LESSON 1
Understanding Waves Motion
By the end of this lesson, you should be able to:
• Describe what is meant by wave motion,
• Recognise that waves transfer energy without transferring matter.
• Compare transverse and longitudinal waves and give an example of each.
Example of vibrating systems,
Vibrating systems produce waves.
When the motor to start the vibrator start vibrating.
At the water surface, water waves are produce.
The direction of propagation of the water waves is from right to left.
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The leaf represents a water particle. How does the water particle move?
As the wave passes by,. The leaf does not move together with the wave, instead it moves up and down about its initial position.
Waves transfer energy as they move along the water particles.
However, the waves do not carry the water particles along with them.
That is why the leaf still remains about its initial position.
This shows that waves transfer energy without transferring matter.
The water particle moves up and down.
When hand to beat the drum. The flame will flicker.
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Sound waves transfer energy from the vibrating drum to the candle flame, causing the flame to flicker.
As the wave passes through the air, air particles move back and forth (or vibrate) about their initial positions.
The air particle transfers energy to the next particle but stays about its initial position.
Thus as the wave passes through the air, energy is transferred without the transferring of matter.
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The red dot represents a particle in the spring.
The wave propagates to the right and the spring particles vibrate up and down.
They are perpendicular or at right angles to each other-
A wave in which the direction of vibration of particles in the medium is perpendicular to the direction of propagation of the wave/ is called a transverse wave.
Examples of transverse waves are water waves, light waves and other electromagnetic waves.
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When the the hand vibrate the spring horizontally The wave propagates to the right and the spring particles vibrate back and forth.
The particle moves back and forth (or vibrates) parallel to the direction of propagation of the wave.
A wave in which the vibration of particles is parallel to the direction of propagation of the wave, is called a longitudinal wave.
A longitudinal wave cannot propagate through a vacuum. This type of wave needs a medium to travel- Sound waves are longitudinal
LESSON 2
General Wave Properties
By the end of this lesson/ you should be able to:
• State what is meant by a wavefront.
• State the direction of propagation of waves in relation to wavefronts.
• Define amplitude.
• Define period.
• Define frequency.
• Define wavelength.
• Define wave speed.
A wavefront is an imaginary line representing all parts of a wave where particles are vibrating in the same phase and have the same distance from the source.
The shape of the wavefront depends on the source. A point source will emit circular wavefronts while a long straight source will emit plane wavefronts.
The direction of propagation of waves is perpendicular to the wavefronts.
Look at the circular wavefronts. What can you say about the direction of propagation of the circular waves?
The direction of propagation of circular waves is radially outwards which is perpendicular to the wavefronts.
Amplitude, a: The maximum displacement from the equilibrium position. Unit: metre (m)
The amplitude, a is the distance from the equilibrium position, 0 to the maximum displacement X or Y.
The amplitude, a is the distance from the equilibrium position, 0 to the maximum displacement X or Y.
When the pendulum swings from A to B and back to A, the pendulum is said to have done one complete oscillation.
Period T: Time taken for one complete oscillation.
Unit : second (s)
The plasticine ball made 10 complete oscillations in 5 seconds.
The ball made 2 oscillations in one second.
Frequency,: The number of complete oscillations made in one second.
Unit: Hertz (Hz) or per second (s1)
What is the frequency of the swinging plasticine ball?
Frequency,= number of complete oscillations
time taken
= 10
5
= 2 Hz
Period is the time required to complete one oscillation,
Period. T = time taken_______________
number of complete oscillations
= 5
10
= 0.5s
Relation between period and frequency
Period, T = time taken____________
number of complete oscillations
Frequency, f = number of complete oscillations
time taken
Frequency is the reciprocal of period, f = 1
T
Wavelength, λ: The distance between two consecutives points which are in phase
Sl unit: metres (m)
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For a transverse wave, the wavelength, λ, can be measured from one crest of the wave to the next crest. The wavelength can also be the distance from one trough to the next trough.
For a longitudinal wave, the wavelength, λ is the distance between two consecutive compressions or rarefactions.
The speed of a wave is the distance travelled by a wave per unit of time.
Speed, v: Distance travelled by a wave per unit time.
Sl unit: metre per second (m s -1)
LESSON 3
Displacement-Time Graph and Displacement-Distance Graph for a Wave
By the end of this lesson, you should be able to:
• Sketch and interpret a displacement-time graph for a wave.
• Sketch and interpret a displacement-distance graph for a wave.
Particle displacement: Horizontal
Vibration of particle is parallel to direction of propagation of wave.
Type of wave: Longitudinal wave
Particle displacement: Vertical
Vibration of particle is perpendicular to the direction of propagation of wave.
Type of wave: Transverse wave
Wave motion can be represented by
(i) displacement-time graph, and
(ii) displacement-distance graph.
The motion of on oscillating spring can be plotted on a displacement against time graph. This results in a sinusoidal graph as shown.
O is called the equilibrium position.
Amplitude, a: The maximum displacement of a particle of a medium from its equilibrium position.
Unit: centimetre (cm) or metre (m)
Period, T, The time for one complete oscillation of a wave, measured between two consecutive points on the graph which are in phase
Unit: seconds (s)
Frequency, f, is the reciprocal of T. of a wave.
f = 1
T
Unit: Hertz (Hz) or s-1
Amplitude, a: The maximum displacement of a particle in a medium from its equilibrium position.
Unit: centimetre (cm) or metre (m)
Wavelength, λ The distance between two consecutive points which are in phase.
Unit: centimetre (cm) or metre (m)
LESSON 4
The Relationship between Speed, Wavelength and Frequency
By the end of this lesson, you should be able to:
• Clarify the relationship between speed, wavelength and frequency. v=fλ
• Solve problems involving speed, wavelength and frequency.
From the displacement against distance graph the distance travelled by the wave, the amplitude, a, of the wave and its wavelength, λ can be determined.
From the displacement against time graph/ the time travelled by the wave and its period T can be determined.
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Speed = distance
time
For one complete oscillation, the distance travelled is the wavelength of the wave. The time taken to travel such distance is period. So,
Speed = wavelength
period
Since period = ___1___ , therefore speed = frequency x wavelength v = fλ
frequency
Measure the wavelength and calculate the speed of the wave.
The frequency of the wave is the same as the frequency of the vibrator which is 50 Hz or 50 s-1
The wavelength, λ, is 2.0 cm or 0.02 m.
Since v = f λ
= 50 s-1 x 0.02 m
= 1.0 ms-1
If the speed of the wave is constant, what happens when the frequency of the wave is increased?
At constant speed, when the frequency increases, the wavelength will decrease.
As sound waves propagate in an open ended tube with constant speed, when the frequency decreases, the wavelength will increase.
Lesson 4
Damping and Resonance in an Oscillating System
By the end of this lesson, you should be able to:
• Describe damping in an oscillating system.
• Describe resonance in an oscillating system.
Motion of the pendulum.
At the start, the pendulum oscillates with maximum amplitude.
The amplitude of the oscillation decreases with time and finally stops.
Air friction causes the amplitude of the pendulum to decrease,
When the pendulum oscillates, it has energy. This energy is used to overcome air friction.
As time passes more energy of the pendulum is being used to overcome air friction. This causes the energy of the pendulum to decrease.
As a result, the amplitude becomes smaller. The pendulum is said to experience damping.
Two identical tuning forks are used for this experiment. Both have the same natural frequency. Only the first tuning fork is made to vibrate.
As the first fork begins to vibrate, the surrounding air molecules will begin to vibrate with the same frequency.
Energy is transferred to the second fork causing it to vibrate at its natural frequency.
When this happens the second tuning fork is said to resonate with the first tuning fork.
When resonance occurs, the tuning fork vibrates at maximum amplitude and produces the loudest sound.
The Barton's Pendulum consists of a metal bob acting as the driver pendulum and a number of paper cones.
When the driver pendulum starts oscillating, the paper cone pendulums begin to oscillate.
Energy from the driver pendulum is transferred to the paper cone pendulums causing them to oscillate.
The paper cone pendulums are oscillating at different amplitudes.
Pendulum 3 has the biggest amplitude. Pendulum 3 has the same length and natural frequency as the driver pendulum.
Pendulum 3 is said to be in resonance with the driver pendulum.
Pendulum 3 receives the most energy and thus oscillates at maximum amplitude.
Musical instruments such as the guitar are set into vibration at their natural frequency when a person plucks the guitar string.
The guitar string is attached to the sound box of the guitar. The vibrating string forces air particles inside the box to vibrate at the same natural frequency as the string.
The sound box resonates with the string and sets more air particles to vibrate
thus producing louder sound.
LESSON 6
Reflection of Waves
By the end of this lesson, you should be able to:
• Describe the reflection of waves in terms of the angle of incidence, angle of
reflection, wavelength, frequency, speed and direction of propagation.
• Draw a diagram to show reflection of waves.
A ripple tank is a shallow glass tank of water used to study the properties of water waves namely reflection, refraction, interference and diffraction,
The ripple tank is usually illuminated from above/ so that the light shines through the water. The ripples on the water show up as dark and bright regions on the screen underneath the tank.
Plane waves are produced. A pattern of bright and dark lines is observed on the screen below the ripple tank.
Circular waves are produced, A circular pattern of bright and dark regions is observed on the screen below the ripple tank.
The dark and bright patterns are formed when rays of light pass through the troughs and crests of the water waves respectively.
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Upon reaching the barrier, the waves are reflected and head in a different direction. Observe the direction of the reflected wave.
The waves will reflect at an angle such that the angle of incidence equals the angle of reflection. This is known as the Law of Reflection.
The reflected waves do not change in wavelength even though the direction changes.
v =f
When the frequency and wavelength are kept constant, the speed also remains constant.
At what position of cylinder B is the ticking of the stop clock the loudest?
Rotate cylinder B to find that position.
The position of cylinder B is at the same angle to the normal as cylinder A. The angle of incidence, i, is equal to the angle of reflection, r. This Is known as the Law of Reflection.
Plane waves are moving towards a barrier at an angle. Determine the direction of the reflected waves. You can do so by following these steps.
1. Draw a straight line to represent the direction of propagation of the incident wave- Make sure the line is perpendicular to the wavefronts
2. Draw the normal, at the point where the line you drew earlier touches the barrier. The normal must be perpendicular to the barrier. Measure the angle of incidence.
3. Draw a line representing the reflected waves from the same point such that the angle of incident r, is equal to the angle of reflection, /.
4. Draw the wavefronts perpendicular to this line.Make sure that the wavelengths of the incident and reflected waves are the same.
LESSON 7
Refraction of Waves
By the end of this lesson, you should be able to:
• Describe refraction of waves in terms of the angle of incidence, angle of refraction, wavelength, frequency, speed and direction of propagation.
• Draw a diagram to show refraction of waves.
In deep sea regions, the water waves take the shape of plane waves This is because the depths of the water are almost the same.
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As the waves approach the shore, they bend according to the shape of the shoreline.
When waves propagate from the deep to the shallow regions, the wavelength decreases.
As the waves are continuously produced by the same source, the frequency of the waves remains constant.
v =fλ; since f is constant and λ decreases thus v decreases.
The speed of the waves depends on the depth of water.
The ripples slow down as they pass through shallow water regions. This causes the wavelength to decrease.
As the waves propagate from the shallow to the deep water regions, the wavelength increases.
As waves propagate at an angle to water of different depths, there is a change in direction of the waves.
The change in direction is due to the change in the speed of the waves.
This phenomenon is called refraction.
What happens to the light waves as they enter the water?
The light waves bend as they enter the water. As light waves propagate from one medium to another, the waves are refracted.
As light waves move through mediums of different optical densities, the speed of the waves changes. This will result in a different wave direction.
The speed of sound waves is faster in warm air than in cool air- This is because warm air is less dense than cool air.
During the day, the layers of air near the surface of the earth are warmer. This causes sound waves to be refracted away from the earth.
During the nighf the layers of air near the earth is cooler- This causes sound waves to be refracted towards the earth.
Determine the direction of the refracted waves
1. Draw a boundary line to separate deep and shallow regions. Label the regions.
2. Draw a line to represent the direction of propagation of incident waves. Mark with an arrow. Label 0 at the point where this line meets the boundary.
3. Draw the normal at point 0.
4. From point 0, draw a line to represent the direction of propagation of refracted waves. Mark with an arrow. When waves propagate from deep to shallow regions, the refracted waves bend towards the normal.
5. Draw the normal at point P.
6. From point P, draw a line to represent the direction of propagation of refracted waves. When waves propagate from the shallow to the deep regions, the refracted wave bends away from the normal. Mark with an arrow.
7. Draw parallel lines which are perpendicular to the direction of propagation of incident and refracted waves- These lines represent the wavefronts.
8. Make sure that the wavelength in the deep regions is bigger than the wavelength in the shallow regions
9. Label the incident angle, i and refracted angle, r. The angles are measured from the normal to the incident and retracted waves.
LESSON 9
Diffraction of Waves
By the end of this lesson, you should be able to:
• Describe diffraction of waves in terms of wavelength, frequency, speed, direction of propagation and shape of waves.
• Draw a diagram to show diffraction of waves
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Describe the pattern of the waves after passing through the gaps of different sizes.
When the gap size is approximately equal to the wavelength the wave pattern after passing through the gap is circular.
When the gap size is bigger than the wavelength, the wave pattern after passing through the gap is less circular.
The wavefronts are bent at the edge of the gap. Wavefronts far from the edges of the gap will pass through without bending.
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The wavelengths remain the same.
What can you say about the direction of the waves after passing through the gap?
The waves bend and change direction near the edges of the gap. This is called diffraction.
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What happens if the length of the barrier is larger than the wavelength?
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The waves bend around the edges and fill up the space behind the barrier. A shadow area is formed behind the barrier.
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When the size of the barrier is smaller or approximately the size of the wavelength, the diffraction pattern of the waves is more obvious.
When the size of the barrier is larger, the shadow area is larger. The diffraction pattern of the waves is less obvious,
Have you noticed that you can hear the sounds of the radio from another room?
Sound waves can be diffracted around corners and through doorways.
Sound has a much longer wavelength than light. So sound can be diffracted easily around buildings or through doorways.
This is why you can often hear people although you cannot see them,
Sound waves are diffracted as they leave their source, for example the radio. When the sound waves meet walls and doorways/ they bend around these barriers.
A laser source, a single narrow slit and a screen is set up to observe the single slit diffraction pattern. What happens to the light as it passes through the single slit?
A diffraction pattern is formed on the screen. Bright and dark lines or fringes are seen on the screen.
When the light passes through the pinhole, a circular bright and dark fringes are seen on the screen. This pattern shows diffraction of light around the edge of the pinhole
The demonstrations show that light can be diffracted. However, the diffraction pattern is not easily seen. This is because the wavelength of light is much smaller compared to the size of the pinhole.
LESSON 9
Interference of Waves
By the end of this lesson, you should be able to
• State the principle of superposition,
• Explain the interference of waves.
• Draw interference patterns.
• Interpret interference patterns.
What happens when two pulses travel simultaneously in opposite directions along the same slinky?
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When two pulses meet, they overlap then continue to move In their original directions.
When the pulses overlap, the displacement of the spring or the resultant amplitude is the vector sum of the individual amplitudes of each pulse.
The combination of two or more waves to form a resultant wave is referred to as superposition.
The principle of superposition states that when two or more waves combine at a point the resultant amplitude is the sum of the amplitudes of the individual waves.
LESSON 10
Interference Patterns
By the end of this lesson, you should be able to:
• Solve problems involving the formula X = ax
λ
To produce a clear interference pattern, the two waves must be in phase with each other, that is, the crest of one wave must be produced at the same time as the crest of the second wave.
The sources that vibrate with the same frequency and in phase with each other are called coherent sources. These kinds of sources produce a clear interference pattern.
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The points where constructive interference occur are called antinodes. The imaginary lines that connect the antinodes are called the antinodal lines.
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The points where destructive interference occur are called nodes. The lines that connect the nodes are called the nodal lines.
a: the separation between the two coherent sources
x : the distance between a nodal line to the next nodal line, or between an antinodal line to the next antinodal line
D: the distance between the source and the pos
