Chapter 1: Waves 1.1Understanding Waves

Motion of Waves 1 An oscillating or vibrating motion in which a point or body moves back and forth along a line about a fixed central point produces waves.

Motion of Waves 2. Examples of waves: (a) Light waves are produced as a result of vibrations of electrons in an atom.

Motion of Waves 2. Examples of waves: (b) Sound waves are produced by vibrating mechanical bodies such as guitar strings or a tuning fork.

Motion of Waves 2. Examples of waves: (c) Water waves are produced by disturbance (or vibration) on a still water surface.

Propagation (Traveling) of Waves 1.When a wave travels through a medium, the particles of the medium vibrate about their equilibrium positions. Direction of waves

Propagation (Traveling) of Waves 2.However, the particles of the medium do not travel in the direction of the wave.

Propagation (Traveling) of Waves 3 A wave transfers energy and the momentum from the source of the wave (the oscillating or vibrating system) to the surroundings.

Propagation (Traveling) of Waves Activity 1.1:To demonstrate that waves transfer energy without transferring matter Apparatus: Radio, candle and matches.

Propagation (Traveling) of Waves Activity 1.1:To demonstrate that waves transfer energy without transferring matter Procedure 1. A candle is placed about 10 cm from the speaker of a radio.

Propagation (Traveling) of Waves Procedure 2. The candle is lit and the movements of its flame is observed.

Propagation (Traveling) of Waves Procedure 3. Then, the radio is turned on and the volume of the sound is gradually increased until a change in the movement of the flame becomes noticeable.

Propagation (Traveling) of Waves Discussion 1. The flame vibrates when the radio is turned on.

Propagation (Traveling) of Waves Discussion 2. This observation shows that the propagation of the sound waves from the vibration of the cone of the speaker transfers energy (or momentum) to the flame and causes it to vibrate.

Propagation (Traveling) of Waves Conclusion Waves transfer energy from a vibrating system without transferring matter.

Wavefronts 1. A wave front is a line or plane on which the vibrations of every points on it are in phase and are at the same distance from the source of the wave. Same Phase

Wavefronts 2. Points in a wave are in phase if they vibrate in the same direction with the same displacement. Same displacement

Plane Wave fronts 1.Figure 1.3 shows the production of plane water waves when a wooden bar vibrates vertically at a constant frequency on the surface of the water.

Plane Wave fronts 2.Lines PQ, RS, TU and VW are straight lines along the respective crests of the waves. These lines are called wave fronts.

Circular Wave fronts 1. When we use a fingertip to touch the surface of water repeatedly, circular wave fronts are produced as shown in Figure 1.4.

Types of Waves There are two types of waves. (a) Transverse wave (b) Longitudinal wave

Transverse Waves 1. A transverse wave is a wave in which the vibration of particles in the medium is at right angle (perpendicular) to the direction of propagation of the wave.

Transverse Waves 2. A model of a transverse wave can be produced by a slinky spring as shown in Figure 1.6.

Transverse Waves 3. Examples of transverse waves are water waves and light waves.

Longitudinal Waves 1. A longitudinal wave is a wave in which the vibration of particles in the medium is parallel to the direction of propagation of the wave.

Longitudinal Waves 2. When the slinky spring is vibrated back and forth along the direction of propagation of the wave at a fixed rate, a longitudinal wave is produced as shown in Figure 1.8.

Longitudinal Waves 3. Example of longitudinal waves is sound waves.

Amplitude, Period and Frequency of a Wave 1.The amplitude, A, of a vibrating system is maximum displacement from its equilibrium position. It is a measure of height of the wave crest or depth of the wave trough. Amplitude

Amplitude, Period and Frequency of a Wave 2.In Figures 1.9 (a) and (b), the distance OQ is the amplitude, where O is the equilibrium position of the vibrating system. Amplitude

Amplitude, Period and Frequency of a Wave 3.The period, T, of a vibrating system is the time taken to complete an oscillation. Period

Amplitude, Period and Frequency of a Wave 4. In the two vibrating (oscillating) systems show in Figure 1.9, a complete oscillation are: (a) from P  Q  P or Q  P  Q, (b) from O  P  Q  O or O  Q  P  O

Amplitude, Period and Frequency of a Wave 5.If a vibrating system makes n complete oscillations in a time of t seconds, the period of oscillation, T of the system is second The SI unit of period is second.

Amplitude, Period and Frequency of a Wave 6 The frequency, f, is the number of complete oscillations made by a vibrating system in one second. The unit of frequency is hertz (Hz) or s -1.

Amplitude, Period and Frequency of a Wave 7 From the formulae of T and f, the relationship between period, T and frequency, f is: T is inversely proportional to f and vice versa.

Amplitude, Period and Frequency of a Wave Example 1: In an experiment, Aziz observes that a simple pendulum completes 30 oscillations in 48.0 seconds. What is (a) the period of oscillation? (b) the frequency of oscillation?

Amplitude, Period and Frequency of a Wave Example 1: Solution (a)

Amplitude, Period and Frequency of a Wave Example 1: Solution (b)

Displacement-time Graph of a Wave 1. The sinusoidal graph in Figure 1.10 is a graph of displacement, s against time, t of a load on a spring.

Displacement-time Graph of a Wave 2 From the graph of s against t in Figure 1.10, the following information is obtained. (a) Amplitude, A = a cm (b) Period of oscillation, T is the time between points: (i) O and F, (ii) C and G or (iii) P and Q.

Displacement-time Graph of a Wave Example 2: Figure 1.11 shows the displacement-time graph of the oscillation of a mass on a spring. Figure 1.11

Displacement-time Graph of a Wave Example 2: From the graph, (a) state the amplitude, (b) calculate the period of the oscillation, (c) calculate the frequency of the oscillation.

Displacement-time Graph of a Wave Example 2: Solution (a)Amplitude, A = 5 cm

Example 2: Solution (b) Period of oscillation, T = 0.04 s

Example 2: Solution (c) Frequency of oscillation,

Displacement-distance Graph of a Wave 1. Figures 1.12 (a) and (b) show the propagation of a water wave and a sound wave.

Displacement-distance Graph of a Wave R: Rarefaction C:Compression

Displacement-distance Graph of a Wave 2. The displacement, s of each particle of the medium at different distances can be shown in a displacement-distance graph as shown in Figure 1.12 (c).

Displacement-distance Graph of a Wave 3. The wavelength,, is the distance between successive points of the same phase in a wave.

Displacement-distance Graph of a Wave For example: (a) the distance between two successive crests or two successive troughs in a water wave,

Displacement-distance Graph of a Wave (b) the distance between two successive compressions or two successive rarefactions in a sound wave. The SI unit of wavelength,, is metre (m).

Displacement-distance Graph of a Wave Example 3: Figure 1.13 shows a displacement-distance graph of a wave. Figure 1.13 Find (a) the amplitude, (b) the wavelength of the wave.

Displacement-distance Graph of a Wave Example 3: Solution (a) Amplitude, A = 4 cm

Displacement-distance Graph of a Wave Example 3: Solution (b) Wavelength, =12 cm

Relationship between Speed (v), wavelength, and Frequency (f) The relationship between speed, wavelength and frequency can be obtained by relating the SI unit of the quantities.

Relationship between Speed (v), wavelength, and Frequency (f) Example 4: A wave of frequency 120 Hz has a wavelength of 5.0 m. What is the speed of the wave?

Relationship between Speed (v), wavelength, and Frequency (f) Example 4: A wave of frequency 120 Hz has a wavelength of 5.0 m. What is the speed of the wave? Solution f = 120 Hz and =5.0m Speed of wave, v = f = 120 x 5 = 600 m s -1

Relationship between Speed (v), wavelength, and Frequency (f) Example 5: The displacement-distance graph in Figure 1.14 shows the motion of a transverse wave. The source of the wave produces 10 complete waves in one second. Figure 1.14

Relationship between Speed (v), wavelength, and Frequency (f) Example 5: Calculate (a) the amplitude, (b) the wavelength, and (c) the speed of the wave.

Relationship between Speed (v), wavelength, and Frequency (f) Example 5: Solution (a) Amplitude, A = 6 cm

Relationship between Speed (v), wavelength, and Frequency (f) Example 5: Solution (b) Wavelength, = 20 cm 1o2o

Relationship between Speed (v), wavelength, and Frequency (f) Example 5: Solution (c) Frequency, f = 10 Hz, = 20 cm Speed, v = f =10x20 = 200 cm s -1