Damping and Resonance

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Damping and Resonance

• 1 In an oscillating system such as the
  oscillation of a simple pendulum, the oscillation
  does not continue with the same amplitudes
  indefinitely.

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Damping and Resonance

• 2 The amplitude of oscillation of the simple
  pendulum will gradually decrease and become zero
  when the oscillation stops. The decrease in the
  amplitude of an oscillating system is called
  damping.

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Damping and Resonance

• 3 An oscillating system experiences damping when
  its energy is drained out as heat energy.
• (a) External damping of the system is the loss
  of energy to overcome frictional forces or air
  resistance.

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Damping and Resonance

• (b) Internal damping is the loss of energy due to
  the extension and compression of the molecules
  in the system.

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Damping and Resonance

• 4 Damping in an oscillating system causes
• (a) the amplitude, and
• (b) the energy of the system to decrease.

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Damping and Resonance

• 4 Damping in an oscillating system causes
• (a) the amplitude, and
• (b) the energy of the system to decrease
• (c) the frequency, f does not change.

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Damping and Resonance

• 5 To enable an oscillating system to go on
  continuously, an external force must be applied
  to the system.

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Damping and Resonance

• 6 The external force supplies energy to the
  system. Such a motion is called a forced
  oscillation.

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Damping and Resonance

• 7 The frequency of a system which oscillates
  freely without the action of an external force is
  called the natural frequency.

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Damping and Resonance

• 8 Resonance occurs when a system is made to
  oscillate at a frequency equivalent to its
  natural frequency by an external force. The
  resonating system oscillates at its maximum
  amplitude.

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Damping and Resonance

• 9 The characteristics of resonance can be
  demonstrated with a Barton's pendulum system as
  shown in Figure 1.17.

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Damping and Resonance

• (a) When pendulum X oscillates, all the other
  pendulums are forced to oscillate. It is found
  that pendulum B oscillates with the largest
  amplitude, that is, pendulum B resonates.

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Damping and Resonance

• (b) The natural frequency of a simple pendulum
  depends on the length of the pendulum. Note that
  pendulum X and pendulum B are of the same length.
  Therefore, pendulum X causes pendulum B to
  oscillate at its natural frequency.

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Damping and Resonance
10 Hz
8 Hz
12 Hz
12 Hz
10Hz
10 Hz
9 Hz
8 Hz
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Damping and Resonance

• 10 Some effects of resonance observed in daily
  life
• (a) The tuner in a radio or television enables
  you to select the programmes you are interested
  in. The circuit in the tuner is adjusted until
  resonance is achieved, at the frequency
  transmitted by a particular station selected.
  Hence a strong electrical signal is produced.

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Damping and Resonance

• 10 Some effects of resonance observed in daily
  life
• (b) The loudness of music produced by musical
  instruments such as the trumpet and flute is the
  result of resonance in the air.

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Damping and Resonance

• (c) The effects of resonance can also cause
  damage. For example, a bridge can collapse when
  the amplitude of its vibration increases as a
  result of resonance.

THE POWER OF RESONANCE CAN DESTROY A BRIDGE. ON
NOVEMBER 7, 1940, THE ACCLAIMED TACOMA NARROWS
BRIDGE COLLAPSED DUE TO OVERWHELMING RESONANCE.
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Damping and Resonance

• (d)Cracking of wine glass

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Chapter 1 Waves

• 1.2 Analysing Reflection of Waves

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Ripple Tank
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Ripple Tank
Main Parts Functions
Lamp To project the image of the water waves onto the white paper below the ripple tank
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Ripple Tank
Main Parts Functions
Motor The vibrations of electric motor causes the plastic sphere to produce spherical waves, and the wooden bar to produce plane water waves
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Ripple Tank
Main Parts Functions
Rheostat Controls the frequency of the water waves produced
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Ripple Tank
Main Parts Functions
Sponge To line the inside of the transparent tray to prevent reflection of water waves from the side of the tray.
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Ripple Tank
Main Parts Functions
Stroboscope To freeze the image of the water waves
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Ripple Tank
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Ripple Tank

• 1 A water wave is a type of transverse wave.

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Ripple Tank

• 2. When waves are produced on the surface of the
  water, a wave crest will act like a convex lens
  while a wave trough will act like a concave lens.

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Ripple Tank

• 3. Hence the crest focuses the light to form a
  bright fringe on the white screen below the
  ripple tank, and the trough diverges the light
  and forms a dark fringe on the white screen, as
  shown in Figure 1.21

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Ripple Tank

• 4. Each bright and dark fringe represents the
  wavefront of the water wave.

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Ripple Tank

• 5. A hand stroboscope can be used to freeze the
  motion of the water waves.

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Ripple Tank

• 6. When the fringe pattern on the white screen
  below the ripple tank is "frozen", the frequency
  of the water waves is given by
• f n x p,
• where
• n number of slits on the stroboscope
• p rate of rotation of the stroboscope

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Ripple Tank

• 7. The wavelength, ?, of the water wave is
  related by v f?.

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Reflection of Waves

• 1 Reflection of a wave occurs when a wave
  strikes an obstacle. The wave undergoes a change
  in direction of propagation when it is reflected.

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Reflection of Waves

• 2 The incident wave is the wave before it
  strikes the obstacle, whereas the reflected wave
  is the wave which has undergone a change in
  direction of propagation after reflection.
• i angle of incidence
• r angle of reflection

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Reflection of Waves

• 3 The phenomenon of reflection of waves obeys
  the Laws of reflection where
• (a) The angle of incidence, i, is equal to the
  angle of reflection, r.

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Reflection of Waves

• 3 The phenomenon of reflection of waves obeys
  the Laws of reflection where
• (b) The incident wave, the reflected wave and
  the normal lie in the same plane which is
  perpendicular to the reflecting surface at the
  point of incidence.

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Reflection of Waves

• Experiment 1.1 To investigate the reflection of
  plane waves
• Problem statement
• What is the relationship between the angle of
  incidence and the angle of reflection of a water
  wave?

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Reflection of Waves

• Hypothesis
• The angle of reflection is equal to the angle of
  incidence.

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Reflection of Waves

• Variables
• Manipulated Angle of incidence of the water
  wave
• Responding Angle of reflection of the water
  wave
• Fixed Depth of water, frequency of dipper

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Reflection of Waves

• Operational definition
• The angle of incidence is the angle between the
  direction of propagation of incident wave and the
  normal. The angle of reflection is the angle
  between the direction of propagation of reflected
  wave and the normal.

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Reflection of Waves

• Apparatus/Materials
• Ripple tank, plane reflector, a piece of white
  paper, wooden bar, lamp, motor, sponge and
  mechanical stroboscope.

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Reflection of Waves

• Procedure
• 1 A ripple tank is filled with water and is set
  up as shown in Figure 1.23. The tank is leveled
  so that the depth of water in the tank is uniform
  to ensure water waves propagate with uniform
  speed.

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Reflection of Waves

• Procedure
• 2 All the inner surface of the ripple tank is
  lined with a layer of sponge to prevent
  reflection of the water waves from the edges.

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Reflection of Waves

• Procedure
• 3 The lamp above the tank is switched on and a
  large piece of white paper is placed below the
  tank.

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Reflection of Waves

• Procedure
• 4 A metallic plane reflector is placed at the
  centre of the tank. The motor with wooden bar
  attached is switched on to produce plane waves
  which propagate towards the reflector.

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Reflection of Waves

• Procedure
• 5 The pattern (on the white paper) of the
  reflected waves produced by the vibrating wooden
  bar is observed with the help of a mechanical
  stroboscope. The incident waves and the reflected
  waves are sketched.

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Reflection of Waves

• Procedure
• 6 Steps 4 and 5 are repeated with the reflector
  repositioned so that the wave is incident at
  angles, i 20, 30, 40, 50 and 60 on the
  reflector as shown in Figure 1.24.

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Reflection of Waves

• Results

Pattern of reflected waves Characteristic of waves
(i) Angle of incidence, i 0? Angle of reflection, r 0? Wavelength, frequency and speed of wave do not change after reflection. Direction of propagation of water changes.
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Reflection of Waves

• Results

Angle of incidence, i Angle of reflection, r
Wavelength, frequency and speed of wave do not
change after reflection. Direction of propagation
of water changes.
Angle of incidence, i, (?) 20 30 40 50 60
Angle of reflection, r, (?) 20 30 40 50 60
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Reflection of Waves

• Conclusion
• The angle of reflection is equal to the angle of
  incidence. The hypothesis is valid.

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Reflection of Waves

• Example 6
• A water wave of frequency 20 Hz appears
  stationary when observed through a stroboscope
  with 4 slits. What is the frequency of rotation
  of the stroboscope?

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Reflection of Waves

• Example 6
• Solution
• Frequency of wave Number of slits x Frequency
  of stroboscope
• 20 4 x f
• f 5 Hz

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Reflection of Waves

• Experiment 1.2 To investigate the reflection of
  sound waves
• Problem statement
• What is the relationship between the angle of
  incidence and the angle of reflection of a sound
  wave?

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Reflection of Waves

• Hypothesis
• The angle of reflection is equal to the angle of
  incidence.

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Reflection of Waves

• Variables
• (a) Manipulated Angle of incidence of the sound
  wave
• (b) Responding Angle of reflection of the sound
  wave
• (c) Fixed Distance of the stopwatch from the
  point of reflection on the wooden board

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Reflection of Waves

• Operational definition
• The angle of incidence of the sound wave is the
  angle between the incident sound wave and the
  normal. The angle of reflection is the angle
  between the reflected sound wave and the normal.

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Reflection of Waves

• Apparatus/Materials
• Two cardboard tubes, stopwatch, a slab of soft
  wood, a wooden board with a smooth surface and a
  protractor.

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Reflection of Waves

• Procedure
• 1 The apparatus is set up as shown in Figure 1.25.

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Reflection of Waves

• Procedure
• 2 The angle of incidence, i 30 is measured
  with a protractor.
• 3 The stopwatch is started.

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Reflection of Waves

• Procedure
• 4 The position of the cardboard tube B is
  adjusted until a loud ticking sound of the
  stopwatch is heard.
• 5 The angle of reflection, r at this position of
  the cardboard tube B is measured.

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Reflection of Waves

• Procedure
• 6 Steps 2 to 5 are repeated with the angles of
  incidence, i 40, 50, 60 and 70.
• 7 The results are tabulated.

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Reflection of Waves

• Results

Angle of incidence, i, (?) 30 40 50 60 70
Angle of reflection, r, (?) 30 40 50 60 70
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Reflection of Waves

• Discussion
• The sound waves from the stopwatch experience a
  reflection after striking the wooden board. The
  slab of soft wood placed along the normal serves
  as a barrier to prevent the sound of the
  stopwatch from reaching the observer directly.

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Reflection of Waves

• Conclusion
• The angle of incidence, i is equal to the angle
  of reflection, r. The laws of reflection are
  obeyed. The hypothesis is valid.

Angle of incidence, i, (?) 30 40 50 60 70
Angle of reflection, r, (?) 30 40 50 60 70
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Reflection of Waves

• Experiment 1.3 To investigate the reflection of
  light
• Problem statement
• What is the relationship between the angle of
  incidence and the angle of reflection of a light
  ray?

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Reflection of Waves

• Hypothesis
• The angle of reflection is equal to the angle of
  incidence.

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Reflection of Waves

• Variables
• (a) Manipulated Angle of incidence of light ray
• (b) Responding Angle of reflection of the light
  ray
• (c) Fixed Position of the plane mirror

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Reflection of Waves

• Operational definition
• The angle of incidence of the light ray is the
  angle between the incident ray and the normal.
  The angle of reflection is the angle between the
  reflected ray and the normal.

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Reflection of Waves

• Apparatus/Materials
• Plane mirror, ray box, plasticine, protractor,
  white piece of paper and a sharp pencil.

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Reflection of Waves

• Procedure
• 1 A straight line, PQ is drawn on a sheet of
  white paper.

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Reflection of Waves

• Procedure
• 2 A normal line, ON is drawn from the midpoint
  of PQ.
• 3 Using a protractor, lines at angles of
  incidence of 20, 30, 40, 50 and 60, with the
  normal, ON are drawn.

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Reflection of Waves

• Procedure
• 4 A plane mirror is erected along the line PQ.

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Reflection of Waves

• Procedure
• 5 A ray of light from the ray box is directed
  along the 20 line. The angle between the
  reflected ray and normal, ON is measured.

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Reflection of Waves

• Procedure
• 6 Step 5 is repeated with the angle of incidence,
  i of 30, 40, 50 and 60.
• 7 The results are tabulated.

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Reflection of Waves

• Results
• The incident ray must be as narrow as possible to
  obtain a narrow and thin reflected ray. It can be
  done by adjusting the lens in the ray box (or a
  laser pen can be used instead).

Angle of incidence, i, (?) 20 30 40 50 60
Angle of reflection, r, (?) 20 30 40 50 60
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Reflection of Waves

• Conclusion
• The angle of incidence, i is equal to the angle
  of reflection, r. The laws of reflection are
  obeyed. The hypothesis is valid.

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Applications of Reflection of waves in Daily Life

• Safety
• (a) The rear view mirror and side mirror in a car
  are used to view cars behind and at the side
  while overtaking another car, making a left or
  right turn and parking the car. The mirrors
  reflect light waves from other cars and objects
  into the driver's eyes.

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Applications of Reflection of waves in Daily Life

• Safety
• (b) The lamps of a car emit light waves with
  minimum dispersion. The light bulb is placed at
  the focal point of the parabolic reflector of the
  car lamp so that the reflected light waves are
  parallel to the principal axis of the reflector.
  Parallel light waves have a further coverage.

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Applications of Reflection of waves in Daily Life

• Defence
• A periscope is an optical instrument. It can be
  constructed using two plane mirrors for viewing
  objects beyond obstacles. The light waves from an
  object which is incident on a plane mirror in the
  periscope are reflected twice before entering the
  eyes of the observer.

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Applications of Reflection of waves in Daily Life

• Medication
• The concept of total internal reflection is used
  in optical fibres. Light entering one end of an
  optical fibre experiences multiple total internal
  reflections as it propagates through the whole
  length of the fibre before emerging at the other
  end. Optical fibres are used to examine the
  internal organs of patients, especially organs
  with internal cavities such as the colon and
  stomach, without operating on the patient.

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Applications of Reflection of waves in Daily Life

• Telecommunications
• (a) Optical fibres have many advantages compared
  to conventional cables in the transmission of
  information. Optical fibres are lightweight,
  flexible, electrically non-conducting (thus are
  not affected by electromagnetic interference) and
  can transmit much more information (information
  is transmitted almost at speed of light, 3 x 108
  ms -1).

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Applications of Reflection of waves in Daily Life

• Telecommunications
• (b) Infrared waves from a remote control of
  electrical equipment (television or radio) are
  reflected by objects in the surroundings and
  received by the television set or radio.