Waves

• Waves are caused by oscillations, which can be exemplified by the oscillation of electrons, which cause radio waves.
• The Doppler effect is the change in frequency of a wave due to its movement towards or away from the observer.
• Waves occur when a disturbance at the source of the wave causes particles to oscillate about a fixed central point, with a maximum displacement from the central point, which is called the equilibrium position.
• When particles reach the maximum displacement, they start to move towards the central point, passing through the central point as they move to the maximum displacement on the other side.
• When two continuous waves of the same type coincide, they superpose, resulting in interference.
• The two dippers in a ripple tank act as two different sources which are in phase and having identical wavelengths and frequencies, making them coherent.
• In the pattern seen in a ripple tank, regions of constructive interference occur where crests meet crests and troughs meet troughs, with a larger amplitude.
• Regions of destructive interference occur where the waves are in antiphase, resulting in cancellation.
• At any point where there is constructive interference, the water is still rising and falling at the same frequency, but with greater amplitude.
• The position of the pattern remains steady, not altering with time.
• The total energy of the system remains constant.
• While there is no energy in the regions of cancellation, there is more energy in the regions of reinforcement.
• The wave is called a progressive wave because it is moving in a particular direction, transferring energy from the point of disturbance, but the particles are not travelling with the wave, merely going up and down.
• Waves can be considered to travel either as plane wavefronts, from a plane source or as circular wavefronts from a point source.
• In 3 dimensions, the waves would propagate spherically from a point source.
• Displacement of a particle is the distance at any given moment from the central or equilibrium position, i.e the undisturbed position, given the Physics symbol s or x, and the SI unit is metre (m).
• The intensity of waves at a point is the power per unit area at that point, with the energy of a wave increasing as the square of its amplitude, but the energy decreases as the square of the distance from the source, which is known as the inverse square law, with the physics symbol for intensity being I and the units being watts per square metre (W m-2).
• Amplitude of a wave, symbol A or r, units metres (m), is the maximum displacement of a particle from its equilibrium position, in other words it is the height of the wave from the average level, and is NOT the height from crest to trough.
• Wavelength is defined as the distance between any two points on adjacent cycles that are in phase, in other words the distance between adjacent peaks or troughs, with the symbol for wavelength being λ (lambda), and the units for wavelength being metre (m).
• Frequency, symbol f, has the unit hertz (Hz), and is the number of waves passing a given point every second.
• Period is the time taken for one complete oscillation, with the symbol being T and the unit being seconds (s).
• Wave velocity, symbol v, units: metres per second (ms-1), tells us the speed of propagation of the wave, i.e how fast it travels, for water waves this is a few cms-1, in air, sound waves propagate at 340 ms-1, for light the speed is 3 x 108 m-1, with the speed of light being given the symbol c.
• Mechanical waves are produced by a disturbance in a material, or a medium, and can be longitudinal or transverse, needing a medium or material to travel in.
• In electromagnetic waves the disturbances are in the form of oscillating electrical and magnetic fields, always transverse, and can travel in a vacuum.
• The difference in the motion of particles is described in terms of the phase difference, which is the fraction of a wavelength by which their motions are different.
• X and Y are two particles, X is at the trough of a wave, whereas Y is at the crest.
• The directions of X and Y are upwards and downwards respectively.
• X and Y are half a wavelength (λ/2) out of phase.
• X and Y are in antiphase.
• W and Z are two particles, both at the starting point of a cycle, their motion, including displacement, velocity and direction, is identical.
• Particles can be any amount out of phase.
• A transverse wave is one in which the displacement of the particles is at 90o to the direction of travel.
• In a transverse wave, the particles move up and down while the wave travels horizontally.
• All electromagnetic waves are transverse.
• A longitudinal wave is one in which the displacement is parallel to the direction of travel of the wave.
• There are regions of high pressure, compression, and regions of low pressure, rarefaction in a longitudinal wave.
• In a sound wave, the air molecules move forwards and backwards, where they are squashed together, a compression results, where they are forced further apart, there is a rarefaction.
• A medium or material is required for both transverse and longitudinal waves.
• The speed of sound in air is 336 ms-1, in water 1400 ms-1, in steel it is 6000 ms-1.
• Examples of longitudinal waves include some kinds of earthquake waves (the pressure or P-wave).