DHS 13 Wave Motion (Notes & Tutorial)

1 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, phase difference, period, frequency, 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 α cos2 θ) to calculate the amplitude and intensity of a plane polarised electromagnetic waver after transmission through a polarising filter. (j) determine the frequency of sound using a calibrated c.r.o. (k) determine the wavelength of sound using stationary waves. H2 PHYSICS (9749) Year 6 (2025) TOPIC 13 : WAVE MOTION

2 12.1 Progressive Waves A progressive wave is a wave in which __________________ from one point to another by means of vibrations or oscillations within the waves, without transporting matter. All waves involve a disturbance from an equili brium position (i.e. an oscillation), and (for progressive waves,) the disturban ce travels from one region of space to another. However, the particles do not move along with the disturbance. 12.2 Transverse and Longitudinal Waves Transverse wave: Vibrations are ____________ to the dire ction of transfer of energy of the wave. Longitudinal wave: Vibrations are _________ to the dire ction of transfer of energy of the wave. Mechanical wave: A wave that requires ______________ for its transmission. (E.g.: sound waves and water waves) Electromagnetic wave: Wave consisting of osc illating electric and magnetic fields that are perpendicular to each other and to t he direction of transfer of energy of wave. It does not require a medium for transmission. It can travel through a vacuum at the speed of light, i.e. 3.0  108 m s−1. Progressive Waves Transverse Waves Longitudinal Waves Electromagnetic Waves Mechanical Waves Mechanical Waves

3 Electromagnetic Spectrum Refer to Annex A for more details on electromagnetic waves.

4 12.3 Characteristics of Waves Key Terms: (a) Displacement ( y): The distance in a specific di rection of a point on the wave from its equilibrium position. (b) Amplitude ( A): Maximum displacement of any point on the wave from its equilibrium position. (c) Period ( T): Period (T) is the time taken for one complete oscillation of a point in a wave. Unit: second. (It is the time taken for the wave to travel a distance of one wavelength) (d) Frequency ( f): Frequency (f) is the number of oscillations per unit time of a point on a wave. Unit: Hertz. 1 Hz is equal to one oscillation (or one cycle) per second. (e) Wavelength ( ): The minimum distance between any two points of the wave with the same phase at the same instant. (f) Wave speed ( v): The speed with which energy is transmitted by a wave. It is related to the wavelength and t he frequency according to the equation v = f. (g) Wave front: An imaginary line or surface joining points which are at the same state of oscillation (i.e. in phase).  Wave fronts are usually drawn one wavelength apart and often thought to represent wave crests.  They are always perpendicular to the direction of wave propagation.  All the points on a wave front have the same distance from the source of the wave. λ Displacement (y) Distance A 0 λ λ Crest Wavelength Wavelength Wavelength Trough Equilibrium Position

5 (h) Ray: The direction in which the energy of a wave is travelling. . Rays are always ____________________ to the wave fronts. More details on the mathematical description of wave can be found in Annex B. Exercise 1 : Prove the expression v = f One wavelength  is equal to the distance travelled by the wave energy during one complete oscillation of the source. The distance travelled by the wave energy during n complete oscillation of the source = n Speed is the distance travelled per unit time by the wave energy i.e. v = t n Frequency is number of oscillations per unit time i.e. f = t n Therefore speed v = f

6 12.4 Graphical Representations of Transverse and Longitudinal Waves 12.4.1 Displacement-Distance Graph (All particles at a certain time.) The displacement-distance graph shows how the displacements of the particles vary with the distance from the source at a particular instant in time. The wavelength can be determined from the graph. 12.4.2 Displacement-Time Graph (One Particle across all time) The displacement-time graph shows how the displacement of a single wave particle varies with time. For a transverse wave particle t1, t3 t5, t7 t6 t2 t0, t4, t8 For a longitudinal wave particle t1, t3 t5, t7 t6 t 2 t0, t4, t8 Displacement from the equilibrium point / m A -A t0 t1 t2 t3 t4 t5 t6 t7 t8 Time / s T Displacement from the equilibrium point / m A -A Distance from source / m  

7 For a longitudinal wave, the vertical axis represents __________________________. e.g. positive represents rightwards and negative represents leftwards. All the particles move in a similar manner with the same amplitude and frequency as the wave. The period can be determined from the graph. E.g. 1 Displacement-distance graph Displacement-time graph (displacement of all particles (displacement of particle A at an instant in time ) with respect to time ) 1) What is the displacements of Particle A, B and C respectively? 2.0 m, 1.0 m , −2.0 m 2) What is the amplitude of the wave? 2.0 m 3) What is the wavelength of the wave? 8.0 m 4) What is the period of the wave? 0.20 s 5) What is the frequency of the wave? 5.0 Hz 6) What is the speed of the wave? 40 ms -1 A B x / m C y / m y / cm 2.0 1.0 0 − 1.0 − 2.0 2.0 4.0 6.0 8.0 0.05 0.10 0.15 0.20 1.0 − 1.0 − 2.0 y / m 0 x / m t / s 2.0

8 E.g. 2 Sketch the displacement-distance graph and the pressure-distance graph Representation for longitudinal wave Compression Rarefaction Compression Air molecules before sound wave passes Air molecules displaced by sound wave A -A Displacement-distance graph for longitudinal wave distance Displacement Displaced to the right Displaced to the left Pressure-distance graph for longitudinal wave Pressure Normal Pressure when wave is absent distance

9 E.g. 3 Ans: C 12.5 Phase and Phase Difference Phase is an angle, in degrees ( ) or radians (r