# 2011 FXA Properties of Waves 58 INTRODUCTION

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1 1.5.1 Properties of Waves 58 INTRODUCTION Waves transfer energy. Waves may be either transverse or longitudinal. Electromagnetic waves are transverse, sound waves are longitudinal and mechanical waves may be either transverse or longitudinal. All types of electromagnetic waves travel at the same speed through a vacuum (space). Electromagnetic waves form a continuous spectrum, the order of which needs to be known in terms of energy, frequency and wavelength. Appreciate that the wavelengths vary from about m to more than 104 m. Waves transfer energy from a source to other places without any matter being transferred (e.g. sound waves transfer sound energy from a loudspeaker without actually transferring the air which carries the sound). Waves can also transfer information (e.g. the use of TV, radio or mobile phones). Waves can be : MECHANICAL CLASSIFICATION OF WAVES ELECTROMAGNETIC Longitudinal waves show areas of compression and rarefaction. Waves can be reflected, refracted and diffracted. Significant diffraction only occurs when the wavelength of the wave is of the same order of magnitude as the size of the gap or obstacle. Waves undergo a change of direction when they are refracted at an interface. Waves are not refracted if they are travelling along the normal. The meaning of the terms frequency, wavelength and amplitude. The wave equation : v = f x λ where v is the speed in m/s f is the frequency in Hz λ is the wavelength in m Radio waves, microwaves, infrared and visible light can be used for communication. Need to be familiar with situations in which these waves are typically used and any associated Hazards, e.g. Radio waves - Television and radio (including diffraction effects) Microwaves - Mobile phones and satellite television Infrared - Remote controls Visible light - Photography Waves which need a substance for their transmission. (e.g. sound waves can be transmitted Through air, water and steel, but not Through a vacuum). EXAMPLES Water waves Sound waves Waves along a spring coil or rope Seismic waves Waves which DO NOT need a substance for their transmission i.e. they can travel through a vacuum. (e.g. light waves travel from stars and galaxies travel through empty space to reach us here on Earth). EXAMPLES Gamma-rays X-rays Ultra-violet (UV) Visible light Infrared (IR) Microwaves Radio waves

2 Waves can also be : Properties of Waves 59 LONGITUDINAL TRANSVERSE The vibrations of a transverse wave are perpendicular to the direction in which the wave travels and transfers energy. The vibrations of a longitudinal wave are parallel to the direction in which the wave travels and transfers energy. motion of coil end motion of coil end wave direction compressions to fixed end wave direction rarefactions A spring coil can be used as shown above to observe TRANSVERSE wave motion. The coil is fixed at one end and the free end is continuously vibrated in a direction PERPENDICULAR to the axis of the coil. A spring coil can be used as shown above to observe LONGITUDINAL wave motion. The coil is fixed at one end and the free end is continuously vibrated in a direction PARALLEL to the axis of the coil. LONGITUDINAL WAVE EXAMPLES TRANSVERSE WAVE EXAMPLES All electromagnetic waves. Sound waves. Transverse waves along water. Primary seismic waves. Secondary seismic waves.

3 1.5.1 Properties of Waves 60 TERMS USED TO DESCRIBE WAVES λ THE WAVE EQUATION Wave speed (v), frequency (f) and wavelength (λ) are related by the equation : A Wave speed = frequency x wavelength A v = f x λ λ (m/s) (Hz) (m) AMPLITUDE (A) / metre (m) Here s a useful memory aid which will help you to work out v, f or λ when you are given the other two variables : The maximum displacement of a wave from its undisturbed position. WAVELENGTGH (λ) / metre (m) This is the distance between two consecutive crests or troughs. v (m/s) v = f x λ PERIOD (T) / second (s) The time taken for one complete wave to pass a fixed point. f (Hz) λ (m) FREQUENCY (f) / hertz (Hz) The number of complete waves passing a fixed point per second. f = v/λ λ = v/f WAVE SPEED (v) / metre per second (m/s) The distance travelled by a wave crest or trough per second.

4 1.5.1 Properties of Waves 61 PRACTICE QUESTIONS (1) 1 (a) Give two examples of mechanical waves. (b) Give two examples of electromagnetic waves. (c) Explain what is meant by a transverse wave and give two examples (d) Explain what is meant by a longitudinal wave and give two examples. 2 (a) Using a diagram to illustrate your answer, explain what is meant by the amplitude (A) and wavelength (λ) of a wave. REFLECTION, REFRACTION AND DIFFRACTION OF WAVES REFLECTION Sound waves are reflected from hard, flat surfaces. When this happens from a wall or a cliff face, the original sound and the reflected sound can sometimes be distinguished as separate (i.e. an echo is heard). Dolphins and bats use echoes to find there way around and to hunt their prey. (b) What is the frequency (f) of a wave and in what unit is it measured? (c) State the wave equation which links wave speed (v), frequency (f) and wavelength (λ). 3 (a) Calculate the speed of a sound wave having a frequency of 2500 Hz and a wavelength of 13.2 cm. (b) Given that all electromagnetic waves have a speed of m/s in air, calculate the wavelength of the radio waves from a station which transmits at a frequency of 1200 khz. Fishing trawlers equipped with echo-sounders use the same principle to measure ocean depth and to locate large fish shoals. (c) Calculate the frequency of sound waves in air which have a wavelength of 0.40 m, given that the speed of sound in air is 340 m/s. 4 The diagram shows four waves, A, B, C and D all drawn to the same scale. (a) Which wave has the lowest frequency? (b) Which wave has the lowest amplitude? A B Reflection of visible light waves enables us to see the world around us. Light waves are incident on objects and are then reflected into our eyes. (c) Which wave has the longest wavelength? (d) Which wave has the greatest amplitude? C D

5 REFRACTION Properties of Waves 62 Remove the block, draw in the emergent ray and join point X to point Y. The line you have drawn gives the direction of the refracted ray. When waves, such as light or sound, arrive at the boundary between two different substances at an angle, their speed changes and this causes them to change direction. This effect is called refraction. Light rays are refracted when they cross the boundary between one transparent medium and another (e.g. air to glass). Use the protractor to measure angles i, r, I and R. What can you say about i and r? What can you say about I and R? Practical Investigation - REFRACTION OF LIGHT Replace the block and direct a light ray along the normal. What happens? glass block incident ray NORMAL i X NORMAL r I y R emergent ray Light rays change direction (i.e. they are refracted) when they are incident at an angle at the boundary between two different optical media. ray box refracted ray i Place the glass block on the paper and carefully mark its position with a pencil. r Remove the block and draw in the normal (at 90 to the block outline) at a point X close to one end. Also draw in an incident ray at an angle i = 50. Use a protractor to do both things. The NORMAL is a line at 90 to the interface between the two media. Carefully replace the block in its marked position and use the ray box to direct a light ray along the drawn incident ray path. The ANGLE OF INCIDENCE (i) is the angle between the incident ray and the normal. Use two pencil dots to mark the direction of the emergent ray. The ANGLE OF REFRACTION (r) is the angle between the refracted ray and the normal.

6 1.5.1 Properties of Waves 63 SOME EFFECTS CAUSED BY REFRACTION OF LIGHT For light travelling from an optically less dense into an optically denser substance (e.g. from air into glass), the light ray is refracted towards the normal. AIR GLASS i r A straight rod which is partly immersed in water appears to be bent. This is because light from points on the rod which are submerged, is refracted away from the normal as it emerges into the air. AIR WATER For light travelling from an optically denser into an optically less dense substance (e.g. from glass into air), the light ray is refracted away from The normal. AIR GLASS r i A swimming pool appears to be shallower than it actually is. Again this is because light from the bottom of the pool is refracted away from the normal as it emerges into the air to enter the observer s eyes. If the light ray is incident normally (i.e. at 90 to the boundary between the two substances), there is no change in direction. AIR GLASS incident ray 90 refracted ray Rainbows are produced when sunlight is refracted through rain droplets, causing the light to be split into a visible spectrum. Containing the colours red, orange, yellow, green, blue, indigo and violet.

7 1.5.1 Properties of Waves 64 REFRACTION THROUGH A TRIANGULAR PRISM REFRACTION OF SOUND When a monochromatic light ray passes through a triangular glass prism, it is refracted towards the normal at A and away from the normal at B. As a result the ray is caused to change direction. monochromatic light ray A B Triangular glass prism When a sound wave travels across the boundary from one substance into another substance of different density, its speed changes and (unless it strikes the boundary normally) it undergoes refraction (i.e. its direction changes). At night the air near the ground is colder and therefore denser than it is higher up. This causes sounds which are travelling upwards to refract back towards the ground making it possible to hear sounds a long way from the source. In the daytime, sound refracts upwards because the air near the ground is warmer and less dense than higher up. When WHITE light (e.g. sunlight) passes through a triangular glass prism, it is split up into its constituent colours and a visible spectrum is formed. This happens because each colour has a different wavelength and is refracted by a slightly different amount. Red light is refracted least and violet light is refracted most. DIFFRACTION OF WAVES DIFFRACTION is the spreading of waves when they pass through a gap or move past an obstacle. DIFFRACTION OF SEA WAVES AROUND A HARBOUR WALL Sea waves incident on a harbour wall are found to spread into the region behind the wall where we would expect the sea to be flat calm. This is an example of diffraction around an obstacle. harbour wall

8 1.5.1 Properties of Waves 65 DIFFRACTION OF WAVES THROUGH A GAP PRACTICAL - DIFFRACTION OF MICROWAVES When the width of the gap is much larger than the wavelength of the waves, the waves are only slightly diffracted. The apparatus shown opposite can be used to show diffraction of microwaves. The transmitter emits microwaves of wavelength = 3 cm. microwave transmitter metal plates X microwave detector Y When the width of the gap is nearly the same as the wavelength of the waves, the diffraction effect is greatest. Firstly, a single metal plate is placed in front of the transmitter. The metal reflects the microwaves, so no microwaves should be detected in the region of geometrical shadow behind the plate. The fact that microwaves can still be detected behind the plate is due to the fact that they are diffracted around the edge of the plate. NOTE : Whether a gap is narrow or not depends on the type of wave. for example, a narrow gap for a sea wave will be a huge gap for a light wave. Two plates separated by a gap of a few cm are then placed in front of the transmitter. The microwaves pass through the gap and when the detector is moved along the line XY behind the gap, it detects microwaves that have spread out from the gap by diffraction. When the size of the gap between the plates is varied, it is found that the diffraction effect is greatest when the gap size is 3 cm. This is because the amount of diffraction is greatest when the size of the gap through which waves are passing is equal to the wavelength of the waves.

10 1.5.1 Properties of Waves 67 THE ELECTROMAGNETIC SPECTRUM Typical Wavelengths of Electromagnetic Waves ELECTROMAGNETIC WAVES : WAVE TYPE TYPICAL WAVELENGTH / m Are electric and magnetic disturbances which transfer energy from one place to another. All travel at the same speed (3.0 x 10 8 m/s) through a vacuum (i.e. in space). Are grouped together according to their wavelength (λ), frequency (f) or energy (E) under the heading of the electromagnetic spectrum. Obey the laws of reflection and refraction. Gamma rays to X-rays to 10-8 Ultraviolet (UV) 10-8 to 4 x 10-7 Visible light 4 x 10-7 to 7 x 10-7 Infrared (IR) 7 x 10-7 to 10-3 Microwaves 10-3 to 10-1 Radio waves 10-1 to 10 6 Obey the wave equation v = f λ. THE ELECTROMAGNETIC SPECTRUM Uses of Electromagnetic Waves Increasing frequency and energy WAVE TYPE USES Increasing wavelength Gamma rays Sterilisation of medical instruments / Killing cancer cells. X-rays To see damage to bones and teeth / Airport security scanners. microwaves Ultraviolet (UV) Sunbeds / Security markings that show up in UV light. Visible light Human sight / Optical fibres. Infrared (IR) Night-vision cameras / Remote controls / Optical fibres. Microwaves Radar / Microwave oven / TV transmissions. Radio waves Radio transmissions.

11 1.5.1 Properties of Waves 68 ULTRAVIOLET (UV) GAMMA (γ)-rays Emitted by very hot objects (e.g. the Sun). Emitted from the nuclei of radioactive atoms. Have very short wavelength or high frequency. Are the most penetrating form of nuclear radiation. Causes tanning, sunburn and excessive exposure can lead to skin cancer. Needed for the production of vitamin D in the body. Can be used to : To kill cancer cells (radiotherapy). To kill harmful bacteria in fresh food and so prolong its shelf life. To sterilise surgical instruments. To reveal faults in welds (γ-radiography) Fluorescent materials absorb UV and then emit visible light. Fluorescent dyes are used in washing powders, security markers and bank notes. UV lamps are used : In shops to check bank notes for forgery. By dentists to harden fillings. X-RAYS VISIBLE LIGHT Produced in x-ray tubes by when high-speed electrons strike a tungsten target. X-rays find their greatest use in medical imaging, especially for the detection of broken bones. They are also used in chest x-rays to identify lung cancer. Forms a very tiny part of the electromagnetic spectrum. Light from the Sun and light bulbs, which is called WHITE light, contains all the colours of the visible spectrum. Airport security scanners use x-rays to inspect the interior of luggage prior to loading onto the aircraft.

12 1.5.1 Properties of Waves 69 MICROWAVES INFRARED (IR) Emitted by all objects. The hotter the object is, the more IR radiation it will emit. Have wavelengths somewhere in between those of infrared radiation and radio waves. Microwaves are used for communications. IR radiation is absorbed by the skin. It causes damage and kills skin cells because it heats up the skin cells. IR radiation is used in the following ways : Signals are transmitted in optical fibre communication systems using IR rather than light. This is because IR is absorbed less than light in the glass fibres. Electric grills, toasters and heaters use IR radiation. IR radiation scanners are used in medicine to detect hot spots on a patient s body, which can mean that the underlying tissue is unhealthy. Satellite TV works using microwave signals beamed from a ground station to a geostationary satellite and then relayed to satellite receivers on Earth. Microwaves are used to transmit the signals because they can pass easily through the atmosphere. Light-emitting diodes (LEDs) used in TV and DVD remote controls work by emitting an IR beam of a specific frequency. Because of its longer wavelength, the IR emitted by living creatures can be distinguished from the background IR given out by cooler objects. Burglar alarms, night-vision equipment and thermal imaging cameras all work on the basis of IR wavelength differentiation. Rattlesnakes have special pits in their eyes which enable them to detect the IR emitted by their prey. Microwaves (as well as radio waves) are Also used to carry mobile phone signals. Microwaves are also used for cooking. Water absorbs microwaves of a particular frequency and this heats the water. This is used to cook foods with some water content in microwave ovens. The food is cooked throughout its volume rather than from the outside in as occurs in normal ovens.

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