Applying Archimedes' Principle

Steel is denser than water. However they still float, why?

Have you ever wondered why hot air balloon floats in the air? Even though the mass of the balloon is big?

Archimedes (287-212 B.C.) was a greek scientist who first discovered that

"an object submerged in a liquid is acted on by an upward buoyant force (or upthrust)."

The buoyant force is due to the surrounding liquid which causes the object to weigh less in the liquid. Archimedes realised that submerged objects always displace liquid upwards, (when you put an ice to a glass of water, the water level rise). Later he did show that the upthrust is equal to the weight of water displaced.

Archimedes' principle states that an object, whether completely or partially immersed in a fluid, is acted on by a buoyant force, which is equal to the weight of the fluid displaced.

Applications of Pascal's Principle in Everyday Life

A hydraulic system is a device in which a small applied force can give rise to a larger force.

The principle in the hydraulic system is widely used in jacks, vehicle brake systems, hydraulic presses and heavy machinery and a few more examples which you can find (for yourself)

Hyraulic Jacks

Hydraulic jacks are used to lift a heavy load such as when changing a car tyre. When the handle is pressed down, a valve closes and the small piston forces hydraulic fluid through another valve to the larger cylinder. The pressure transmitted results in a large force on the load.



When the handle is raised, valve B closes and hydraulic fluid flows from the buffer tank through valve A into the small cylinder. The handle is moved up and down repeatedly until the load is sufficiently lifted up.

The large piston can be lowered at the end by opening the release valve to allow all the hydraulic fluid to flow back into the buffer tank.

Hydraulic Brakes

Hydraulic brakes are used in cars, lorries and motorcycles.

In a hydraulic brake system, a liquid, known as brake fluid,
is used to transmit pressure from the brake pedal to all the wheels of the vehicle.


When the brake pedal is pressed, the piston of the control cylinder applies a pressure on the brake fluid and this pressure is transmitted, via a system of pipes, to each cylinder at the wheels.

The cylinder at the wheels cause a pair of pistons to push a pair of friction pads to press against the surface of the brake discs or brake drums. The frictional forces between these brake components cause the vehicle to slow down and stop.

When the brake pedal is released, a spring restores the brake discs to their original positions.

Hydraulic Pumps

Hydraulic pumps are used to raise cars in a motor workshop.

The machine is equipped with a small cylinder connected to a large cylinder. Both cylinders are filled with oil.

Compressed air is introduced into the small cylinder in which the compressed air exerts a pressure on the surface of the oil.

This pressure is transmitted by the oil to the large cylinder where the pressure acts on a large piston to produce a force which is large enough to lift a car.

Hope this helps!

Basic Hydraulic System

A hydraulic system operates based on Pascal's principle.

In this hydraulic system, a small force, F1 is applied to the small piston resulting in a large force , F2 at the piston K. The pressure, due to the force, F1, is transmitted by the liquid to the large piston.

Pressure, P = F1/A1

This pressure is transmitted through the liquid and acts on the base of the large piston.

Force on the large piston, F2 = P X A2.
= (F1/A1) X A2.

The large force causes the load to rise.

Also F2/F1 = A2/A1

Output force / input force = output piston area / input piston area

Because of the much larger surface area, A2 of the piston K compared to the surface area, A1 of the piston, the resultant force, F1.


This shows that a large force can be produced by a small force, using Pascal's principle.

Hydraulic systems act as a force multiplier where A2/A1 is the multiplying factor.

For example, if A2=5A1, then F2 = 5F1

since F2 = F1 X (A2/A1)

A hydraulic system must not contain any air bubbles in any portion of its hydraulic fluid system.

The presence of air bubbles in the hydraulic fluid system will reduce the efficiency of the system as part of the applied force will be used to compress the air bubbles.

Analysing Pascal's Principle: Transmission of pressure in liquid

Liquid pressure can be used to transfer energy from one place to another. Have you ever wondered how this idea is being adopted in some of the machines such as hydraulic garage lift, hydraulic car jacks and excavator?

Transmission of Pressure in a Liquid
1. The molecules in a liquid are quite close and in contact with each other. As a result, liquids are practically incompressible.

2. When a piston is pushed in by a force, F, a pressure is applied to the water.

Pressure, P = F /A , A = cross sectional of the piston.

3. The applied pressure is transmitted uniformly throughout the water in accordance with Pascal's principle.

4. Pascal's principle states that pressure exerted on an enclosed liquid is transmitted equally throughout the liquid.

5. Pascal's principle is also known as the principle of the transmission of pressure in a liquid.

6. Pascal's principle is important for the understanding of hydraulics, the study of transfer of forces through liquids.

Instruments for measuring atmospheric pressure

Instruments for measuring atmospheric pressure:

1. Mercury Barometer

A mercury barometer consists of a thick-walled glass tube, which is closed at one end.

The tube is completely filled with mercury and inverted several times to remove air bubbles. The tube is then completely filled again with mercury.

After all air has been removed, the open end of the glass tube is inverted into a container of mercury.

The mercury column drops until it reaches a height about 76 cm above the lower surface. The space between the top of the mercury and the end of the tube should contain no air; it is a complete vacuum.

The column of mercury in the tube is supported by the atmospheric pressure and its height depends on the magnitude of the atmospheric pressure

2. Fortin Barometer

A fortin barometer is a type of mercury barometer which has a higher accuracy.

This barometer has a vernier scale which gives a more accurate reading of the atmospheric pressure. The mercury level in the container can be adjusted by a screw until the pointer touches the surface of the mercury. This eliminates the zero error.

The atmospheric pressure is measured in mm Hg.


3. Aneroid Barometer
An aneroid barometer does not use any liquid. It consists of a sealed metal chamber in the form of a flat cylinder with flexible walls. The chamber is partially evacuated and a spring helps prevent it from collapsing.

The chamber expands and contracts in response to changes in atmospheric pressure. The movement of the chamber walls is transmitted by a mechanical lever system which moves a pointer over a calibrated scale.

The Aneroid Barometer can be used a an altimeter (to determine altitude) by mountaineers or pilots to determine an airplane's altitude. The scale can be calibrated to give readings of altitude equivalent to a range of values of atmospheric pressure.

- an aneroid barometer is also used as a weather glass to forecast the weather.
Rain clouds form in large areas of lower pressure air, so a fall in the barometer reading often means that bad weather is coming.

Instruments for measuring Gas Pressure

There are several instruments for measuring gas pressure, I will explain only two here

1. Manometer

A manometer consists of a U-tube filled with a liquid (mercury, water or oil) with a certain density.

The manometer is used to measure the difference in pressure between the two sides of the U-tube.

When the manometer is not connected to the gas supply, i.e. when both arms are open to the atmosphere, the liquid levels in both arms are equal.

To measure the pressure of a gas, the other arm is connected to the gas pipe and the gas pressure acts on the surface of the liquid in the respective arm.

if the gas pressure is greater than the atmospheric pressure, the liquid in the respective arm (say arm B) will be pushed downwards. Under equilibrium conditions, (same pressure from both arms), the level of the liquid will be at the same level.

2. Bourdon Gauge
A Bordon gauge consists of a coil of flattened copper tube with an oval cross section connected to a lever system.

When the gas supply is connected, the pressure in the gas acts to straighten the copper coil.

The movement of the copper coil is transferred to the lever system which actuates a pointer to move across a scale which has been calibrated to give readings of pressure.

The unit of measurement used in the Bourdon gauge is Pascal. Bourdon gauges are normally connected to gas cylinders to give an indication of the quantity of gas in the cylinders.

Bourdon gauges are more robust than manometers and more suitable for measuring higher pressures. But they have to be calibrated before they can be used.

Atmospheric pressure and altitude

Atmospheric pressure and altitude

1. Atmospheric pressure decreases with altitude, or the height above of sea level. At higher altitudes, the density and temperature of the air are lower. As a result, the frequency of collisions of the molecules is decreased (lower). Hence, atmospheric pressure is lower.



Total pressure below the surface of a liquid.

1. The formula for liquid pressure, P = hpg, is used to determine the additional pressure due to the weightmof the liquid at any point below the liquid's surface.

2. As a result, the total pressure acting at a depth, h below the liquid's surface is the sum of the pressure due to the weight of the liquid (P) and the atmospheric pressure acting on the liquid's surface.

Total pressure acting on an object below a water with a depth of h = atmospheric pressure + hpg.

Application of Atmospheric pressure

Applications of atmospheric pressure:

Drinking Straw

1. When drinking with a straw, one has to suck the straw. This causes the pressure in hte straw to decrease.

2. The external atmospheric pressure, which is greater, will then act on the surface of the water in the glass, causing it to rise through the straw.


Rubber Sucker

1. When the rubber sucker is put onto a smooth surface, usually a glass or tiled surface, the air in the rubber sucker is forced out. This causes the space between the surface and the sucker to have low pressure.

2. The contact between the rubber sucker and the smooth surface is airtight.

3. The external atmospheric pressure, which is much higher, acts on the rubber sucker, pressing it securely against the wall.

Siphon

1. A rubber tube can be used to siphon liquid from a container at a higher level to another at a lower level. For example, we can remove petrol from the petrol tank of a vehicle or dirty water from aquarium.

2. The tube is first filled with the liquid and one end is placed in the liquid in the container A. The other end is placed at a level which must be lower than the surface of the liquid in container A.

3. The pressure in the rubber at the lower end is equal to atmospheric pressure plus the pressure due to h cm column of liquid. As the pressure at the lower end is greater than the atmospheric pressure, the liquid flows out.

Vacuum Cleaner

1. vacuum cleaner applies the principle of atmospheric pressure to remove dust particles. When it is switched on, the fan sucks out the air from space inside the vacuum (space A). Space A then becomes a partial vacuum.

2. The atmospheric pressure outside, which is greater, then forces air and dust particles into the filter bag. This traps the dust particles but allows the air to flow through an exit ath the back.

Lift Pump

1. A lift pump is used to pump water out of a well or to a higher level. The greatest height to which the water can be pumped is 10 m. This is equivalent to the atmospheric pressure.

2. When the plunger is lifted, the upper valve closes and the lower valve opens. The atmospheric pressure, acting on the surface of the water, causes water to flow past valve B into the cylinder.

3. When the plunger is pushed down, the lower valve closes and the upper valve opens. Water flows above the plunger.

4. When the plunger is next lifted, the upper valve closes again and the lower valve opens once more. the atmospheric pressure, acting on the surface of the water, forces water past the lower valve into the cylinder. Simultaneously, the water above the plunger is lifted and flows out through the spout.

5. This process is repeated until sufficient water is obtained.

Understanding Gas pressure and Atmospheric pressure

1. Existence of Gas pressure:

Imagine when someone throws a stone to you. It feels painful isn't it. Imagine all of your classmates throw stones at you, will you feel less or more painful? That's the same thing with gas. Gas molecules moving at a high speed in a large number will cause greater pressure on a wall or surface (but considerably less than that of the stones perhaps??)

2. Kinetic Theory of gases

The kinetic theory of gases is based on the following assumptions:

The molecules in a gas move freely in random motions and possess kinetic energy.
The forces of attraction between the molecules are negligible
The collisions of the molecules with each other and with the walls of the container are of elastic collisions.

The molecules of a gas in a container move in all directions to fill the entire space of the container
until they collide with its walls.

The collisions of the gas molecules with the walls of the container are elastic collisions and the molecules rebound with the same speed which results in a change in momentum for each molecule.

The total change of momentum when the gas molecules collide with the walls of the container in one second produces a force which acts on the walls of the container.

By the definition of Pressure = Force / Area (P = F/A)


3. Factors Affecting Air or Gas Pressure

a. Pressure increases when the density of gas increases.
b. Pressure increases when temperature increases due to kinetic energy of molecules increases.

Atmospheric Pressure

1. Existence of Atmospheric pressure

.According to the kinetic theory of gases, gases consist of molecules which are far apart and in random motion at high speeds.

The gas molecules have mass and experience the gravitational pull. The result is that gases
have weight.

The atmosphere is a thick layer of air that surrounds the Earth. You may probably have known this.

The atmosphere exerts a pressure called atmospheric pressure which is caused by the weight of the thick layer of air above the Earth's surface.

Atmospheric pressure acts on every object on the surface of the earth. No one is in exception.

Activity to show the existence of Atmospheric Pressure

Fill a glass with water to the brim. Cover it with a thick cardboard. Invert it downwards. The water does not fall down. Why? because atmospheric pressure supports the cardboard (and water) from falling. The resultant force on the cardboard is greater than the weight of water. Even in the existence of gravity!

Boil an empty tin half-filled with water. Cap the tin. Let it cool under running tap water. Wallaa....the tin will get crumpled as the water cools down. As the steam condenses, the pressure
inside the metal tin decreases, The external atmospheric pressure which is Higher, crushes the tin.

Mercury Barometer

1. A mercury barometer consists of a thick-walled glass tube, which is closed at one end.

2. The tube is completely filled with mercury and inverted several times to remove air bubbles.
The tube is then completely filled again with mercury.

3. After all air has been removed, the open end of the glass tube is inverted into a container of mercury.

4. The mercury column drops until it reaches a height of about 76cm above the lower surface. The space between the top of the mercury and the end of the tube should contain no air; it must be in a complete vacuum.

5. The column of mercury in the tube is supported by the atmospheric pressure and its height depends on the magnitude of the atmospheric pressure.

6. Since the atmospheric pressure at sea level can support a vertical column of mercury 76 cm or 760 mm high, we can, for convenience, express mm Hg as a unit of pressure. 1 Standard atmospheric pressure (1 P atm) = 76 cm Hg or 760 mm Hg (also known as one atmosphere).

P atm = 76 cm Hg = 10 000 Pa.

1 P atm = 76 cm Hg = 10 000 Pa = 1 bar.

7.  In unit m water: P atm = 10 m water.

Understanding Pressure in Liquids

1. For a liquid at rest, the pressure at a certain point in the liquid is the same in all directions.

2. The pressure in a liquid is due to

a) Density of the liquid, p.
b) Depth of the liquid, h, below the surface liquid.
c) Acceleration of the gravity, g.


3. The pressure on a liquid is proportional to the density of the liquid, p and the depth, h, at which the liquid is measured.

4. The pressure in a liquid at rest (static liquid) is independent of the shape (area and slope) of the container.

5. The applications of pressure in liquids are:
i) Dams
ii) Domestic Water supplies

i) Dams

Dams are very much thicker at the bottom than at the top, since the pressure at the bottom is the greatest.

Large dams are built for the hydroelectric generation of electricity.

The high pressure on the deep-water side of the dam causes water to flow through these holes at great speed turning the turbines in the holes and generate the electricity.

ii) Domestic Water Supplies

The main water comes from a reservoir but in order to maintain a constant high pressure to the consumer, it is pumped to the top of a water tower located on high ground.

The main pressure is determined by the height, h.

Hope this helps!

Understanding Pressure

Pressure involves the concept of force and surface area.

1. Pressure on an area, A is the normal force, F, which is being applied perpendicularly to the area.

2. Pressure on an area, A is expressed as the normal force, F per unit area, A.

3. P = (F/A)

4. This SI unit for pressure is the pascal, Pa, where 1 Pa = 1 N/m2 (metre square).

5. Pressure is increased:

• if the force, F applied to a given area, A is increased
• if a given force, F is applied to a smaller area, A

6. If a balloon is pressed against by a finger, the balloon will only change its shape a bit.

If the balloon is pushed against by a needle with the same force, the balloon will burst.

This is because a finger has a larger surface area (A) than a needle. Hence, the needle exerts much pressure than the finger and perforates through the surface of the balloon, making a hole and freeing the air inside the balloon (or pops the balloon instead!)

Analysing Electromagnetic Waves

1. Electromagnetic waves consist of vibration of magnetic field and electric field which are perpendicular to each other.

2. Therefore, Electromagnetic waves are transverse waves.

3. The velocity of electromagnetic waves in vacuum is 3 X 10 (8)(to the power of eight) meter per second.

4. Differences in wavelength between electromagnetic waves producer a spectrum of electromagnetic waves.

Electromagnetic waves sorted starting from High Frequency to the Lowest Frequenct

Gamma rays

X-Rays

Ultraviolet

Visible Light

Infrared

Micro Waves

Radio Waves




Hope you all have an idea :)

Speed of Sound, Loudness and Amplitude of Sound

Speed of Sound

1. The speed of sound,v, in a medium can be defined as v = fλ, where λ is the wavelength and f is the frequency. The SI units of v is ms-1, f is Hz and λ is  m (metre).

2. The speed of sound in solid is greater than in liquid, and the speed of sound in liquid is greater than in gas.

3. The speed of sound is unaffected by pressure. As an example, iIf the atmospheric pressure changes, the speed of sound in air remains constant.

4. The speed of sound increases with temperature. At the peak of high mountains, the speed of sound is less than that at sea level. This is not due to the lower pressures but because of the lower temperatures at the peak of mountains.

Loudness and amplitude of sound

1. The loudness of sound is considered to be high or low according to the hearing ability of a person.

2. Loudness is influenced by the amplitude of the sound wave.

3. Amplitude has several definitions, according to http://cse.ssl.berkeley.edu/light/measure_amp.html. Amplitude is

• a measurement from the lowest point that the wave hits to the highest point the wave hits.
• a measurement of the top half of the wave.
• a measurement of the distance between two nearest peaks or two nearest troughs.
• a measurement of the bottom half of the wave.

Pitch and Frequency of Sound


1. The pitch of sound or a musical note is an indication of how high or how low the sound is. Is is a subjective judgement which varies with different individuals.

2. The pitch of a sound is determined by its frequency: a high pitch corresponds to a high frequency.

3. Frequency is how many oscillations a wave complete in a given period of time. Hence you can see that high frequency waves are thinner than low frequency waves because more oscillations are made in the high frequency waves as compared to the low frequency waves within the same period of time.

Analysing Sound Waves

1. Sounds are mechanical waves. They are caused by vibrating objects. Hence, all vibrating objects produce sound. As an example: The strings of a guitar, the skin of a drum and a tuning fork vibrate to produce sound.


2. By using a loudspeaker as an example,  the vibrating cone of a loudspeaker produces sound by vibration.

3. Its vibrating diaphragm is continually compressing and stretching the air next to it.

4. This produces a series of compression and rarefaction travel through the air away from the loudspeaker.

5. Compression is a region of increased pressure and rarefaction is region of decreased pressure. The resulting succession of compression and rarefaction makes up the sound waves.



6. Sound wave is longitudinal in nature because the air molecules vibrate in a direction which is parallel to the direction of propagation is essentially due to the vibration of molecules of its medium.

7. Compression and rarefaction need a material which can be compressed and stretched. This explains why we do not hear any sound from the outer space which mainly consists of vacuum.

Amplitude and Frequency of Sound Waves

1. The amplitude of sound waves depends on its loudness. The louder the sound, the bigger is its amplitude.

2. The frequency of sound waves depends on its pitch. The higher the pitch of the sound, the higher is its frequency.

Applications of sound waves

1. Sound can be generated at a wide range of frequency.

2. Sound waves generated between 20 Hz and 20 kHz can be heard by normal human ears and are known as audio waves.

3. Those below 20 Hz are called infrasound and those above 20 kHz are known as ultrasound.

4. A bat can navigate in complete darkness by emitting very high-pitched sound waves in the ultrasonic range. When the waves hit a nearby object, they are reflected and received by the bat. The time lag between the emission of the sound waves and sensation of the reflected waves helps  the bat to estimate the position of the object accurately. The bat then adjust its direction to avoid knocking the object.

5. Dolphins use ultrasonic frequency of about 150 kHz for communication and navigation.

6. Ultrasonic rulers in ships use ultrasonic echoes to measure distance.

7. High intensity ultrasonic shockwaves can be used to break kidney stones.

8. Opticians and goldsmiths use ultrasonic cleaner to clean spectacles, jewellery and ornaments. The water used for the cleaning purpose is vibrated by ultrasound. The vibrations shake off dirt attached to these objects.

9. Dentists also use ultrasonic beams to vibrate and shake off dirt and plaque off the the teeth of patients.

Analysing Interference of Waves

Principle of Superposition

1. The principle of superposition states that at any instant or moment, the wave displacement of the combined motion of any number of interacting waves at a point is the sum of the displacements off all the component waves at that point.

2. a + a = 2a

a + -a = 0

-a + -a = -2a

Source: www.pitt.edu


Interference of Waves

1. Interference is the superposition of two waves originating from two coherent sources. Sources which are coherent produce waves of the same frequency,f, amplitude,a, and are in phase.

2. The superposition of two waves emitted from coherent sources gives either constructive or destructive interference.

3. Constructive interference occurs when the crests or throughs of both waves coincide to produce a wave with crests and troughs of maximum amplitude.


4. Destructive interference occurs when the crest of one wave coincides with the trough of the other wave, thus cancelling each other with the result that the resultant amplitude is zero.

5. An antinode is a point where a constructive interference occurs, whereas a node is a point where destructive interference occurs. The antinodal lines join all antinodes and the nodal line joins all nodes.

Relationship between lambda, a, x and D (will be discussed later)

Interference of Light waves

1. Waves emitted from two coherent sources have the same frequency,f or wavelength and in phase.



2. Light emitted by a single source of consists of waves which extend over a wide range of wavelengths and are not in phase. because of this, it is difficult to have two sources of light which are coherent.

3. In 1801, Thomas Young produced two coherent light sources in his experiment now referred to as Young's double slit experiment.

a) Yellow light emitted by a sodium-vapour lamp has a very narrow frequency band. for all its practical purposes, it can be considered as a monochromatic light which is light of only one frequency or wavelength.

b) Slits s1 and s2 give rise to two coherent light sources since the light passing through them are from the same monochromatic light, the sodium vapour light.

c) Interference occurs as a result of the superposition of the two light waves originating from s1 and s2. A pattern consisting of a series of parallel and alternating bright and dark fringes is formed.

d) The bright fringes are the region where constructive interference occurs, whereas the dark fringes are regions of destructive interference.

Analysing Diffraction of Waves

1. Diffraction of waves is a phenomenon in which waves spread out as they pass through an aperture or round a small obstacle.

Source: http://www.launc.tased.edu.au/online/sciences/physics/diffgaps.gif

2. The effect of diffraction is obvious only if

a) the size of the aperture or obstacle is small enough.
b) the wavelength is large enough

3 Characteristics of diffracted waves:

a) Frequency, wavelength and speed of waves do not change.
b) Changes in the direction of propagation and the pattern of the wave.

Diffraction of Light

1. Light is diffracted if it passes through a narrow slit comparable in size to its wavelength.
However, the effect is not obvious as the size of the slit increases. This because the wave-lengths of light are very short.

2. Diffraction of light is hardly noticeable compared with diffraction of sound waves and water waves because the wavelength of light is very short or small (approx: 10-7 m)

3. Light waves will be diffracted if

a) Light is propagated through a pin hole or a tiny slit where its size is similar to that of the light wavelength (around one hundredth of a millimetre or less)

b) the light source is monochromatic, i.e. light of one colour, and therefore one wavelength only.

Analysing Refraction of Waves

Any type of wave can be refracted, refracted is a change in direction. Refraction occurs when the speed of a wave changes, as it moves from one medium to another.

Refraction of Plane Water Waves

1. Water waves undergo refraction (bending) when its speed changes. Refraction is accompanied by a change in speed and wavelength of the waves.

Source: http://www.school-for-champions.com/science/images/waves_obstacles_refraction.gif

2. Water waves travel faster (with higher velocity, v) on the surface of deep water then they do on shallow water. Thus, if water waves are passing from deep into shallow water, they also will slow down. This decrease in speed will also be accompanied by a decrease in wavelength. The change of speed of the wave causes refraction.

3. After refraction, the wave has the same frequency,but a different speed, wavelength and direction.

4. When a water wave travels from deep water into shallow water, the wave is refracted towards normal. Conversely, the wave is refracted away from the normal when the water wave travels from shallow water into deep water.

Refraction of Light

1. A swimming pool seems much shallower than it actually is; a spoon appears bent when part of it is in water and a boy's legs look shorter when immersed in pool. All these effects are due to the refraction of light.

2. When a ray propagates from one medium to an optically dense medium, the ray refracts towards the normal. Conversely, a ray propagating from one medium to an optically less dense medium is refracted away from the normal.

3. The speed of light decreases as it propagates in the glass block, causing it to alter the direction of propagation. Since the incident ray and the refracted ray are from the same source, the frequency remains the same. Hence, the wavelength of the ray in the glass is shorter than the ray in the air.

Source: http://micro.magnet.fsu.edu/optics/lightandcolor/images/refractionfigure1.jpg

Refraction of Sound waves

1. The sound of a moving train at a distance is clearer at night than that in the day time. This is due to the effects of the refraction of sound waves.

2. At night-time, the layers of air close to the ground are cooler than the layers further from the ground.

3. Sound travels at a slower speed in cold air. As a result, the sound waves are refracted in the path of a curve (due to total internal reflection) towards the ground instead of disappearing into the upper layers of the air.

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/imgsou/refr2.gif

Analysing Reflection of Waves

1. Reflection of waves occur when a wave strikes an obstacle. The wave undergoes a change in the direction of propagation or transmission when it is reflected.

2. The incident wave is the wave before it strikes the obstacles, whereas the reflected wave is the wave after it strikes the obstacle.


3. Reflection of waves can be explained the Laws of Reflection where:

i) The angle of incidence, i is equal to the angle of reflectance, r.

ii) 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.

Source: http://www.qrg.northwestern.edu/projects/vss/docs%20/media/Communications/reflection.gif

Applications of reflection of Waves in Daily Life

Safety

i) 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.

ii) 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.

Defence

i) 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.

Telecommunications

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

Damping and Resonance of Waves

Displacement –time and Displacement –distance graphs.

Wave motion occurs because of the vibration of particles from their resting position.

We can show the displacement of particle (from its rest position) at different times by plotting a DISPLACEMENT-TIME graph.

We can show the displacements of particles of the wave at a certain time by plotting a DISPLACEMENT-DISTANCE graph.


The relationship between speed, wavelength and frequency.

Frequency (f)= Velocity (v) / Wavelength (λ)
v = f x λ

Damping in an oscillating system

Any motion that repeats itself in equal intervals of time is called a PERIODIC MOTION.

If a particle in a periodic motion moves back and forth over the same path, we call the motion OSCILLATORY or VIBRATORY.

Many of these oscillating bodies do not move back and forth between precise time fixed limits because frictional forces DISSIPATE the energy of the motion. Thus a pendulum stops swinging after some time.

The amplitude of oscillation of the simple pendulum will gradually decrease and become zero when the oscillation stops.

The decrease of in the amplitude of an oscillating system is called damping.

Two types of damping:
1. External damping: loss of energy to overcome frictional forces or air resistance.
2. Internal damping: loss of energy due to the extension and compression of the molecules in the system.

Damping in an oscillating system causes the amplitude and energy of the system to DECREASE but frequency DOES NOT change.

Source: http://www.a-levelphysicstutor.com/images/waves/reson-damp01.jpg

We CANNOT eliminate frictional force from the periodic motion of an object BUT we can cancel out its damping effect by feeding energy into the oscillating system so as to COMPENSATE for the energy dissipated by the frictional force.

For Example, the oscillating pendulum in a pendulum clock uses energy derived from the fall of a weight pulling a chain in the clock to supply external energy.

Resonance In An Oscillating System

When a system oscillates there is a loss of energy due to damping.
If the loss of energy is replaced by an external force of the same frequency, the system will continue to oscillate and may reach a bigger amplitude.

The external force supplies energy to a system, such a motion is called a forced oscillation.

Natural frequency is the frequency of a system which oscillates freely without the action of an external force.

RESONANCE occurs when a system is made to oscillate at a frequency EQUIVALENT at a frequency to its natural frequency by an external force. The resonating system oscillates at its MAXIMUM AMPLITUDE.

Here Resonance 1(R1) is more than Resonance 2 (R2)

The characteristics of resonance can be demonstrated with a Barton’s pendulum system.



Source: http://www.antonine-education.co.uk/Image_library/Physics_4/Further_Mechanics/Bartons_Pendula.JPG

You can read more about Barton's pendulum here:

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1598.0


Some effects of resonance observed in daily life:

The tuner in the radio or TV enables you to select 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 produced.

The loudness of music produced by musical instruments such as the trumpet and flute is the result of resonance in the air.

The effect of resonance can also cause damage. For example, a bridge can collapse when the amplitude of its vibration increases as a result of resonance. aka when it vibrates at its natural frequency.

Understanding Waves

Waves

Understanding Waves

Wave and Energy

A Wave is a disturbance that transfers energy between 2 points through vibrations (or oscillations) in a medium, without transferring matter between the two points.

Example 1: When you hold the end of a rope and a friend of yours wave the rope at the other end up and down, then a wavy movement appears. This is a movement of the rope and it transfers energy but NOT the rope.

Example 2: When you throw a stone on the surface of a calm pond, a circular ripple will appear and subsequently other smaller ripple will appear from the point of origin, these waves will eventually turn into a few big circles which then encompass  smaller circular ripples in the middle. What happen is, the kinetic energy from the stone is transferred to the water in the form of ripples, which is an example of wave.

There are two types of waves:

1. Transverse waves
2. Longitudinal waves

Transverse waves

Transverse wave is a wave in which direction of vibration is perpendicular to the direction of movement of wave.

Examples are : water waves, waves on a string, radio waves, light waves and electromagnetic waves.

Longitudinal waves

Longitudinal wave is a wave in which the direction of vibration is parallel to the direction of travel of the wave

Examples are: sound waves and waves on a slinky spring.(which consists of regions of rarefaction and compression).

Wavefronts

Wavefront is a line that joins all the points vibrating in phase, such as a line passing through similar wave crests. It consists of crest and trough. Crest is the peaky part of the wave and trough is the lowest part of the wave.

Wavefront is perpendicular to the direction of wave movement.

Oscillating System:

Waves are produced by oscillating systems (or vibrations) in a medium.

An oscillation is a to and fro movement along a fixed path.

Examples are: Swinging pendulum(horizontally) and a Spring swinging up and down (vertically).

What u must now is that:

One complete oscillation is a to and fro movement of a body when it has returned to its original position and is moving in the same original direction.

Amplitude, a, is the maximum displacement from the resting position.

Period, T, is the time taken to make one complete oscillation.

Frequency, f, is the number of oscillations produced in one second.