Wave motion lecture notes and Tutorial

1 Lecturer: Mr Eugene Tan Email: tan.sweehong@dhs.sg Content • Progressive waves • Transverse and longitudinal waves • Polarisation • Determination of frequency and wavelength Learning Outcomes Candidates should be able to: (a) show an understanding 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 = fλ. (c) recall and use the equation v = fλ. (d) show an understanding that energy is transferred due to a progressive wave. (e) recall and use the relationship, intensity ∝ (amplitude)2. (f) analyse and interpret graphical representations of transverse and longitudinal waves. (g) show an understanding that polarisation is a phenomenon associated with transverse waves. (h) determine the frequency of sound using a calibrated c.r.o. (i) determine the wavelength of sound using stationary waves. 10.1 Progressive Waves A progressive wave transfers energy from one point to another by means of vibrations or oscillations within the waves. All waves involve a disturbance from an equilibrium position (i.e. an oscillation), and (for progressive waves,) the disturbance travels from one region of space to another. However, the particles do not move along with the disturbance. 10.2 Transverse and Longitudinal Waves Progressive Waves Transverse Waves Longitudinal Waves Electromagnetic Waves Mechanical Waves Mechanical Waves H1 / H2 PHYSICS (2013) TOPIC 10: WAVE MOTION

2 Transverse wave: Transverse wave is a wave in which the oscillation of the particles in the wave is perpendicular to the direction of transfer of energy of the wave. (E.g.: electromagnetic waves) Longitudinal wave: Longitudinal wave is a wave in which the oscillation of the particles in the wave is along the direction of transfer of energy of the wave. (E.g.: sound waves) Mechanical wave: A wave that requires a medium for its transmission. (E.g.: sound waves and water waves) Electromagnetic wave: Wave consisting of oscillating electric and magnetic fields that are at right angles to each other and to the 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 × 10 8 m s-1. (E.g.: radio waves, visible light, X-rays and microwaves) Electromagnetic Spectrum Type of Radiation Range of wavelength Range of Frequency Radio Waves 6 cm to 300 km (1 x 103 to 5 x 109) Hz Microwaves 10-3 m to 10-1 m (109 to 3 x 1011) Hz Infrared Radiation 7.8 x 10-7 m to 0.5 x 10-3 m (6 x 1011 to 4 x 1014) Hz Light (Visible Spectrum) 3.8 x 10-7 m to 7.8 x 10-7 m (4 x 1014 to 8 x 1014) Hz Ultraviolet Radiation 6 x 10-10 m to 3.8 x 10-7 m (8 x 1014 to 5 x 1017) Hz X-Rays 10-12 m to 10-9 m From 3 x 1020 Hz Gamma Rays 10-14 m to 10-10 m (3 x 1018 to 3 x 1022) Hz Note: Range of different radiations may overlap each other. Visible Spectrum Type of Radiation Range of wavelength Range of Frequency Red m 7107 −×=λ (6.22 to 7.80) x 10-7 m (3.84 to 4.82) x 1014 Hz Orange (5.97 to 6.22) x 10-7 m (4.82 to 5.03) x 1014 Hz Yellow (5.77 to 5.97) x 10-7 m (5.03 to 5.20) x 1014 Hz Green (4.92 to 5.77) x 10-7 m (5.20 to 6.10) x 1014 Hz Blue (4.55 to 4.92) x 10-7 m (6.10 to 6.59) x 1014 Hz Violet m 7104 −×=λ (3.90 to 4.55) x 10-7 m (6.59 to 7.69) x 1014 Hz Source: Longman A-Level Course in Physics Volume 1 Refer to Annex A for more details on electromagnetic waves.

3 10.3 Characteristics of Waves (a) Displacement (y): The distance in a specific direction from the equilibrium position of the simple harmonic motion. (b) Amplitude (y 0 or A): Maximum possible displacement from the equilibrium point in either direction. (c) Period (T): Time taken for a particle in the wave to undergo one complete oscillation. Unit: second. (equals to the time taken for the wave energy to travel a distance of one wavelength) (d) Frequency (f): Number of oscillations per unit time made by the oscillating particle. ƒ = T 1 . Unit: Hertz. 1 Hz is equal to one oscillation (or one cycle) per second. (e) Wavelength (λ): The shortest distance between any two successive points on a progressive waves which are vibrating in phase. (f) Wave speed (v): Distance travelled per unit time by the wave energy in the direction of the transfer of the wave energy. It is related to the wavelength and the frequency according to the equation v = fλ. From the definition of speed, Speed = Time Distance For one cycle, (i) the time taken is one period, T. (ii) the distance travelled is a wavelength, λ. Therefore, v = T λ Since f = T 1 Hence v = f λ Displacement (y) Distance y0 0 Crest Wavelength Wavelength Wavelength Trough Equilibrium Position

4 (g) Wave front: An imaginary line or surface joining points which are at the same state of oscillation (i.e. in phase). E.g.: a line joining crest to crest in a wave. (h) Ray: The pat h taken by the wave. This is used to indicate the direction of transfer of wave energy . Rays are always at right angles to the wave fronts (i.e. wave fronts are always perpendicular to the direction of transfer of wave energy). More details on the mathematical description of wave can be found in Annex B. s Wave fronts ray

5 10.4 Graphical Representations of Transverse and Longitudinal Waves 10.4.1 Displacement-Distance Graph The displacement-distance graph shows how the displacem ents of the particles vary with the distance from the source at a particular instant in time. The wavelength can be determined from the graph. (one complete sine curve or cosine curve) 10.4.2 Displacement-Time Graph The displacement -time graph shows how the displacement of a single wave particle varies with time. For a longitudinal wave, the vertical axis represent s horizontal displacement, 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. (one complete sine curve or cosine curve) For a transverse wave particle t1, t3 t5, t7 t6 t2 t0, t4, t8 For a longitudinal wave particle t1, t3 t5, t7 t6 t2 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 λ λ

6 E.g. 1 Displacement-distance graph Displacement-time graph (displacement of all particles (displacement of one particle at an instant) e.g. Particle A with respect to time ) 1) What is the displacements of Particle A, B and C respectively? 2 m, 1 m , −2 m 2) What is the amplitude of the wave? 2m 3) What is the wavelength of the wave? 8 m (Note: wavelength is the distance of one sine or one cosine curve on the displacement - distance graph) 4) What is the period of the wave? 0.20 s (Note: period is the duration of one sine or one cosine curve on the displacement – time graph) 5) What is the frequency of the wave? 5 Hz 6) What is the speed of the wave? 40 ms-1 A B x / m C y / m y /