Transcript
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.
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.
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.
Damping and Resonance
• (b) Internal damping is the loss of energy due to the
extension and compression of the molecules in the
system.
Damping and Resonance
• 4 Damping in an oscillating system causes
• (a) the amplitude, and
• (b) the energy of the system to decrease.
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.
Damping and Resonance
• 5 To enable an oscillating system to go on
continuously, an external force must be applied to
the system.
Damping and Resonance
• 6 The external force supplies energy to the
system. Such a motion is called a forced oscillation.
Damping and Resonance
• 7 The frequency of
a system which
oscillates freely
without the action
of an external force
is called the natural
frequency. g
lT 2
Tf
1
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.
Damping and Resonance
• 9 The characteristics of resonance can be
demonstrated with a Barton's pendulum system as
shown in Figure 1.17.
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.
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.
Damping and Resonance
10Hz
8 Hz
10 Hz9 Hz
12 Hz
10 Hz8 Hz
12 Hz
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.
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.
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.
Damping and Resonance
• (d)Cracking of wine glass
Chapter 1: Waves
1.2 Analysing Reflection of Waves
Ripple Tank
Ripple Tank
Main Parts Functions
Lamp To project the image of the water waves onto the white
paper below the ripple tank
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
Ripple Tank
Main Parts Functions
Rheostat Controls the frequency of the water waves produced
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.
Ripple Tank
Main Parts Functions
Stroboscope To freeze the image of the water waves
Ripple Tank
Ripple Tank
• 1 A water wave is a type of transverse
wave.
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.
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
Ripple Tank
• 4. Each bright and dark fringe represents the
wavefront of the water wave.
Ripple Tank
• 5. A hand stroboscope can be used to freeze the
motion of the water waves.
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
Ripple Tank
• 7. The wavelength, , of the water wave is
related by v = f.
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.
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
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.
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.
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?
Reflection of Waves
• Hypothesis
• The angle of reflection is equal to the
angle of incidence.
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
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.
Reflection of Waves
• Apparatus/Materials
• Ripple tank, plane reflector, a piece of white paper,
wooden bar, lamp, motor, sponge and mechanical
stroboscope.
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.
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.
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.
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.
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.
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.
Reflection of Waves
• ResultsPattern 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.
Reflection of Waves
• Results
Angle of incidence, i, () 20 30 40 50 60
Angle of reflection, r, () 20 30 40 50 60
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.
Reflection of Waves
• Conclusion
• The angle of reflection is equal to the angle of
incidence. The hypothesis is valid.
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?
Reflection of Waves
• Example 6
• Solution
• Frequency of wave = Number of slits x Frequency of
stroboscope
• 20 = 4 x f
• f = 5 Hz
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?
Reflection of Waves
• Hypothesis
• The angle of reflection is equal to the angle of
incidence.
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
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.
Reflection of Waves
• Apparatus/Materials
• Two cardboard tubes, stopwatch, a slab of soft
wood, a wooden board with a smooth surface and
a protractor.
Reflection of Waves
• Procedure
• 1 The apparatus is set up as shown in Figure 1.25.
Reflection of Waves
• Procedure
• 2 The angle of incidence, i = 30° is measured with
a protractor.
• 3 The stopwatch is started.
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.
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.
Reflection of Waves
• ResultsAngle of
incidence, i, ()
30 40 50 60 70
Angle of
reflection, r, ()
30 40 50 60 70
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.
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
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?
Reflection of Waves
• Hypothesis
• The angle of reflection is equal to the angle of
incidence.
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
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.
Reflection of Waves
• Apparatus/Materials
• Plane mirror, ray box, plasticine, protractor, white
piece of paper and a sharp pencil.
Reflection of Waves
• Procedure
• 1 A straight line, PQ is drawn on a sheet of white
paper.
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.
Reflection of Waves
• Procedure
• 4 A plane mirror is erected along the line PQ.
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.
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.
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
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.
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.
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.
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.
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.
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).
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.
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