Extra

• Intensity is the power per unit area of the radiation falling onto a surface is known as the intensity of the radiation. This is also referred to as the radiant flux. Intensity = Power/ Area or I = P/A measured in Wm^-2
• A wavefront is a line, or surface, in a wave, along which all points are in phase
• The reduction in wavelength causes the wavefronts to change direction. As the wavefronts are perpendicular to the motion, the path of the waves is deviated towards the normal when the speed is reduced and away from the normal when it is increased
• Sonar and radar are methods that are widely used to send out pulses of radio and sound waves and noting the times and direction of the reflected pulses. Bats and dolphins are examples of animals that emit and receive high-frequency sounds to navigate.
• Ultrasound describes sound waves of frequency greater than the upper limit of human hearing.
• Amplitude scans are used to determine the depth of boundaries between tissues or bone and tissue. Pulses of ultrasound are emitted by a transducer and directed into the body at the region to be investigated. A coupling get is applied to the body at the point of entry
• In an ultrasound, the fraction of sound that is reflected depends on the difference in a property is known as the acoustic impedance. The acoustic impedance depends on the density of the medium so a much bigger reflection occurs at a tissue-bone boundary than at a tissue-muscle interface
• When two or more waves of the same type meet at a point, the displacement would be the sum of those individual waves
• When the waves add together to give maximum amplitude, which gives constructive superposition. However, when the waves combine to produce zero amplitude, destructive superposition occurs

  
• Superposition can only occur for identical wave types. It would not be possible for a sound wave to combine with a light wave. Also, superposition would not happen if two transverse waves polarised at right angles were to meet
• In some situations where two or more sources will overlap a pattern of maxima and minima would be produced where the waves combine constructively or destructively at fixed positions relative to the sources. This is known as interference
• Path difference is the distance from each source to a particular point. The positions of maximum amplitude occur when the path difference is zero or a whole number of wavelengths when the waves are always in phase and constructive superposition takes place. When the path difference is an odd half wavelength, the waves are π radians out of phase and the amplitude will be zero
• Coherent sources have the same frequency and maintain a constant phase relationship
• Stable interference patterns only occur if the waves are the same type, the sources are coherent (they have the same wavelength and frequency and maintain a constant phase relationship), the waves have similar amplitude at the point of superposition
• An interference pattern can be observed using a ripple tank. Circular wavefronts are generated on the surface of the water by two prongs attached to an oscillator. Where a trough from one source meets a trough from the other - or a crest meets a crest- maximum disturbance occurs
• In the ripple tank, the calm water indicates the destructive interference where a trough meets a crest
• In 1800, Thomas Young devised a method to produce coherent light sources from wavefronts generated by passing single wavelength (monochromatic) light through a fine slit and then using a double-slit arrangement. The bright and dark lines observed through a microscope eyepiece gave Young the evidence he needed to support his theory of the wave nature of light. The lines are referred to as Young's Fringes. They are shown in the formula: λ = Sx/D where S is the slit width, x is the fringe separation and D is the distance from slits to the microscopic eyepiece
• In precision engineering and particularly in the optical industry, surfaces need to be ground. Interferometers use the patterns created by the recombination of a laser beam that has been split into two separate beams. Small changes in the path difference are detected by a shift in the fringe pattern
• Standing waves (Stationary waves) are created by the superposition of two progressive waves of equal frequency and amplitude moving in opposite directions
• The points of zero amplitude within a standing wave are called nodes and the maxima are called antinodes

  
• Standing waves differ from travelling waves: standing waves store energy, whereas travelling waves transfer energy from one point to another, the amplitude of standing waves varies from zero at the nodes to a maximum at the antinodes, but the amplitude of all the oscillations along a progressive wave is constant, the oscillations are all in phase between nodes, but the phase varies continuously along a travelling wave
• Standing waves in a string can be investigated using Melde's experiment. A thin length of string is attached to an oscillator, passed over a pulley wheel and kept slack by a weight hanging from its end. The frequency of the oscillator is adjusted until nodes and antinodes are clearly visible. A strobe lamp can be used to 'slow down' the motion so that the standing wave can be studied in more detail. The wavelength of the wave is found by measuring the distance between alternate nodes
• String instruments such as guitars all produce standing waves on strings stretched between two points. When struck, the energy in the standing wave is transferred to the air around it and generates a sound
• The principle of stringed instruments can be demonstrated using a sonometer. When the string is plucked at its midpoint, the waves reflected from each end will interfere to set up a standing wave in the string. As both ends are fixed, they must be nodes, so the simplest standing wave will have one antinode between two nodes - that is the length of the string will be half a λ. Using the expression  v = √(T/μ) and v = fλ, the frequency of the wave generated by strings is f = v/λ = 1/2l x √(T/μ)
• In general, for stringed instruments, the frequency is greater for shorter strings, strings with greater tension, strings that have a lower mass per unit length that is thinner strings of the same material or strings made from a lower-density material
• In the fixed ends of vibrating strings, there must be nodes and the simplest standing wave has a single antinode at the midpoint. The frequency of that wave is called the fundamental frequency of that string. By striking the string off centre it is possible to create several standing waves on the same string
• The waves that are emitted by vibrations other than the fundamental frequency are called overtones. Overtones that have whole number multiples of the fundamental frequency are harmonics
• The possible wavelengths in a tube open at each end and a tube closed at one end. The waves are traditionally drawn as displacement-time variations along the tube. At the open end, the reflections always create antinodes. At the closed ends, where the particles are unable to oscillate, nodes are formed. The fundamental frequency of the open-ended pipe is therefore twice that of the closed pipe. In the diagram, it shows the first two overtones from the closed tube are the third and fifth harmonic

  
• Diffraction is when a wave passes through a gap or is partially obstructed by a barrier, the wavefront spreads out into the shadow region
• If there is a higher frequency, the λ shortens the spreading is reduced. However, narrowing the distance of the gap between two barriers causes even more spreading
• The diffraction pattern shows the central maximum edged by a series of lower-intensity maxima and minima as opposed to the regular pattern of interference from a double slit. The central maximum will broaden when the slit width is reduced. It can be shown using the formula: sinθ = λ/a where a is the slit width, the angle θ between the central maximum and the first minimum