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Qatar International School Science Department Section3; Properties of waves 3.1 General wave properties. UHS 3a Describe what is meant by wave motion as illustrated by vibration in ropes, springs and by experiments using water waves. Use the term wavefront. Give the meaning of the term wavefront. We know what we mean by a wave, such as a wave on water, but it is not easy to give a scientific definition of what we mean by a wave. A wave or wave-motion means ‘the transfer of energy through a medium by vibration of the medium’ there are two important points here; the vibration and the movement of energy. e.g. a sound wave; the air vibrates and sound energy moves. e.g. a wave in a slinky spring or (tight rope) we shake one end of the slinky (putting in kinetic energy) and a ‘vibration’ moves along the spring. We call this vibration a wavefront. e.g. waves on water, we can use a ripple tank to see water waves. As we disturb the water, we cause wavefronts to move away from the disturbance. Definition of wavefront. The set of points reached by a wave at the same instant as the wave travels through a medium. The medium means what ever the wave is moving through, e.g. if a sound wave is moving in air, then air is the medium. The lines formed by ripples on a pond, as the wave spreads through the pond correspond to circular wave fronts. The distance between any wavefront and the next is called the wavelength (see below) Disturb water here wavefronts here Distinguish between transverse and longitudinal waves and give suitable examples. There are two types of waves; transverse and longitudinal waves. A transverse wave is when the vibration of the medium is perpendicular to the direction of the wave movement. E.g. waves on water, light waves. A longitudinal wave is when the vibration of the medium is parallel to the direction of the wave movement. E.g. sound waves. Created by Mr. Phillips Page 1 of 16 Qatar International School Science Department Give the meaning of speed, frequency, wavelength and amplitude. Recall and use the equation v = f λ. Speed of a wave means distance/time (like any other object). Symbol v, units m/s. Frequency means how many waves there are in one second. The equation is number of waves divided by time. Symbol f, units /s or Hz. Wavelength is the length of one wave. Wavelength is also equal to the distance between one wavefront and the next. Symbol λ, units m. Amplitude is the height of one wave Symbol a, units m.. Time period (or period) is the time for one wave. Symbol T, units s. The wave equation states v = f λ or in words speed = frequency x wavelength. Another useful equation is period = 1 in symbols T = 1 Frequency f λ a λ a λ Worked example. Given the speed of sound in air is 330m/s and the wavelength of a certain sound is 1.0m, calculate the frequency of the sound. Can this sound be heard by a human? Answer; Use v = f λ where v = 330 and λ =1 330 = f x 1 so f = 330Hz. This sound can be heard, because it is in the audible range (20 to 20000 Hz). Example. Find the speed and Period of a wave which has frequency 200Hz and a wavelength 0.5m. Created by Mr. Phillips Page 2 of 16 Qatar International School Science Department Describe the use of water waves to show (i) reflection at a plane surface (ii) refraction due to a change of speed (iii) diffraction produced by wide and narrow gaps. We can see waves on the surface of water by using a ripple tank. We can see three wave effects, and you should be able to recognize or draw the three diagrams below. Note the most common requirement in IGCSE is to do the diffraction diagrams, these are also the easiest diagrams. But you need to know the difference between the wide and narrow gap diagrams. Diffraction in water waves. Diffraction through a narrow gap Through a narrow gap (about equal to the wavelength). λ λ Waves are circular after passing through the gap. Wavelength is the same as before the gap (λ in the diagram is the same before the gap as after the gap). Note that the wavefronts become longer as the wave spreads out. Diffraction through a wide gap. Through a wide gap (much larger than the wavelength). Waves are straight in the region between the lines after passing through the gap. There are diffraction effects only at the edge of the waves. Wavelength is the same as before the gap (λ in the diagram is the same before the gap as after the gap). Note the straight part does NOT become longer, but the curved part can become longer. Example. Draw the diffraction of the waves through the gaps shown below. Created by Mr. Phillips Page 3 of 16 Qatar International School Science Department Reflection. Water waves follow the law of reflection, angle of incidence equals angle of reflection. As shown in the diagram below. The wavelength is the same before and after the reflection. The first diagram shows the incident waves changing direction after being reflected. This may be enough to answer the IGCSE question. However if you are required to show a wave which is partly incident and partly reflected this is more complicated and is shown below the first diagram. Diagram showing the bent wave fronts which are partly reflected while still having a part of the wave moving towards the reflecting surface. (without labels) Wavelength is the same as before the reflection (λ in the diagram below is the same before the gap as after the reflection). Note that the wavefronts are the same size before and after the reflection. Same diagram as above, but with explanatory labels. λ Reflective surface After reflection wavefronts are at 900 to direction arrow after reflection direction arrow after reflection λ Before reflection wavefronts are at 900 to direction arrow before reflection direction arrow before reflection Created by Mr. Phillips Page 4 of 16 Qatar International School Science Department Refraction. As a wave moves into shallower water its wavelength becomes less. (Or it becomes larger as it enters deeper water). When we draw the refraction diagram the wavefronts are closer in the shallower water, and this means the wave direction changes, so the wave bends as it goes into shallow water. (It will bend the other way entering deep water, but almost all exam questions ask about wave moving from deep to shallow). Steps in drawing the diagram are shown in the example below. Worked example. On the diagram to complete the wavefronts shown, also show the next few wavefronts after the water wave enters shallow region of water in a ripple tank. First we complete the direction arrow of the wave after it enters the shallow water. We choose the angle of refraction, but choose an angle about half way between the perpendicular and the original direction as shown in step 1. Then draw the new wavefronts in the shallow region at 900 to this direction line to complete the diagram as shown in step 2. Step 1 - direction Step 2 - wavefronts Note that the direction of the new wave is the first step, and after that the wavefronts automatically take on the new direction if you correctly draw them at 900 to this new direction arrow. Created by Mr. Phillips Page 5 of 16 Qatar International School Science Department Interpret reflection, refraction and diffraction using wave theory. Wave theory just means learn the table below. For each wave effect, that is reflection, refraction and reflection, you need to know the effect on speed, frequency and wavelength (these are the properties of a wave called wave properties). You have two choices, either memorize the table or remember how the table is completed. To complete the table there are three steps. 1. The frequency never changes. 2. Use the diagrams above to see if the wavelength changes (the wavelength is the distance between the wavefronts, see page 1). 3. use v = f λ (you now know if λ changes and if so then v changes in the same way; if λ increases so does v, if λ decreases so does v). Wave property frequency wavelength Stays the same Stays the same Stays the same Stays the same Stays the same Decreases speed Wave effect reflection diffraction refraction Created by Mr. Phillips Stays the same Stays the same Decreases Page 6 of 16 Qatar International School Science Department 3.2 Light 3.2(a) Reflection of light. Describe the formation, and give the characteristics, of an optical image by a plane mirror. Use the law angle of incidence = angle of reflection. Formation of an image by a mirror. When light hits a mirror it will reflect, but if it enters your eye you see it AS IF it came from a straight line. The object means the original object that the light actually comes from. The image means what we see, even though the light came from the object it looks AS IF it came from the image. Characteristics of an image formed by a mirror. A mirror will always give a virtual image. The image is as far behind the mirror as the object is in front. It is the same size as the object, and is laterally inverted (this means the left becomes the right). In summary the image is virtual upright same size as the object same distance behind the mirror as the image is in front. Laterally inverted. The law of reflection The angle of reflection equals the angle of incidence. In symbols, i = r The meaning of ‘real’ and ‘virtual’ when referring to an image. A real image is one where the light actually passes through the image. A real image could appear on a screen. A virtual is one where the light does not actually passes through the image. A virtual could not appear on a screen. Created by Mr. Phillips Page 7 of 16 Qatar International School Science Department Perform simple constructions, measurements and calculations. We use the law of reflection to find the position of an image, and we always describe it with the characteristics above. A construction just means an accurate drawing. The diagram on the right shows rays from each end of an object obeying the law of reflection as they enter the eye of a observer. The solid lines show the actual path of the light, while the dotted lines show where the light APPEARS to have come from (the eye sees light AS IF it came in a straight line). Each ray has been drawn as shown below. Angle of Incidence Incident ray i mirror Angle of reflection r reflected ray Normal (900 to the mirror) Examples. Draw a construction to find the position of the image of man B seen by man A in each diagram below. A r B r B r A r Created by Mr. Phillips Page 8 of 16 Qatar International School Science Department 3.2(b) Refraction of light. Describe an experimental demonstration of the refraction of light. Use the terminology for the angle of incidence i and angle of refraction r. Experimental notes. 1) ray box. We can use a light box to create a ray of light. A ray means a beam of light which is approximately parallel so it travels in a straight line. A bulb will give out light in all directions but we simply shield the light in a box and only allow light to go in one direction. We can draw a light ray as a straight line on a ray diagram. Light bends when it goes from one medium to another (medium means the material light is moving in, e.g. air or glass). The bending effect is called refraction. We can use a light ray from a ray box to see this. Note most diagrams do not draw a ray box, we start with a parallel ray of light. Diagram of a ray box. Bulb gives light in all directions Box shields light and stops it going in most directions Created by Mr. Phillips light ray comes out of the hole in one direction There is a hole in the box on one side only Page 9 of 16 Qatar International School Science Department 2) Optical pins. An optical pin is a pin used to trace a light ray. We can look at several optical pins and if they appear to be in a straight line then they fall on the same ray of light. This may be a straight ray, or a ray bending (refraction). IGCSE questions on optical pins usually require you to draw the position of pins on a diagram, the idea is to draw the pins as far apart as possible. You may be asked to give some methods of making the experiment with pins as accurate as possible (or reducing errors, which means the same thing). Answers include; view the base of the pin, make sure the pins are vertical, use thin pins, put the pins far apart. The experimental demonstration referred to is shown below, using a glass block. The angle of incidence is the angle between the incident light ray and the normal, called i, and the angle of refraction is the angle between the refracted ray and the normal. Both angles are also shown below. Describe the passage of light through parallel sided transparent material. A parallel sided transparent material simply means a rectangular glass or plastic block. We can use a ray box and see the light ray directly, or we can view optical pins. Normal (900) to surface of the block Incident ray i r Glass block Light ray comes out of the block parallel to the original incident ray. Recall and use the definition of refractive index n in terms of speed. Recall and use the equation n = sin i /sin r. We have studied how light bends when it crosses the boundary between one medium and another. The amount of refraction is measured by the refractive index, symbol n. You need to know two equations for refractive index Refractive index = speed of light in air speed of light in the medium Created by Mr. Phillips Page 10 of 16 Qatar International School Science Department Refractive index = sin i sin r = sin angle of incidence sin angle of refraction Worked example. If the angle of incidence is 450 and the angle of refraction is 300, calculate the refractive index of the medium. Calculate the speed of light in the medium (speed of light in air is 300 000 000 m/s. Answer; Refractive index = sin i sin r = sin 45 = 1.41 sin 30 Refractive index = speed of light in air = 300 000 000 speed of light in the medium speed in the medium so, speed of light in the medium = 300 000 000 /1.41 = 212 000 000 m/s. Example. On the diagram below draw a normal and label angle of incidence and refraction. Use a protractor to measure the angle of incidence and refraction, and then calculate the refractive index of the glass. Complete the diagram by drawing the ray after it passes out of the block on the lower face. Draw on your diagram suitable positions for four optical pins used to trace the ray. Glass block Created by Mr. Phillips Page 11 of 16 Qatar International School Science Department Give the meaning of critical angle. Describe internal and total internal reflection. The critical angle refers to a situation where light is inside a glass block and trying to leave (i.e. going from more dense to less dense medium). The light will refract as shown in the diagram above and in diagram 1 below. Note there is a weak reflected ray, some light s reflected from the inside of the block, this is reflected off the inside of the block and so it is called internal reflection. If the angle of incidence increases, we reach a situation shown in diagram 2 where the refracted ray has an angle of refraction equal to 900. In this case the angle of incidence is called the critical angle, because it is the change over point between diagram 1 and 3. Definition of critical angle; The critical angle (C) is the angle of incidence which gives an angle of refraction 900. If the angle of incidence increases any more it is impossible for the light to refract (since the angle of refraction would be greater than 900 so the light would not leave the glass) and so all the light reflects. This is called Total Internal Reflection (TIR). This is shown in diagram 3. Diagram 1 Diagram 2 Diagram 3 C r = 900. Refraction at 900 and internal reflection Refraction and weak internal reflection No refraction, total internal reflection (TIR) Describe the action of optical fibres. An optical fibre uses TIR to guide a ray of light along the fibre. As each reflection is TOTAL internal reflection, no light is lost regardless of how many reflections there are. T.I.R. T.I.R. T.I.R. Optical fibre Light enters Created by Mr. Phillips Light leaves Page 12 of 16 Qatar International School Science Department State the approximate value of the speed of electromagnetic waves. Use the term monochromatic. The speed of light in air or in vacuum is 300 000 000 m/s or 3 x 108 m/s you need to memorise this number. All electromagnetic waves have the same speed in a vacuum. Worked example. State the speed of xrays moving in air. Answer; 3 x 108 m/s Monochromatic The word monochromatic means one frequency. The only colours of visible light which are monochromatic are the three primary colours; red, green or blue. All other colours are a mixture of colours. We often use monochromatic light in an experiment to avoid diffraction, you may come across an IGCSE question stating ‘red light enters the block’ this just means we do not get dispersion. The light will act as shown in the diagrams above, which are actually using monochromatic light. Created by Mr. Phillips Page 13 of 16 Qatar International School Science Department 3.3 Sound. Describe the production of sound by vibrating sources. Describe the longitudinal nature of sound waves. Describe compression and rarefaction. When a guitar makes a sound the string vibrates. When a drum makes a sound the drum skin vibrates. When we speak our vocal cords vibrate. When we hold a ruler on the desk and make it vibrate we hear a sound. All sound is created by a vibration. The vibration of the object causing sound causes the air near to the object to vibrate as areas of high and low pressure as shown below. This is a LONGITUDINAL wave made up of areas of high called compressions and low pressure called rarefactions. Example a vibrating ruler causing high and low pressure. Ruler moves upwards causing high pressure in the air above the ruler (compression) vibrating ruler moves upwards and down desk Ruler moves downwards causing low pressure in the air above the ruler (rarefaction) Relate the loudness and pitch of sound waves to amplitude and frequency. We can use a vibrating ruler to see the effect of amplitude and frequency on the sound we hear. If we make the ruler short it vibrates faster, this is HIGH FREQUENCY and we hear a HIGH PITCH SOUND. If we hit the ruler harder it vibrates more, this is HIGH AMPLITUDE and we hear a LOUD SOUND. We can see the same effect with any other instrument such as a guitar, a thin string vibrates faster and gives a high pitch, plucking the string harder causes a larger amplitude and gives a louder sound. In General; HIGH FREQUENCY = HIGH PITCH SOUND. LARGE AMPLITUDE = LOUD SOUND. Created by Mr. Phillips Page 14 of 16 Qatar International School Science Department State the approximate range of audible frequencies. We can use a signal generator and a speaker to create sounds of different frequency. Very high pitch and very low pitch sounds can not be heard. A healthy young person can hear a wider range of sound than an older person due to damage to the ear through out life. A typical healthy person can hear sound between 20Hz and 20000Hz. You need to be able to state these values. Describe an experiment to determine the speed of sound in air. State the order of magnitude of the speed of sound in air, liquids and solids. Show an understanding that a medium is required in order to transmit sound waves. Experiment to measure the speed of sound. To calculate speed we need distance and time. Sound is fast so we need to use a large distance or the time is too short to measure. Light travels so fast we can ignore the time it takes for light to travel the distance involved in the experiment. Two people stand far apart, and measure the distance between them. One makes a sound by banging wooden sticks (or firing a gun etc.). As the other person sees the movement he starts the stopwatch, when he hears the sound he stops the stopwatch. This gives the time for sound to travel from one person to the other. Use speed = distance/time to calculate the distance. Man with a stopwatch starts timing when he sees sticks come together, stops when he hears sound of sticks. Man with sticks, when he bangs them it makes a sound. Light travels to the eye (almost) instantly sound travels to the ear much more slowly Large distance. E.g. 100m or more Created by Mr. Phillips Page 15 of 16 Qatar International School Science Department Sound and different mediums The medium means the material which sound (or any wave) is passing through. Sound can travel through a gas (e.g. air) or through a liquid (e.g. when swimming under water you can still hear) or through a solid (e.g. we can hear through a wall). Most objects travel more easily through air, but sound is the reverse; sound travels faster through solids (5000m/s) and slowest through gas (330m/s). This is because the strong bonds in a solid transmit the vibrations easily. In lower school we see an experiment where we suck out air from a big jar with an alarm in clock inside. We see the sound get quieter. If all the air is removed we hear no sound at all because sound can not move through a vacuum, note light can do so (e.g. light from the sun passes through space to reach Earth). Big jar Alarm clock making sound. As air is removed the sound gets quieter showing sound needs a medium to move through. To vacuum pump (sucks air) Describe how the reflection of sound may produce an echo. When a sound wave hits a solid object it can reflect in the same way as a light wave reflects from a mirror. If we hear the reflected sound we call it an echo. Often we will hear the original sound directly then a few seconds later we hear the echo as the sound reflects from a distant object like a building. The reflection moves a longer distance and so takes longer to reach us compared to the direct sound. Example, this is very common when watching fireworks. firework Reflected sound takes more time as it travels a longer distance Direct sound building Created by Mr. Phillips Page 16 of 16