Chapter 1 - Wave (form 5)

1.Equilibrium Position

An equilibrium position is a point where an oscillating object experiences 0 resultant forces. Top

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Complete Oscillation

A complete oscillation occurs when the vibrating object moves to and fro from its original position and moves in the same direction as its original motion.

Amplitude

Amplitude is the maximum displacement of an object from its equilibrium position. The SI unit for amplitude is meter, m.

Period Period is defined as the time required for one complete oscillation or vibration.

Frequency Frequency, f is the number of complete oscillations that take place in one second. The SI unit for frequency is hertz, Hz. Important Formula:

Displacement - Time Graph

From a Displacement - Time graph, we can find: 1. the amplitude 2. the period 3. the frequency of an oscillation

Natural Frequency The Natural frequency of an oscillating system is the frequency of the system when there is no external force acting on it.

Damping • • •

Damping is the decrease in the amplitude of an oscillating system. An oscillating system experiences damping when its energy is losing to the surrounding as heat energy. The frequency of the system remains unchanged.

Graph of Damping The Displacement - Time Graph

The Amplitude - Time Graph

Internal and External Damping Damping can be divided into: • •

external damping, where an oscillating system loses energy to overcome frictional force or air resistance that act on it. internal damping, where an oscillating system loses energy due to the extension and compression of the molecules in the system

Force Oscillation In a damped oscillation, external force must be applied to the system to enable the oscillation to go on continuously. Oscillation with the help of external force or forces is called a force oscillation.

Resonance In a force oscillation, if the frequency of the external force is equal to the natural frequency of the system, the system will oscillates with maximum amplitude, and this is named as resonance.

Barton's Pendulum

When pendulum X oscillates, the other pendulums are forced to oscillate. Pendulum D will oscillates with the largest amplitude. Pendulum X and D have equal length and consequently equal natural frequency. Therefore resonance happens to pendulum D, and it oscillates with maximum amplitude.

Wave • •

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A wave is a disturbance or variation that propagates through a medium, often transferring energy. Waves travel and transfer energy (its amplitude) and information (its frequency) from one point to another, with no permanent displacement of the particles of the medium. The particles of the medium are oscillate around an almost fixed positions.

What is phase? • •

A phase is the current position in the cycle of something that changes cyclically. Two vibrating particles are in the same phase if their displacement and direction of motion are the same.

Wavefront

A wavefront is a line or a surface that connects points that are moving at the same phase and has the same distance from the source of the waves.

Wavefront is always perpendicular to the direction of wave propagation.

Wavelength

The wavelength (l) is defined as the distance between two successive particles which are at the same phase (exactly the same point in their paths and are moving in the same direction.). As shown in the diagram, A and B are in the same phase, therefore the distance between A and B is the wave length of the wave.

Types of wave - Transverse Wave

A transverse wave is a wave where the particles of the medium vibrate in a direction that is perpendicular to the direction of the wave motion. Example: Light wave, ripple, radio wave

Types of Wave - Longitudinal Wave

A longitudinal wave is a wave where the particles of the medium vibrate in a direction that is parallel to the direction of the wave motion. Example: Sound Wave

Formula for velocity of wave

Reflection of Straight And Circular Wave

From Deep to Shallower Region When plane waves move from deep to shallow water, their wavelength become shorter and the velocity decreases. The frequency of the wave remain unchanged. This can be illustrated by placing a piece of rectangular Perspex of suitable thickness in the tank to reduce the local water depth.

Refraction of Water Wave The change in wavelength and speed causes a change the waves direction when they cross the boundary. In other words, refraction occurs.

Refraction - Deeper to Shallower Region

When water waves are propagating from deeper region to a shallower region, the wave will be refracted approaching the normal.

Refraction - Shallower to Deeper Region

When water waves are propagating from shallower region to a deeper region, the wave will be refracted away from the normal.

Some Other Pattern of Refraction

Natural Phenomenon Involves Refraction The effect of refraction causes seaside near to a cape is stony while sea near to a bay is sandy.

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At the middle of the sea, the wavefront is a linear line. When waves move close to the coast line, the wavefronts start to curve and follow the topography of the coast line.

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At the bay, the energy of the wave spread to a wider area, and cause the amplitude to reduce. At the cape, the energy of the wave is converged to a smaller area, therefore the amplitude of the wave increases.

Diffraction Diffraction is the spreading of a wave when it travels through an opening or a small obstacle.

Characteristic of Diffraction 1. 2. 3. 4.

Wavelength does not change. Frequency does not change. Speed of diffracted does not change. The amplitude of the wave decreases after diffraction.

Diffraction happen when waves encounter an obstacle

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Waves spread to a wider area after passing the obstacle. The wavelength and the frequency remain unchanged after diffraction.

Diffraction happen when waves pass through an opening

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Waves spread to a wider area after passing through the opening. The wavelength and the frequency remain unchanged after diffraction.

Factors Affecting the Magnitude of Diffraction Wavelength

Shorter wavelength - Diffracted less

Longer wavelength - Diffracted more

In the diagram above, we can see that as the wavelength of a wave is longer, it will be diffracted more compare with a wave with shorter wavelength.

Factors Affecting the Magnitude of Diffraction - Size of Opening

Small opening - Diffracted more

Bigger opening - Diffracted less

Diagram above shows that the magnitude of diffration will reduce when the size of opening increases.

Principle of Superposition The principle of superposition states that where two or more waves meet, the total displacement at any point is the vector sum of the displacements that each individual wave would cause at that point.

Coherent Wave Two wave sources which are coherent have the same frequency (therefore same wavelength) and in phase or constant phase difference.

Interference The effect of superposition of two coherent waves is interference. Interference is the phenomenon when two or more waves overlap in the same region of space at the same time.

Constructive interference

Superposition of waves which have same phase (2 crest or 2 trough) to produce a resultant wave which vibrates with maximum amplitude.

Destructive Interference

Superposition of waves which are anti-phase (crest and trough) to produce a resultant wave which vibrates with minimum amplitude.

Node and Antinode

An anti-node is a point of maximum amplitude where constructive interference occurs. Whereas a node is point of zero amplitude where destructive interference occurs. The anti-node line joins all anti-node points. The node line joins all node points.

Interference's Formula

Sound Wave • • •

Sound wave is a mechanical wave that requires a medium for its propagation. Therefore sound wave cannot propagate in vacuum. The medium for propagation can be solid, liquid or gas. Sound waves propagate fastest in solid and slowest in gas.

Sound Wave as a Longitudinal Wave

Sound wave is a series of compression and rarefaction of layers of air molecules repeatedly through space. The forward and backward vibration of the air molecules in the direction of motion of a sound wave shows that sound is a longitudinal wave.

Types of Sound Wave •

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Human ear is capable of hearing sound with frequency in the range of 20Hz – 20,000Hz, and the sound wave with frequency in this range is called an audio/Sonic wave. Sound wave with frequency lower than 20Hz is called an Infrasonic Wave. Sound wave with frequency higher than 20,000Hz is called an Ultrasonic wave.

Infrasonic

Audio/Sonic

Ultrasonic

<20Hz

20Hz – 20000Hz

>20 kHz

Speed of Sound Wave • • • •

Speed of sound wave in solids is greater than in liquids, which is greater than in gases. Speed of sound in air is not affected by pressure, but is affected by the temperature. As temperature increases, speed of sound in air (and other gases) is also increases. Sound usually travels more slowly with greater altitude, due to reduced temperature.Speed of sound can be calculated by the equation

Pitch and Loudness

Loudness is influenced by the amplitude of the sound wave.The greater the amplitude of sound wave, the higher the loudness of the wave. The pitch of a sound is high or low of the sound. The pitch of sound is determined by its frequency. The higher the frequency, the higher the pitch.

Reflection of Sound Wave

The clicking sound of the stop watch can be heared clearly when the angle of incidence, i is equal to the angle of reflection, r. Sound waves obey the law of reflection. That is, the angle of incidence is equal to the angle of reflection.

Refraction of Sound Wave 1

The amplitude of the sound wave increases when a balloon filled with carbon dioxide is placed between the speaker and the microphone.

Explanation: • •

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Carbon dioxide is denser than air. The sound wave is refracted approaching the normal when the wave propagates from the air into the balloon, and away from normal when moving out from the balloon. As a result, the balloon acts as a biconvex lens and converge the sound wave at a point.

Refraction of Sound Wave 2

The amplitude of the sound wave decreases when a balloon filled with helium gas is placed between the speaker and the microphone.

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Helium gas is less dense than air. The sound wave is refracted away from the normal when the wave propagates from the air into the balloon, and closer to the normal when moving out from the balloon. As a result, the wave is diverged to a wider area and causes the amplitude of the sound wave decreases.

Refraction - Natural Phenomenon

The sound of a distance train is clearer at night. Explanation: At night, the air closer to the ground is cooler than the air further from the ground. Sound wave travel slower in cool air. As a result, the sound wave is refracted in the path of curve towards the ground instead of spreading to a wider area (as at daytime).

Diffraction of Sound Wave

The street cleaner can hear the sound of the radio even though it is behind an obstacle. Explanation: The sound of the radio spreads around the corner of the wall due to diffraction of sound wave.

Interference of Sound Wave

Alternating loud and soft sounds are detected as the microphone is moved from left to right. Explanation: The two loud speakers are sources of two coherent sound waves as they are connected to the same audio signal generator. The alternating loud and soft sounds are caused by interference of the sound wave.

Formula of Interference Wavelength of the sound wave is given by the equation

Properties of Electromagnetic Waves • • •

Electromagnetic wave can travel in free space. They travel in straight lines at a speed of approximately 300000 km/s. They are electric, magnetic and transverse in nature.

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Electromagnetic waves are electrically neutral. Electromagnetic wave show characteristic of polarization.

Polarisation of Transverse Wave

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A transverse wave can be polarized. Plane polarized light will be produced when light travels through a polarizing material like polaroid. Polaroid is a type of material that only allows light waves of one plane to pass through. This means that only a portion of the source light gets to pass through the polaroid.

Radio Wave Source Electrical oscillating circuit (consists of a capacitor and an conductor connected in series) Application • • • •

Telecommunications Broadcasting: Radio and television transmission Astronomy study

Microwave Source Oscillating electrical charge in a microwave transmitter

Application • • •

Satellite transmissions Radar systems to detect objects (size, form and position) Cooking

Infrared Radiation Source Hot bodies, the sun and fires Application • • • • • •

Night vision Thermal imaging and physiotherapy Remote controls for TV/VCR Heating in physiotherapy Thermometer Cooking

Visible Light Source The sun, hot objects, fires, light bulbs, fluorescent tubes Application • • •

Sight Photosynthesis in plants Photography

Ultraviolet Light Source Very hot objects, the sun, mercury vapour lamps Application • • • • • •

Identification of counterfeit notes Production of fluorescent effects Production of vitamin D in the skin Sterilisation to destroy germs Pest control Disinfecting drinking water

X-Ray Source X-ray tubes where high energy electrons bombarding a metal plate. Application • • • •

Radiotherapy Radiography (X-ray photograph) Detection of cracks in building structures Crystallography

Gamma Ray Source Radioactive substances Application • • •

Cancer treatment Sterilisation of equipment Pest control in agriculture

Reflection of Light Wave The characteristic of reflection of light enables us to see objects. Objects that do not emit light are not seen in the dark. An object only is seen if light is incident on it a reflected back to our eyes

Refraction of Light Wave When light travels one medium to another of differing density, its speed changes. Speed of light is higher in a medium of less density as compare with one higher density. The change in velocity of light when it travels from one media to another of different density results in the refraction phenomenon.

Diffraction of Light Wave -Single slit experiment

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Light is diffracted if it passes through a narrow slit. Diffraction pattern is made up of the bright bands and dark bands of different width. The central band is wider and brighter. The dark and bright bands of narrower width are alternatively observed on the left and right side of the central bight band.

Conditions for diffraction to take place are: Light source must be monochromatic. That is, the light must possess only one wavelength. Slit size must be small enough as compare with the wavelength of light.

Factors affecting the pattern of diffraction Size of the slit - Smaller size, diffracted more Colour of the light - Longer wavelength, diffracted more Distance of the screen from the slit

Young's Double Slit Experiment

Young's double-slit is made up of two slits ruled on a piece of slide and painted with 'aquadak'. •

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When monochromatic light passes through the Young's double-slit, diffraction of light occurs and two coherent sources (same amplitude, frequency and phase) are produced as shown in the diagram above The two coherent sources will overlap and superpose to produce the effects of constructive and destructive interference. Constructive interference generates bright fringes while destructive interference produces dark fringes. Fringe size of bright fringes and dark fringes are about similar in size. Fringe separation between any dark fringe and a neighboring bright fringe which alternates in position with the former is the same.