normal.
A smooth surface gives specular reflection and a clear image; a rough surface gives diffuse reflection, scattering the light. Refraction happens when a wave changes speed on entering a new medium: slowing down bends it towards the normal, speeding up bends it away. The frequency never changes; the wavelength does.
Sound is a longitudinal wave and needs a medium, so it cannot travel through a vacuum. It travels fastest in solids, more slowly in liquids and slowest in gases, because particles in a solid are strongly coupled and pass the disturbance on rapidly. Spacing alone does not set the speed; the stiffness and the density of the material both matter.
Sound waves cause the eardrum to vibrate, and those vibrations are passed on through the solid structures of the ear. The range of normal human hearing is roughly 20 Hz to 20 000 Hz.
The speed of sound in air is about 330 m/s. It is why you see lightning before you hear thunder.
Ultrasound is sound above 20 000 Hz. It partially reflects at a boundary between two media, and timing the echo gives the depth of the boundary. That is the basis of medical imaging and of sonar depth measurement.
Seismic waves from earthquakes reveal the Earth's structure. P-waves are longitudinal and travel through solids and liquids; S-waves are transverse and cannot travel through a liquid, which is how the liquid outer core was discovered.
The spectrum runs, in order of increasing frequency and decreasing wavelength: radio, microwave, infrared, visible light, ultraviolet, X-rays, gamma rays.
Visible light is a very narrow band in the middle. Radio waves have the longest wavelength; gamma rays the shortest, and therefore the greatest energy per photon.
All electromagnetic waves are transverse, all transfer energy from source to absorber, and all travel at the same speed in a vacuum, about \(3\times10^8\) m/s.
They need no medium, which is how energy reaches Earth from the Sun.
Different substances absorb, transmit, refract or reflect electromagnetic waves differently, depending on the wavelength. Refraction happens because the wave changes speed as it crosses a boundary.
Radio waves can be produced by oscillations in an electrical circuit, and absorbing them can induce oscillations in another circuit, which is the basis of radio. Changes in atoms and their nuclei can generate and absorb electromagnetic waves across a wide range of frequencies; gamma rays in particular come from changes in the nucleus.
Radio is used for broadcasting and microwaves for satellite communication and cooking. Infrared is used for heaters, thermal imaging and some communications. Visible light is used for vision and for fibre-optic communication. Ultraviolet is used in energy-efficient lamps and sun tanning, and X-rays and gamma rays in medical imaging and treatment.
Higher-frequency waves carry more energy per photon. Ultraviolet causes skin ageing and increases the risk of skin cancer; X-rays and gamma rays are ionising and can cause mutations in cells. How much harm is done depends on the type of radiation and the size of the dose.
A convex (converging) lens brings parallel rays to a focus; a concave (diverging) lens spreads them out so they appear to come from a focal point behind it.
The distance from the lens to the focal point is the focal length. A ray through the centre of a thin lens passes straight through, which is one of the standard construction rules. Magnification is \(\text{magnification} = \frac{\text{image height}}{\text{object height}}\).
Visible light is the narrow band the eye detects, running from red at the longest wavelength to violet at the shortest.
In white light, an opaque object appears the colour it reflects most strongly and absorbs the other wavelengths; a white object reflects all wavelengths roughly equally, and a black one absorbs most of the light falling on it. A colour filter transmits the wavelengths associated with its own colour and absorbs the others.
Every object emits and absorbs infrared radiation continuously, and the hotter it is the more it emits.
Dull, matt surfaces tend to be better emitters and absorbers of infrared than shiny metallic ones. A survival blanket is shiny for this reason.
A perfect black body absorbs all the radiation that falls on it, reflecting and transmitting none. It is therefore also the best possible emitter.
An object's temperature depends on the balance between what it absorbs and what it emits. Absorbing more than it emits makes it warm up; emitting more than it absorbs makes it cool. A steady temperature means the two rates are equal.
