Energy is often moved from place to place by means of waves. For example, sound from a loudspeaker, warmth from a fire, etc.

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1 The Nature o f Energy is often moved from place to place by means of waves. For example, sound from a loudspeaker, warmth from a fire, etc. Waves can be classified into two: a. Mechanical waves b. Electromagnetic waves Mechanical waves These waves consist of vibrations in a material medium, which then transmits them. For example, the disturbance caused in water when a stone falls in it produces water waves. The material medium, i.e. the water is responsible fro the transmission of the waves. Such waves can be seen or heard and include waves on a stretched string, water waves, sound waves, etc. Electromagnetic waves These consist of a disturbance in the form of varying electric and magnetic forces. Contrary to mechanical waves, these waves do not require a medium in which to travel, and travel faster in a vacuum than in matter. For example, radio signal, light and X-rays. There are two main types of waves: Transverse waves These are waves in which the motion of the particle is at right angles to the direction of travel of the wave. For example, water waves. Longitudinal waves A longitudinal wave is one is which the particles of the transmitting medium, vibrate in the same direction of travel of the wave. Such a wave could be produced on a stretched slinky spring by vibrating it to and fro. Some parts of the spring are pushed closer together (compressions) and some parts are pulled further apart (rarefactions).

2 It is the same with a sound wave in air. In some places the molecules of air are pushed together at a slightly higher pressure (compression) and in some places the molecules are further apart at a slightly lower pressure (rarefaction). The wavelength of a sound is the distance between two successive compressions or rarefactions. The number of compressions/rarefactions per second gives the frequency of the wave. Sound waves obey the wave equation, i.e. v = fλ. Describing waves This is a graphical representation of a wave which helps to explain the terms used. a. The wavelength λ (lambda) is the distance between successive crests or troughs (unit: metres m) b. The amplitude a is the height of a crest or trough from rest position (unit: metre m) c. The frequency f of a wave is the number of complete waves per second (unit: Hertz Hz) d. The periodic time T is the time taken for one complete wave (unit: second s) e. The velocity v of a wave is the distance travelled by a wave in one second (unit metres per second m/s) The periodic time T and frequency f of a wave are related by the formula:

3 T = 1 f The wave equation The velocity of a wave is the product of the frequency and the wavelength of the wave. Velocity = frequency wavelength or v = fλ Worked examples: Waves of wavelength 20cm travel across a pond at a frequency of 0.25Hz. Calculate the velocity of the waves. v = fλ v = v = 0.05m/s A wave of T = 0.05s and of wavelength 10cm travels across a lake. Calculate the velocity of the wave. f= 1 T f = 1 = 20Hz 0.05 v = fλ v = v = 2m/s

4 The wave equation holds for all types of waves and is used when dealing with different forms of energy such as light and sound. When using the wave equation on would note, apart from other things, that one of the differences between light and sound is their speed. AND Since light is a form of electromagnetic radiation its speed is m/s whereas that of sound depends on the material through which it is travelling. Usually, the greater the density, the faster it moves and therefore it is greater in solids than in liquids or gases. Speed of Sound Material Speed Air (0 C) 330m/s Water 1 400m/s Concrete 5 000m/s Steel 6 000m/s To estimate the speed of sound, stand a measured 50m from a large wall. Clap, or bang sticks together, and listen to the echo. Then try to clap in an even rhythm of clap-echo-clap-echo-clap while friend times 100 of your claps with a stopwatch. During the time from one clap to the next clap, the sound would have time to go to the wall and back twicethat is a distance of 200m. In the time of 100 claps. The sound would travel = m. Speed = distance = time time in seconds The difference between the speed of light and the speed of sound therefore explains why we see lightning before we hear the clap of thunder although both happen at the same time!! Another important difference between light and sound is that while light is an electromagnetic wave and all electromagnetic waves are transverse in nature, sound is a form of longitudinal wave. Sources of sound, such as musical instruments, have some part that vibrates. For example, when a tuning fork is banged on cork, it vibrates and produces a sound.

5 The sound travels through air, to our ears and we hear it. Sound waves are mechanical waves, therefore one could show that air is necessary for the transmission of sound by enclosing a ringing bell in a vacuum. The sound is not heard, even though the striker hits the gong. Therefore, unlike light, sound does not travel through a vacuum. Other materials, including solids and liquids transmit sound. In fact, the denser the material, the better it would transmit sound. Human beings hear only sounds that have frequencies from about 20Hz to 20kHz. These are the limits of audibility. The upper limit decreases with age. Sounds that have a frequency which is too high for the human ear to detect are called ultrasounds. Ultrasounds can be heard by some animals, such as dogs, bats and dolphins. Uses of ultrasounds include ultrasonic scanning carried out in hospitals to monitor the progress of unborn babies in the mother s womb, in industry to clean very delicate pieces of apparatus without having to take them apart and echo-sounding used in navigation. These uses of sound are only possible because of one important property that sound has in common with light reflection. Visible light is mainly produced by the Sun. This energy in the form of light travels at a very high speed ( m/s) and takes about 7 minutes to arrive here on our planet. Our eyes are sensitive to light. The reflected light from the objects around us, is captured by this light sensitive organ and so we are able to see all these objects. Objects that produce their own light are called luminous sources, for example: the Sun, stars, electric lamps, television screens.

6 Objects that do not produce their own light but which reflect light from other luminous sources are called non-luminous sources, for example: the Moon, table, chair, persons and most objects around us. Light rays The head lamp of a car or a torch produces a beam of light. This is made up of a collection of light rays. The ray of light with its arrow gives the direction in which light is travelling. For experiments with light, we usually use a narrow beam of light which is produced by a ray box. The fact that you cannot see round corners helps us to conclude that light travels in straight lines. Reflection When light falls on a surface, it may either be transmitted, reflected or absorbed. Usually it undergoes a mixture of all three. Reflection of light can be either regular or diffuse. Diffuse reflection occurs if light falls on a rough surface and is scattered in all directions. For example, light falling on a sheet of paper. Regular reflection occurs if a beam of light falls on a smooth surface such as a plane mirror. All the light is reflected to the other side as a parallel beam.

7 The laws of reflection 1. The angle of incidence equals the angle of reflection. 2. The incident ray, the reflected ray and the normal all lie in the same plane. (This means that they can all be drawn on the same sheet of paper.) The periscope Periscopes are used in submarines so that the crew can explore the region above the surface of the sea. They can be also used to see over other obstacles, such as crowds and also over walls for instance during bird watching. The periscope is made of two plane mirrors fixed at an angle of 45. Light from the object falls on the first mirror and this is then reflected onto the second mirror. In this way, the observer can see the object by looking at the second mirror. Plane Mirrors Mirrors consist of a glass sheet which is silvered at the back. The silvering ensures that all the light falling on it is reflected back. A sheet of glass (without the silvering) acts as a poor mirror since only a small percentage of light that falls on it is reflected back.

8 Real and Virtual images A real image is one which can be produced on a screen and is formed by rays which actually pass through it. A virtual image cannot be formed on a screen and is produced by rays which seem to come from it but do not pass through it. In a plane mirror, the rays from an object appear to come from a point behind the mirror. Images in a plane mirror Reflection of Sound As mentioned previously, reflection is not a property which belongs to light alone, but sound, since it comes in the form of waves also exhibits this property. Sound is reflected very well by hard, flat surfaces such as walls and cliffs, and they obey the law of reflection such as light does. If the distance between the sound source and the reflecting surface is long enough, one may hear an echo. If the distance is short (15m or less) then the echo joins up with the original sound to give a reverberation (prolonged sound). At the cinema, the walls are covered by sound-absorbing material to reduce reverberations to an acceptable level.

9 An example of sound being reflected is in the use of ultrasound investigation of an unborn baby inside the other s womb. This is possible because the sound waves (of frequencies we can t hear) are reflected back by the baby. Echo-sounding Another use for reflection of sound waves which is very different but which in theory is quite similar is echo-sounding. Ships can use echoes to find the depth of the sea. An echo-sounder emits sound waves down towards the seabed. When the waves strike the seabed, they are reflected back up to the surface. A sound detector listens for the echo. The deeper the sea, the longer it is before the echo is heard. Sound waves used in this way are called SONAR. This stands for SOund Navigation And Ranging. Fishing boats often use sonar to detect shoals of fish. Refraction Refraction is another property which belongs to waves. Swimming pools appear shallower than they actually are and a pencil appears bent if half of it is immersed in water. Before we can understand why this happens, we must first see what happens to light when it passes from one optical material into another. Boundary: The line dividing one medium from another. Incident ray: The ray hitting the boundary. Refracted ray: The ray moving away from the boundary. Point of incidence: The point where the incident ray hits the boundary.

10 Normal: This is an imaginary line drawn perpendicular to the boundary. Angle of incidence: The angle between the normal and the incident ray. Angle of refraction: The angle between the normal and the refracted ray. Emergent ray: The ray that emerges out of the block. The laws of refraction 1. Light is bent towards the normal when it enters a denser medium at an angle and away from the normal when it enters a less dense medium at an angle. 2. The incident ray, the refracted ray and the normal all lie in the same plane. The refractive index (η) The refractive index η is a measure of the amount of bending that takes place when light passes through two different media. The larger η is, the larger the amount of bending that takes place. For example: From the above one can see that the amount of bending that occurs at an air/glass boundary is larger than that of an air/water boundary. Note that the refractive index η has no units. The speed of light in air is m/s, while its speed in a transparent material is much less. In fact it is this change in speed that produced refraction. The refractive index therefore can be found by finding the ratio of the two speeds. Refractive index η = speed of light in air speed of light in the transparent substance

11 Apparent depth Another way of finding the refractive index η is by measuring the real depth of an object and the image of its apparent depth. The depth that the water appears to be when viewed from above is known as the apparent depth. This is an important consideration for spearfishing from the surface because it will make the target fish appear to be in a different place, and the fisher must aim lower to catch the fish. The object below appears to be further up than it actually is due to refraction. This is due to the bending of light rays as they move from the water to the air. Once the rays reach the eye, the eye traces them back as straight lines which intersect at a higher position than where the actual rays originated. This causes object to appear higher and the water to appear shallower than it really is. In order to find the refractive index of a substance using the above, one would need to measure both the real and apparent depth and use them in the formula: η = real depth apparent depth Worked example: A coin is placed at the bottom of a 40 cm deep pond. The refractive index for water is How deep does the coin appear to be? 1.33 = 0.40m apparent depth therefore 1.33 apparent depth = 0.40m So apparent depth = 0.40m = 0.3m 1.33

12 Total Internal Reflection The inner surface of a semi-circular glass block behaves like a mirror. This is called total internal reflection. The ray of light is not bent at the first surface since it is falling normally (that is at 90 ). Total internal reflection happens if the ray strikes the inside surface of the block at an angle greater than the critical angle. -If the angle of incidence is smaller than the critical angle, the ray is reflected as usual. -If the angle of incidence is equal to the critical angle the ray will emerge along the boundary. -If the angle of incidence is greater than the critical angle total internal reflection will take place. Total internal reflection only occurs when light travels from a more optically dense material into a less optically dense material, for example, glass to air.

13 Uses of total internal reflection Totally reflecting prisms Light entering the first surface of the glass prism goes straight through since it falls normally on that face. Inside the prism, it meets the second face at an angle of 45. This angle is larger than the critical angle for glass (42 ) and so total internal reflection take place. This second face acts as a mirror and turns the light through 90. For this reason, such prisms are used in periscopes. Other reasons for using prisms instead of mirrors in periscopes are that: a. mirrors produce multiple images due to multiple reflections in the glass. b. the silvering at the back of mirrors is easily damaged c. prisms reflect light more effectively than mirrors A prism can be used in a different way as shown in the diagram. The ray of light entering the first surface is undeviated and is reflected through an angle of 90 at both faces, since total internal reflection occurs as previously above. This means that light is turned through an angle of 180. Such prisms are used in the bicycle reflector, cats eyes and binoculars.

14 Optical fibres An optical fibre consists of a long glass fibre whose thickness may vary from a fraction of a millimetre to 50mm. When light is shown at one of its ends, it can travel inside the glass fibre, from one end to the other, even when it is bent. This is possible because the angle of incidence inside the glass fibre is larger than the critical angle and so total internal reflection traps all the light and conveys it to the other end. It is as if the glass is silvered on the outside. These optical fibres are used in hospitals (endoscopy) for viewing inside the body and are also widely used in the telecommunication industry where information in the form of sound and vision are sent through these fibres. Dispersion When white light passes through a prism, a spectrum is produced. The rainbow is formed in a similar way. It seems that white light (light produced by the Sun or light bulb) is a mixture of several colours and can be split up by a prism. We say that light has been dispersed by the prism to form a visible spectrum. It was Newton who first discovered the spectrum and he same to the conclusion that : a. white light is a mixture of seven colours which the prism separates out b. the refractive index of glass is different for different colours i.e. they are slowed down by different amounts on entering the prism.

15 The pure spectrum The above method of producing a spectrum Gives an impure spectrum, which means that The colours in it are overlapping. Separate bands of the colours of the spectrum i.e. a pure spectrum can be obtained by using a lens to focus each colour of the spectrum as shown in the figure opposite. Recombining the spectrum The colours of the spectrum can be recombined by: a. arranging a second prism so that the light is deviated in the opposite direction b. using an electric motor to rotate at high speed a disc with the spectral colours painted on its sectors.

16 Reflection A straight metal obstacle is placed in the tank so that it reflects any water waves that fall on it. The diagrams show the type of reflection obtained when using a straight and curved obstacles. From the first diagram it is very clear that the law of reflection is obeyed and that the angle of incidence is equal to the angle of reflection. Refraction This can be studied by placing a thick sheet of plastic in the tank to adjust the depth so that the water is very shallow over the plastic. In this way there will be areas of shallow and deep water in the tank. On studying the pattern of waves obtained, it will be seen that the waves in the shallow area have shorter wavelengths than the waves in the deep area. However, both waves will have the same frequency since they are produced by the same source. Using the wave equation, one can see that this decrease in wavelength is due to the fact that the velocity of the waves has decreased in the shallow area. As shown in the second diagram, if the same experiment is repeated but this time, the incident wavefront is at an angle other than the normal with the deep/shallow water, the direction of the waves is seen to turn towards the normal as they pass from deep to shallow water.

17 Diffraction If two straight obstacles are placed some distance apart in a ripple tank, and straight waves are directed to it, there is slight bending towards the edges. If waves pass through a wide gap, diffraction is negligible. If the gap width is about the same size as the wavelength of the waves, the waves passing through are circular. This is called diffraction. Diffraction happens with all sorts of waves including light and sound. Audible sounds have wavelength from about 1.5cm (frequency 20kHz) up to 15m (20Hz) and so suffer diffraction by objects of similar size, for example a doorway 1m wide. This explains why we hear sounds round corners. Wavelength of visible light are too small to be diffracted by doorways or windows, therefore they do not suffer diffraction but pass straight through. As a result light waves can only travel in straight lines and not round corners! Diffraction of light waves however, is possible in the lab using special microscopic A A.G.C..

18 Lenses are used in many optical instruments, for example, telescopes, microscopes, cameras, etc. Your eyes possess very special lenses which are able to focus on what you see around you. A lens consists of a piece of glass having spherical surfaces are there are two types of them. A convex lens is thickest at the centre and thinnest at the edges. A concave lens is thinnest at the centre and thickest at the edges. When a parallel beam of light passes through a convex lens, the light is converged inwards. Therefore a convex lens is a converging lens. A concave lens, on the other hand, diverges all the light that passes through it. A concave lens is therefore a diverging lens. The centre of a lens is known as the optical centre C and the line through C perpendicular to the lens is called the principal axis. A convex lens produces a real image. When light parallel to the principal axis of a lens is refracted by the lens, the light passes through a point on the principal axis called the principal focus F. The distance between C and F is the focal length f of the lens. The thicker the centre of a convex lens, the smaller the focal length of the lens and vice versa. Ray diagrams for convex lenses When an object is placed somewhere in front of a convex lens, the size, nature and location of the image produced depends on the position of the object in front of the lens. The characteristics of the images produced can be found by first knowing at least 2 out of 3 constructions.

19 Construction 1: Parallel rays of light are refracted through the principal focus F. Construction 2: Refracted rays through F are refracted parallel to the principal axis after refraction by the lens. Construction 3: Rays of light passing through the centre of the lens travel straight on.

20 Magnification An image may be magnified if it larger than the object, or diminished if it is smaller than the object. The magnification is a ratio of the height of image to the height of object. Magnification = height of image h i height of object h o or Magnification = image distance CI object distance CO A magnification of 1 would mean that the image and the object are of the same size. Optical instruments Lenses are used in objects we use everyday, such as the camera, projector and magnifying glass. The first two produce real images while the third produces a virtual image. The following diagrams show how. The camera The projector

21 Drawing ray diagrams 1. Draw a long central line (the principal axis). Draw a shorter line at right angles to represent the lens. 2. Where distances are given, chose a scale for the size and position of the object. 3. Mark in the object and the position of F and 2F (twice the focal length), on each side of the lens. 4. Starting from the top of the object, draw the two constructions. 5. Where the refracted rays cross, is the position of the top of the image. 6. Measure the position and size of the image (using scales) and say whether it is: inverted or erect (upright) magnified or diminished real or virtual Finding the focal length of a lens Method A: Window method (Rough method) Rays of light coming from very far objects, such as rays passing through the window at the other side of the room, are considered to be parallel. When parallel rays of light are refracted by a convex lens, the image is produced on its principal focus. The focal length of a convex lens can be found by moving the lens between the window and the wall on the other side of the room. The distance between the sharpest image on the wall and the centre of the lens can be measured by means of a ruler and is the focal length of the lens. Method B: Plane mirror method (accurate method) An illuminated object, lens of unknown focal length and a mirror are arranged as shown. The lens is moved between the object and the mirror until a sharp image of the object is formed on the screen beside the object. When this happens, the light from the object must have been refracted by the lens, and a parallel beam of light falls on the mirror. In turn, the mirror reflects the light back along the same path. The focal length is the distance between the image/object and lens.

22 The electromagnetic spectrum consists of two parts; a. the visible spectrum and b. the invisible spectrum The electromagnetic spectrum is made up of a large family of waves, and although they differ greatly in their wavelengths, all electromagnetic waves: 1. are wave-like radiations which carry energy from one place to another, 2. travel through a vacuum at m/s, i.e. the speed of light, 3. are transverse in nature, 4. exhibit reflection, refraction and diffraction effects, 5. obey the equation c=fλ, where c is the speed of light, and 6. lose intensity with distance from the point source. RADIO

23 Radio waves are detected by an aerial with a TV set or radio set Microwaves are detected by a microwave receiving dish. In medicine, infra-red scanners are used to produce a thermograph to detect hot spots under the body s surface. Hot spots can often mean that the underlying tissue is unhealthy. They can also be used to detect circulation problems which are shown as cooler areas under the skin. Astronomers take infra-red photos to get data about the temperatures of planets and stars. IR is used in industry to dry paints on cars. IR is detected by the skin, a blackened thermometer or a thermistor.

24 Our eyes are more sensitive to some wavelengths of the visible spectrum than to others. Your eye is most sensitive to green-yellow light. Visible light can be detected by the eye or photographic film. Dark skin is able to absorb more UV so reducing the amount reaching deeper tissue. UV is detected by photographic film. X-ray photos are also used by engineers to check welds and metal joints. In factories, X-rays can be used to check that food does not have metal or stones in it. They are detected by photographic film.

25 Gamma-rays can also be used to check that two pieces of metal have welded together properly. They can also be used to trace leaks from pipelines carrying oil or gas. γ-rays are detected by means of a Geiger- Muller (G-M) tube. A A.G.C..

26 WORKSHEET WAVES 1. If the vibrations of a wave are at right angles to the direction of the wave, it is called a wave. If the vibrations of a wave are along the direction on the wave, it is called a wave. A water wave is a wave and a sound wave is a wave. 2. The diagram shows straight waves approaching a straight barrier at 45. Complete the diagram to show how these waves are reflected. 3. The diagram shows the crests of circular water waves which are travelling outward and about to meet a straight reflector. a. Describe the source and its action by which a continuous series of such waves could be produced. b. Find from the diagram the wavelength of the waves. c. On the diagram draw the first reflected wave crest.

27 4. Continue the diagrams to show what happens to the waves once they cross the boundary into shallow water. 5. Show what happens to the waves as they pass through the gap.

28 6. A small boat floats up and down on waves on the sea. It takes 4s to make one complete up and down movement. What is the frequency of the waves? 7. A certain sound wave has a frequency of 170Hz and a wavelength of 2m. What is the speed of sound? 8. A coast guard sees a distress rocket burst in the sky and 5 seconds later he hears the bang. If the speed of sound is 330m/s, how far is the exploding rocket from the coast guard? 9. An echo sounder in a ship produces a sound pulse and an echo is received from the sea bed after 0.4s. Assuming the speed of sound in water is 1 500m/s, calculate the depth of the sea bed. 10. A man is kidnapped, blindfolded and imprisoned in a room. How could he tell if he was in a bare room or a furnished room? 11. The behaviour of waves in water can be studied with a ripple tank. (a) (i) Explain how the waves are made more visible. (ii) How can continuous ripples be studied more easily? (b) The wave fronts which are the crests of waves can be represented in diagrams as a series of straight lines. (i) How do the wave fronts relate to the direction of travel of the wave? (ii) On the diagram below, draw the direction of travel of the reflected wave and show the wave fronts. 60 (iii) What is the angle of the reflected wave?

29 12. An observer looks at a water tank and according to him half of the tank is filled with water. If the height of the tank is 180cm, find the real height of the water in the tank. (η water = 1.33). 13. a. The diagram above shows part of the electromagnetic spectrum. Name: i. The missing types of radiation (p) and (q). ii. The radiation with the smallest wavelength iii. The radiation with the highest frequency iv. A method of detecting ultraviolet v. The origin of gamma radiation. 14. This question is about cooking food in a microwave cooker and in a conventional electrical one. The microwave cooker uses electromagnetic waves of 0.12m. a. Underline the part of the electromagnetic spectrum which includes this wavelength: gamma rays, ultraviolet, visible, infra-red, radio. b. Complete the following sentence about the conventional cooker: The radiation from the heating elements comes mainly from the part of the electromagnetic spectrum. c. If the speed of the microwaves is m/s ( m/s), find their frequency. A A.G.C..