ASRJC Wave Motion Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 11-1 Additional Notes Topic 11: Wave Motion Content: • Progressive waves • Transverse and longitudinal waves • Polarisation • Determination of frequency and wavelength Learning Outcomes: Candidates should be able to: (a) show an understanding of and use the terms displacement, amplitude, period, frequency, phase difference, wavelength and speed. (b) deduce, from the definitions of speed, frequency and wavelength, the equation v = f. (c) recall and use the equation v = f. (d) show an understanding that energy is transferred due to a progressive wave. (e) recall and use the relationship, intensity  (amplitude)2. (f) show an understanding of and apply the concept that a wave from a point source and travelling without loss of energy obeys an inverse square law to solve problems. (g) analyse and interpret graphical representations of transverse and longitudinal waves. (h) show an understanding that polarisation is a phenomenon associated with transverse waves. (i) recall and use Malus’ law (intensity  cos2 θ) to calculate the amplitude and intensity of a plane polaris ed electromagnetic wave after transmission through a polarising filter. (j) determine the frequency of sound using a calibrated oscilloscope. (k) determine the wavelength of sound using stationary waves. (To be discussed in Superposition)

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 11-2 Additional Notes • The propagation of light and sound are examples of wave phenomena. • Waves originate from a source which is oscillating. These oscillations then spread and bring energy away from the source in the form of waves – the disturbance travels from one region of space to another. • A wave is a means by which energy may be transferred from one place to another as a result of oscillations. This takes place without the physical transfer of any material between the points. Waves can be classified using: • Medium through which the wave travels through: Mechanical or electromagnetic • Motion of waves: Progressive or stationary • Mode of transport: Transverse or longitudinal A.1 Medium through which the wave travels through – Mechanical waves and electromagnetic waves Mechanical waves: • Mechanical waves require a medium to propagate. Examples include: o waves in a slinky coil or a rope o water waves o sound waves o seismic waves which travel along the Earth’s crust during an earthquake Electromagnetic waves • Electromagnetic waves are generally termed “light” but this term includes the entire electromagnetic spectrum (gamma rays, X-rays, ultraviolet rays, visible light, infrared rays, microwaves and radio waves). • All these forms of light travel at a constant speed in a vacuum (c = 3.00 x 108 m s–1) but have different frequencies (different wavelengths). • Electromagnetic waves do not require a medium to travel. Introduction A Classification of Waves For this section, it is sufficient to understand the nature of these waves

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 11-3 Additional Notes Note: There is really no absolute value where a particular EM radiation (e.g. X-rays) start or end e.g. 10-1 nm may be considered as gamma rays. 400 nm 700 nm

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 11-4 Additional Notes A.2 Motion of waves: Progressive waves vs Stationary waves Progressive waves: • Progressive waves (or travelling waves) are waves in which energy is carried from one point to another by means of vibrations or oscillations within the wave. • The profile (the wavefronts) of the wave appears to be moving although the particles in the medium do not get transported along with the wave (a wavefront is a line or surface which marks out all those points on a wave that have the same phase). (refer to Appendix for more details on wavefront) Stationary waves: • Stationary waves or standing waves are waves in which the vibrational energy (associated with the waves) is stored (i.e. the energy is not transferred). • The profile of the wave does not appear to move. Energy withi n the wave is said to be localised (the energy at a specific location maintains a constant value). • This will be covered in greater detail in the Topic “Superposition”. A.3 Mode of transport (Direction of Oscillation): Transverse vs Longitudinal Waves Transverse wave: • A transverse wave is a wave in which the oscillations of the particles in the wave are at right angles to the direction of transfer of energy of the wave. Longitudinal wave: • A longitudinal wave is a wave in which the oscillations of the particles in the wave are along the direction of transfer of energy of the wave. • Within a longitudinal wave, there are regions of compression where the particles are closer to each other, and regions of rarefaction where the particles are further from each other.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 11-5 Additional Notes Sound waves as longitudinal waves • When the loudspeaker cone at A moves forward, it compresses the air in front of it. As the sound wave passes through air, air molecules vibrate left and right. • Energy is transferred from A to B but there is no transfer of matter from A to B. Check Your Understanding 1 1) Radiowave is a longitudinal wave. (True / False) 2) When sound travels from the vocal chords to the ears of a listener, the molecules at the vocal chords must have travelled to the listener’s ear. (True / False) There are two types of graphs associated with waves. They complement each other in representing a particular wave, as waves have both a spatial component as well as a time component. B.1 Displacement-Distance Graph Displacement-distance (or displacement-position) graph • A wave consists of not just one particle, but a series of particles all connected together (like a string of beads). • Each particle oscillates about its own equilibrium position with the sam e frequency (i.e. same period). • This collective string of particles form the wave profile or the shape of the wave. • For each particle, we can define: o Displacement y, its distance from its equilibrium position. Displacement is a vector quantity, so it can have a positive or negative value. o Amplitude y0: its maximum displacement. Amplitude is always positive (magnitude only). o Period of oscillation T: The time taken for the particle to complete one cycle. B Graphical Representation of Waves Note: A wave can transfer energy in different dimensions. Wave on rope is a 1-D wave, wave on water surface is a 2-D wave, while sound and light waves from point sources are 3-D waves. vsound This compression is a disturbance. It travels at the wave speed, vsound. B A

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 11-6 Additional Notes • A displacement-distance graph shows the displacements of many particles at a given instant in time. (a snapshot of the wave) • The crest of the wave is where there is maximum positive displacement; the trough of the wave is where there is maximum negative displacement. • The wavelength  is the shortest distance between any two successive points on a progressive wave which are vibrating in phase, or equivalently, the distance between two successive crests (or troughs). Displacement-position graph for longitudinal waves (e.g. sound waves) • For longitudinal waves the displacement of the particles are in the same direction as the transfer of energy of the wave (e.g. for a sound wave travelling to the right, the particles oscillate left and right). As a result, the representation of the displacement- distance graph does not resemble the actual movement of the particles. • For a longitudinal wave, the displacement -distance graph also allows the