Chapter 1: Waves

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Chapter 1 Waves

• 1.1 Understanding Waves

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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.

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Motion of Waves

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

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Motion of Waves

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

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Motion of Waves

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

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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
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Propagation (Traveling) of Waves

• 2.However, the particles of the medium do not
  travel in the direction of the wave.

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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.

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Propagation (Traveling) of Waves

• Activity 1.1 To demonstrate that waves transfer
  energy without transferring matter
• Apparatus
• Radio, candle and matches.

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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.

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Propagation (Traveling) of Waves

• Procedure
• 2. The candle is lit and the movements of its
  flame is observed.

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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.

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Propagation (Traveling) of Waves

• Discussion
• 1. The flame vibrates when the radio is turned on.

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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.

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Propagation (Traveling) of Waves

• Conclusion
• Waves transfer energy from a vibrating system
  without transferring matter.

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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
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Wavefronts

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

Same displacement
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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.

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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.

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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.

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Types of Waves

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

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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.

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Transverse Waves

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

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Transverse Waves

• 3. Examples of transverse waves are water waves
  and light waves.

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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.

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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.

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Longitudinal Waves

• 3 . Example of longitudinal waves is sound waves.

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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
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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
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Amplitude, Period and Frequency of a Wave

• 3 . The period, T, of a vibrating system is the
  time taken to complete an oscillation.

Period
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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

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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.

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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.

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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.

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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?

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Amplitude, Period and Frequency of a Wave

• Example 1
• Solution
• (a)

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Amplitude, Period and Frequency of a Wave

• Example 1
• Solution
• (b)

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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.

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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.

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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

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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.

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Displacement-time Graph of a Wave

• Example 2
• Solution
• (a) Amplitude, A 5 cm

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

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• Example 2
• Solution
• (c) Frequency of oscillation,

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Displacement-distance Graph of a Wave

• 1. Figures 1.12 (a) and (b) show the propagation
  of a water wave and a sound wave.

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Displacement-distance Graph of a Wave
R Rarefaction
CCompression
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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).

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Displacement-distance Graph of a Wave

• 3. The wavelength, ?, is the distance between
  successive points of the same phase in a wave.

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Displacement-distance Graph of a Wave

• For example
• (a) the distance between two successive crests
  or two successive troughs in a water wave,

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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).

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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.

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Displacement-distance Graph of a Wave

• Example 3
• Solution
• (a) Amplitude, A 4 cm

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Displacement-distance Graph of a Wave

• Example 3
• Solution
• (b) Wavelength, 12 cm

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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.

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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?

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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
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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

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Relationship between Speed (v), wavelength, ? and
Frequency (f)

• Example 5
• Calculate
• (a) the amplitude,
• (b) the wavelength, and
• (c) the speed of the wave.

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Relationship between Speed (v), wavelength, ? and
Frequency (f)

• Example 5
• Solution
• (a) Amplitude, A 6 cm

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Relationship between Speed (v), wavelength, ? and
Frequency (f)

• Example 5
• Solution
• (b) Wavelength, 20 cm

1o
2o
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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