1© Manhattan Press (H.K.) Ltd. Pulse Continuous waves Continuous waves 8.1 Characteristics of waves Wave motion Wave motion Graphical representation of waves Graphical representation of waves Factors affecting the speed of waves Factors affecting the speed of waves Wave intensity Wave intensity

2 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 2) A wave is generated when there are disturbances repeated periodically. How to generate a wave?

3 © Manhattan Press (H.K.) Ltd. Classify a wave according to … Energy transfer: i.e. progressive waves VS stationary waves Medium of propagation: i.e. mechanical waves VS electromagnetic waves Direction of oscillation of particles: i.e. transverse waves VS longitudinal waves 8.1 Characteristics of waves (SB p. 2)

4 © Manhattan Press (H.K.) Ltd. Pulse A pulse on a slinky spring is produced by moving the end of it … 8.1 Characteristics of waves (SB p. 2) forth and back up and down

5 © Manhattan Press (H.K.) Ltd. Characteristics of a pulse 1. The pulse carries energy from one end to the other end of the spring. 2. The pulse moves with constant speed along the spring. 3. Each particle in the spring is displaced through a small distance before returning to its original position. 8.1 Characteristics of waves (SB p. 3) Go to More to Know 1 More to Know 1

6 © Manhattan Press (H.K.) Ltd. Continuous waves If a rope is shaken continuously up and down, a series of pulses called a wave is produced. 8.1 Characteristics of waves (SB p. 3) Equilibrium positions wavelength crest trough amplitude Go to More to Know 2 More to Know 2

7 © Manhattan Press (H.K.) Ltd. Wave motion - a complete oscillation 8.1 Characteristics of waves (SB p. 4) t = 0 t = T

8 © Manhattan Press (H.K.) Ltd. Velocity, frequency & wavelength 8.1 Characteristics of waves (SB p. 5)

9 © Manhattan Press (H.K.) Ltd. Frequency & period 8.1 Characteristics of waves (SB p. 5) The frequency ( f ) of a wave is the number of oscillations per second. The frequency ( f ) of a wave is the number of completed oscillations per second. Go to Example 1 Example 1

10 © Manhattan Press (H.K.) Ltd. Wave intensity 8.1 Characteristics of waves (SB p. 6) The intensity (I) of a wave is the rate at which energy is transferred by the wave to a unit area which is perpendicular to the direction of propagation of the wave. where P is the source power and A is the surface area. The unit is W m –2.

11 © Manhattan Press (H.K.) Ltd. Wave intensity 8.1 Characteristics of waves (SB p. 6) Go to Example 2 Example 2 I  a2I  a2 For a sinusoidal wave moving through a medium, each particle in the medium moves in simple harmonic motion. Since the energy of a particle moving in simple harmonic motion with amplitude a is, we have:

12 © Manhattan Press (H.K.) Ltd. Graphical representation of waves 8.1 Characteristics of waves (SB p. 7) The displacement-time graph shows the displacement of a particle at different times. 1. Displacement-time graph If the motion of the source is simple harmonic, the displacement-time graph is a sine function.

13 © Manhattan Press (H.K.) Ltd. Graphical representation of waves 8.1 Characteristics of waves (SB p. 7) The displacement-distance graph shows the displacement of particles at different positions at one instant. 2. Displacement-distance graph

14 © Manhattan Press (H.K.) Ltd. Instantaneous motion of particles 8.1 Characteristics of waves (SB p. 7) Particles d, e, f are moving up Particles a, b, h, i, j are moving down Particles c, g, k are momentarily at rest Particles a, e, i are of highest speed Go to Example 3 Example 3

15 © Manhattan Press (H.K.) Ltd. 1. All electromagnetic waves have same speed in vacuum but different speeds in a medium: Wave speed in a medium: 8.1 Characteristics of waves (SB p. 8) Factors affecting the speed of waves where c = speed of light, n r = refractive index of the medium. Go to More to Know 3 More to Know 3

16 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 8) Factors affecting the speed of waves 2. The propagation of mechanical waves depends on the vibrations of particles in the medium. Therefore, the wave speed depends on the mass and elasticity of the medium. If the mass of the particles in the medium is greater, the wave speed is lower. If the elasticity of medium is greater, the wave speed is higher.

17 © Manhattan Press (H.K.) Ltd. Wave speed 8.1 Characteristics of waves (SB p. 8) (b) The speed of longitudinal wave in solid is: where E = Young modulus,  = density (a)The speed of transverse wave along a stretched string is: where T = tension,  = mass per unit length Go to Example 4 Example 4

18 © Manhattan Press (H.K.) Ltd. End

19 © Manhattan Press (H.K.) Ltd. Energy transfer A wave can transport energy from one place to another without the transfer of matter. Return to Text 8.1 Characteristics of waves (SB p. 3)

20 © Manhattan Press (H.K.) Ltd. Periodic motion Wave motion is a periodic motion. Return to Text 8.1 Characteristics of waves (SB p. 3)

21 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 5) Q: Q: A typical sound wave of human speech has a frequency of 600 Hz, whereas the frequency of red light is about 4.3 × Hz. In air, light travels at 3 × 10 8 m s –1 and sound at 344 m s –1. Find the wavelengths of the two waves. Solution

22 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 5) Solution: For both waves, v = fλ For the sound wave: λ = = = 0.57 m For the light wave: λ = = 6.98 × 10 –7 m Return to Text

23 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 6) Q: Q: A light source has an average power of 200 W. Calculate the intensity of the light source at a point 6 m from the source. Solution

24 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 6) Solution: The wave intensity is given by I = = = 0.44 W m –2 Return to Text

25 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 7) Q: Q: The figure shows the simple harmonic motion of a particle in a medium through which a wave is moving with a speed of 5.0 km s –1 from left to right. What is (a) the frequency of oscillation, (b) the amplitude of oscillation, and (c) the wavelength of the wave? Solution

26 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 7) Solution: (a) From the graph, period of oscillation, T = 20  s  Frequency, f = = = 5.0  10 4 Hz (b) Amplitude of oscillation = 2  m (c) Using v = f, Wavelength, = = = 0.1 m Return to Text

27 © Manhattan Press (H.K.) Ltd. Young modulus Young modulus is a measure of the stiffness of a material. It is defined as: E = where σ = tensile stress; ε = tensile strain. Young modulus and the concept of elasticity will be discussed in more detail under the topic of Matter. 8.1 Characteristics of waves (SB p. 8) Return to Text

28 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 9) Q: Q: The tension on the longest string of a piano is N, and the mass per unit length of this string is kg m –1. What is the speed of a wave on this string? Solution

29 © Manhattan Press (H.K.) Ltd. 8.1 Characteristics of waves (SB p. 9) Solution: The wave speed on this string is: v = = = m s –1 Return to Text