COMMUNICATES CONTEXT. Figure 5.0.1

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1 2 THE CONTEXT WORLD COMMUNICATES What do surfing, SMS texting, heating up a meat pie in a microwave oven and using a laser beam to read the music off a CD have in common? They all involve the physics of waves. Waves connect almost every area of physics and engineering in both practical and deeply theoretical ways. On the practical side, waves are used in almost every method of communication, both modern and ancient. Sound, light, earthquakes and electrical signals travelling along wires are all examples of waves. All musical instruments involve the physics of waves. Even inside your brain, waves of electrical activity bounce around continuously. Waves can transport both energy and information. From a theoretical perspective, the behaviour of waves ties together almost all areas of physics, such as optics, astronomy and acoustics. The strange physics of quantum mechanics, which defies commonsense (it seemingly allows objects to be in two places at once) but is responsible for almost all of modern electronics, says that everything, including the person reading this book, has wave-like properties. The radio waves that carry signals to mobile phones and radios, the infra-red rays that warm you while sitting next to a fire, X-rays used in hospitals, visible light, the microwaves in your oven and ultraviolet rays that can give you both a suntan and sunburn are all examples of a special class of waves called electromagnetic waves. In this module, we will learn what waves are and how they behave. We will also learn how they can be used to communicate over long distances. Figure Waves connect the world through physics. 78

2 Figure INQUIRY ACTIVITY EXPLORING INFRA-RED WAVES Many modern devices use infra-red technology for communication. Infra-red is a type of electromagnetic wave. The television remote control is one device that transmits infra-red waves. These waves carry information that tells your television to turn on or off or to change channel or volume. They are produced by a lightemitting diode (LED), which looks like a small, clear plastic bubble visible on the front end of some remote controls. Try the following activities with your remote control. 1 Most modern cameras, including video, digital and mobile phone cameras, can pick up infra-red waves. Point the remote control at the camera lens, push a button on the remote control and look at the camera viewing screen. Can you see the infra-red waves? What do you see when you press different buttons? 2 Find the range of your remote control. What is the maximum distance you can be from the television before the remote control stops working? Do fresh batteries make a difference? 3 Can you make infra-red waves bounce or travel around corners? Try pointing the remote control at a wall or mirror opposite the television or going into an adjoining room out of sight of the television. Will the remote control still work? 4 Do infra-red waves pass through matter? Cover the LED on the remote control with various materials, such as your hand, a piece of paper, aluminium foil, plastic sandwich wrap and glass. What materials can the infra-red waves penetrate? 79

3 5 Moving oscillation, propagation, radiation, medium, mechanical waves, electromagnetic waves, energy transformation, sinusoidal, crest, trough, displacement, transverse wave, longitudinal wave, compression, rarefaction, amplitude, wavelength, equilibrium position, frequency, period energy around: waves What is a wave? A wave is any wiggle, any vibration (or oscillation), that can travel from one place to another. When a wave travels, we say it is propagating. You can see many everyday examples of waves, such as waves on a surf beach, ripples on the surface of a pond or the flapping of a flag. Some waves, such as soundwaves and light waves, are not so obvious to the eye. The word radiation means any disturbance that propagates outwards from its source, so virtually all waves can be thought of as forms of radiation. Figure The swimmers are moved up and down as the water wave travels past them. 5.1 Waves carriers of energy As we found in Section 4.1, energy is the ability to move an object. All waves have this ability, so we say that they carry energy. For example, the light waves that leave the hot surface of the Sun carry energy to the Earth, thereby warming up the Earth s atmosphere. They also drive the movement of air and water vapour in the form of wind and storms. When a sound wave enters your ear, the energy it carries causes your eardrum to vibrate, which you hear as sound. When you go surfing, you are propelled along as a wave gives you its energy. However, if you are just standing still some distance from the shore as the wave goes past, you simply bob up and down with the surrounding water. If the water is moving up and down, how does the wave move forwards? If you disturb the surface of a body of water, the water molecules in the surface oscillate up and down, pushing or pulling on others in front of them and passing some of their energy on, causing them to oscillate as well. These molecules then push or pull on others in front of them and so on. This disturbance therefore travels horizontally. In a surface water wave, a disturbance (and the energy it carries) travels along horizontally, even though the individual molecules are just oscillating up and down in more or less the same position. 80

4 THE WORLD COMMUNICATES You can see another example of this with a rope tied at one end to a wall (Figure 5.1.2). Tie a ribbon somewhere along the rope. Shake the free end of the rope to make a wave move along it. Although the wave moves along the rope, the ribbon just moves up and down in the same position on the rope. Figure hand motion A wave travels along a rope. wave direction ROUND AND ROUND I n reality, surface water waves have a special property: the molecules move in a circular motion rather than just up and down. So part of the motion is forwards and backwards as well as up and down. Try to notice this the next time you are bobbing up and down in the waves you ll find that you also move forwards and backwards a little. PHYSICS FEATURE DESTRUCTIVE WAVES The destructive power of earthquakes is nothing more than wave motion travelling through the ground. Sometimes the earthquake occurs in the ground beneath the ocean, which can transfer some of the wave energy to the water. This can produce a giant water wave called a tsunami, which can destroy villages, towns and cities that are close to the coast. In 1946 a tsunami struck Hawaii and more than 150 people died. Also, in 1964 a magnitude 9.2 earthquake in Alaska caused a tsunami that destroyed the northern Californian town of Crescent City and killed 122 people in the Pacific region. In response, a tsunami warning system was developed to cover the North American west coast and most countries in the Pacific basin. Initially, the tsunami warning system consisted of a series of tidal gauges fixed to buoys at various locations around the Pacific Ocean. When unusual seismic activity was detected, field officers were notified and the individual tide gauges were checked. If local tide heights varied from normal values, a tsunami warning was issued. Remote sensing and satellite technology have transformed the process and now allow for much earlier detection of tsunamis and real-time forecasts. A system comprising 39 Deep-ocean Assessment and Reporting of Tsunami (DART) stations are located at sites in Pacific regions with a history of generating destructive tsunamis. DART stations consist of two parts: a tsunameter, which is a platform that is anchored to the seafloor to record temperature and pressure variations; and an anchored surface buoy that is equipped to broadcast data to satellites. The tsunameter converts the temperature and pressure measurements into a sea level height measurement. The sea level height is transmitted to the surface buoy using an acoustic signal. The surface buoy transmits the sea level heights to a satellite, which in turn transmits the information to the tsunami warning centre. Two DART stations are operated by Australia: one is between Tasmania and the South Island of New Zealand, and the other is in the Coral Sea south of the Solomon Islands. You can see up-to-date data collected by DART stations in the Pacific region at the NOAA website, accessed via the companion website at A similar tsunami warning system is currently being developed for the Indian Ocean as a consequence of the tragic Boxing Day Tsunami in 2004, which killed more than people. Figure A tsunami very big and very fast! 81

5 5 Moving energy around: waves CHECKPOINT Define the terms energy and wave. 2 Explain how energy is transferred in a water wave without moving the individual water molecules. Figure Describe waves as a transfer of energy disturbance that may occur in one, two or three dimensions, depending on the nature of the wave and the medium. Water waves propagate in two dimensions on the surface of water. 5.2 Wave motion in one, two and three dimensions You may have heard the term three-dimensional (or 3-D). What does this mean? Solid objects like cubes fill up space. Such objects have three characteristic sizes or dimensions: length, width and height. Flat surfaces, such as squares, are called two-dimensional (2-D) because they have only two dimensions. A square has width and length as its dimensions. A straight line has only length, so it is one-dimensional (1-D). So what does this have to do with waves? Stretch a slinky spring and give it a pinch so that you can see a wave pulse travel along the spring. This is called 1-D wave motion. In 1-D wave motion, the wave travels (or propagates) along one direction in a line. The same is true if you wiggle a rope tied to a wall. The rope oscillates side-to-side, but the wave propagates in a line along the rope. The movement of a guitar or violin string is also an example of 1-D wave motion. If you drop pebbles into a pond, you ll find that waves travel outwards from the disturbance along the surface of the water in the form of circular waves. Circular waves demonstrate 2-D wave motion, which is possible for any wave motion that is restricted to travelling along a surface (Figure 5.2.1). If you put your hands on the wood of an acoustic guitar next to the hole, you will feel the whole surface vibrating. This is another example of 2-D wave motion. Three-dimensional waves are those that can travel in all directions. An example is the motion of sound waves through air, travelling spherically outwards from the source. You know that if someone speaks, you will hear them no matter where you are in the room since sound can travel in all directions in air (Figure 5.2.2). A dramatic example of a 3-D wave is the sound from an explosive, which travels in all directions and through anything in its path. This wave also throws hot particles in three dimensions as well. Figure Sound propagates in three dimensions in air. 82

6 CHECKPOINT 5.2 THE WORLD 1 Complete the table to summarise one-dimensional (1-D), two-dimensional (2-D) and three-dimensional (3-D) waves. COMMUNICATES WAVE TYPE EXAMPLE MEDIUM DESCRIPTION 1-D Travels in one direction along a line 2-D Ripples on a pond 3-D Air 5.3 Medium for wave travel Almost all waves you will encounter need a medium (plural media) through which to travel. A wave medium is any material that has a kind of springiness or elasticity a tendency to bounce back after you disturb it. Some examples of waves (and their media) are ripples (water surface), sound waves (air), earthquakes (rock) and a wicked bass riff (guitar string). All waves that require a material substance as the medium are called mechanical waves. Identify that mechanical waves require a medium for propagation while electromagnetic waves do not. TRY THIS! HEARING CHURCH BELLS FROM A SPOON Cut a 1 m length of string and tie a spoon at its centre. Now put the ends of the string to each ear and have someone strike the spoon with another spoon. You should hear the sound of church bells! The wave starts out as vibrations in the spoon and then the energy is transferred to the string, which becomes the wave medium. Finally, the energy is transferred to your fingers and into your ears very efficiently, making a surprisingly loud and rich sound. Figure Hearing church bells 83

7 5 Moving energy around: waves GRAVITATIONAL WAVES Gravitational waves are another kind of wave that does not need a medium. Albert Einstein s theory of general relativity predicted their existence in Although there is some recent indirect astronomical evidence for them, they have not yet been directly detected. An important property of a wave medium is that the material of the medium does not normally travel with the wave. The particles within the medium oscillate back and forth, staying more or less in the same location, while the wave propagates over long distances. For example, if someone shouts and you hear them a kilometre away, the sound wave has travelled through the medium (air) for a kilometre. However, the air molecules that were near the mouth of the person shouting stay there they do not reach your ears. Surprisingly, there is an important type of wave that requires no medium: electromagnetic (EM) waves, such as radio waves, microwaves, infra-red rays, visible light, ultraviolet rays, X-rays and gamma rays. Unlike other waves, EM waves can propagate through empty space (or vacuum). All EM waves propagate through a vacuum at the speed of light, which is about 300 million m s 1. EM waves are used for most of our electronic communication. They are used in mobile phones, television, radio and communication via satellites. As you will see in Section 8.1, an EM wave consists of oscillating electric and magnetic fields that can move through vacuum. EM waves do not only travel through a vacuum, however. They can propagate along the surface of a conducting wire, such as copper, under the influence of the wave motions of the electrons inside the wire. This is how the signals get in and out of your home landline telephone. EM waves, including visible light, can also propagate (more slowly) through transparent materials, which is why you can see through air or glass. electric field direction of motion magnetic field Figure Albert Einstein Figure EM radiation has electric and magnetic fields at right angles to each other and to the direction of propagation of the wave. CHECKPOINT Identify the property that is common to all mechanical waves. 2 Identify three examples of EM waves. 3 Compare EM and mechanical waves. 84

8 THE WORLD COMMUNICATES 5.4 Energy transformation in devices A loudspeaker (or speaker for short) lets you hear sound from electronic devices, such as a CD player, television, radio and mobile phone. Wires connect the device and the speaker. The wave motion of the electrons along the wires is converted into sound waves by the speaker. We can say that electrical energy in the wires is being transformed into mechanical energy in the speaker, which then transfers its energy to waves in the air so that you can hear sound waves. An interesting situation arises when we do not connect wires to the speaker but just leave them hanging in air. Surprisingly, the wave energy still leaves the wires, but this time it produces a wave that is composed of electric and magnetic fields that can travel through a vacuum at the speed of light. In other words, the wave energy produces EM waves. In EM waves, the electric and magnetic fields oscillate at right angles to each other and to the direction of propagation (see Figure 5.3.2). A wire suspended in the air so that it can transmit EM radiation is otherwise known as a transmitting antenna or aerial. This is the principle behind how television and radio stations transmit their programs to you (Figure 5.4.1). An antenna can also be used in reverse to detect an EM wave. For example, the antenna of a mobile phone (in most models it is hidden inside the casing of the phone) is used to both transmit and receive phone calls. The receiving antenna for your television is more visible. The EM waves that we use in communication are generally known as radio waves. However, this only covers a very small range of all possible EM waves. Energy transformations in mobile phones The energy transformations in a mobile phone are given in the flow chart in Figure Suppose Alice is talking through her mobile phone to Bob who is listening through his. The microphone in Alice s phone transforms the mechanical sound wave energy into electrical wave energy. Because the electrical energy is too weak to continue the chain of energy transformations, the amplifier electronics become actively involved to amplify (increase the intensity of) the weak electrical signal. The extra energy for amplification comes from the battery of the phone. The electrical energy in the mobile phone s wiring is transformed into an EM wave by the phone s antenna. The EM wave is then transmitted through the air and captured by a receiving antenna called a base station or mobile phone tower. Inside the receiving antenna, the energy of the EM wave is transformed back into electrical wave energy, which runs through the base station s wiring. Figure Describe the energy transformations required in one of the following: mobile telephone fax/modem radio and television. Telstra Tower on Black Mountain, in the Australian Capital Territory. It is used to transmit television, radio and mobile phone signals. The red and white structure on top is the transmitting antenna. Analyse information to identify the waves involved in the transfer of energy that occurs during the use of one of the following: mobile phone television radar. 85

9 5 Moving energy around: waves air exchange (amplify) air Figure sound energy (in air) electromagnetic energy (in air) electromagnetic energy (in air) electromagnetic energy (in air) electromagnetic energy (in air) sound energy (in air) Alice s mobile phone electrical energy microphone (in wire) antenna First base station antenna underground cable Second base station underground cable antenna Bob s mobile phone antenna speaker electrical energy (in wire) electrical energy (in wire) electrical energy (in wire) electrical energy (in wire) electrical energy (in wire) amplify amplify amplify amplify Waves carry energy between transmitter and receiver. The energy transformations are represented by the thicker arrows. base station central telephone exchange In the base station, the signal is amplified again and transmitted through an underground cable to a central telephone exchange. At the exchange, the signal is amplified again and the switching circuits ensure that the phone call is connected to the intended receiver in this case, Bob. Through another underground cable, the telephone exchange redirects the call to a second base station in the area where Bob is; however, this time the base station acts as a transmitter, amplifying and then transforming the electrical energy in the signal into EM energy by an antenna to be transmitted through the air again. Bob s phone antenna then captures the EM wave and converts it into electrical energy, which is amplified yet again. Finally, this energy is converted into mechanical energy (sound) by the speaker in the phone. (See Figure ) Note that amplification had to be introduced at several steps between Alice and Bob. These steps are not strictly just energy transformations. Extra energy had to be introduced that was not in the original wave; otherwise the EM wave your phone receives would be too weak to detect. Look carefully at the flow chart in Figure and you will see that between consecutive energy transformations, there is always an amplification step. Figure base station Waves carry energy between transmitter and receiver. CHECKPOINT Outline how an antenna works. 2 Explain why an amplifier is used in mobile phone base stations. 86

10 THE WORLD COMMUNICATES 5.5 The wave model Sine waves The simplest possible wave is called a sine wave. (You should remember the shape of a graph of the function y = sin x from mathematics.) Sometimes the word sinusoidal is used to describe such waves. It simply means sine waveshaped. The highest points on a sine wave are called peaks (or crests). The lowest points are called troughs. The shapes of waves can be complicated, such as water waves on a very windy day, but even the most complicated waves can be thought of as combinations of sine waves of various sizes. Therefore, if we can understand sine waves, we can explain the behaviour of all waves (Figure 5.5.1). To represent simple wave motions as a sine wave, we need to correctly choose the way we label the x- and y-axes. For example, when you wiggle a rope up and down and set up a sine wave that moves away from you, the x-axis represents the direction in which the wave propagates. The y-axis represents the displacement of a particle in the rope, which is how far a particle in the rope has oscillated from its original undisturbed position. A wave in which the direction of wave propagation is at right angles (90 ) to the direction of the displacement of the oscillating particles is known as a transverse wave. In the case of the rope, the crests of the wave propagate at right angles to the direction of motion of your hand wiggling the rope. Say you marked a particular part of a rope with a pen. You will notice that the mark just moves up and down while the crests of the wave move horizontally, perpendicular to the motion of the mark. On the other hand, in sound waves, for example, the arrangement of air molecules is compressed (pressure increased) and then expanded (pressure decreased) repeatedly. When the direction of motion (displacement) of the particles that make up the wave is parallel to the propagation direction of the wave, it is called a longitudinal wave (or compression) (Figure 5.5.2). The expansions are also called rarefactions. (This is discussed further in Section 7.1.) Another example of this type of wave occurs when you compress part of a slinky spring and let it go. You can see the longitudinal wave moves along the length of the slinky spring (Figure 5.5.3). air molecule movement y Figure Define and apply the following terms to the wave model: medium, displacement, amplitude, period, compression, rarefaction, crest, trough, transverse waves, longitudinal waves, frequency, wavelength, velocity. All waves can be represented as combinations of sine waves. PRACTICAL EXPERIENCES Activity 5.1 Activity Manual, Page 35 x wave direction compression rarefaction Figure Sound waves in air are longitudinal waves. 87

11 5 Moving energy around: waves Present diagrammatic information about transverse and longitudinal waves, direction of particle movement and the direction of propagation. Figure compression rarefaction A longitudinal wave in a slinky spring Features of sine waves Sine waves can come in different sizes. The two measures of size are amplitude and wavelength. The meanings of these are illustrated in Figure 5.5.4, which shows various features of a sine wave travelling horizontally. wavelength amplitude A crest particle movement B wave velocity displacement CHECKPOINT 5.5 Figure The features of a wave trough C wavelength Imagine that the sine wave in Figure represents the cross-section of ripples on a pond. The ripples travel horizontally, but the particles at the surface of the water oscillate up and down. The x-axis represents the surface of the water if it were undisturbed by ripples and is called the equilibrium position. The highest points in a wave are the crests. The lowest points are the troughs. The maximum distance a particle oscillates from its equilibrium position to either a peak or trough is called the amplitude. The symbol for amplitude is A. The distance along the x-direction between a peak (or trough) and its nearest neighbour is called wavelength. The symbol for wavelength is λ (lambda), which is the Greek equivalent of the letter l. If you watch any particular position on the water surface, the number of peaks (or troughs) that pass that point per second is called the frequency (f ). Frequency is therefore the number of wavelengths that pass per second. The unit of frequency is cycles per second or Hertz (Hz). The number of seconds between two adjacent peaks (or troughs) is called the period (T ). Another way of thinking about it is that period is the time taken to complete one wavelength. If you think about it carefully, you should see that: f = 1 T 1 Compare the direction of oscillation and the direction of energy transfer in a longitudinal wave and a transverse wave. Use diagrams in your answer. 2 Draw and label a diagram of a sinusoidal wave to clearly illustrate the crest, trough, amplitude and wavelength. D 88

12 THE WORLD COMMUNICATES 5.6 The wave equation How fast does a wave travel? Imagine again, as you did in Section 5.1, that you are watching ripples on a pond travel past a particular point. Remember from Chapter 1 that the magnitude of velocity v is given by: v displacement = = time Now period T is the time taken between peaks. Since the distance between peaks is the wavelength λ, the position of any peak moves through a displacement of λ in a time T. Therefore: v = λ but f T s t = 1 T Quantify the relationship between velocity, frequency and wavelength for a wave: v = f λ. v = λf where v is the speed (the magnitude of velocity) in metres per second (m s 1 ), f is the frequency in hertz (Hz), and λ is the wavelength in metres (m). This is true for all travelling waves, even if they are not pure sine waves. The speed of sound in air at a temperature of 20 C is about 344 m s 1. So if we know the frequency of the sound, we can work out its wavelength. The speed of sound changes with the temperature of the air; it increases with increasing temperature. Worked example QUESTION Imagine that you are on a boat in the middle of the ocean and you are bobbing up, down and up again once every 2 s due to the water waves. You notice that the crests of the waves are about 10 m apart. a Calculate the frequency of the waves. b Calculate the speed of the waves. SOLUTION a Use the period T of the wave to determine the frequency. We are told the period is 2 s because we move down the crest and then back up again during this time. The frequency is given by: f = 1 T = 1 = 0.5 Hz 2 PRACTICAL EXPERIENCES Activity 5.2 Activity Manual, Page 43 Solve problems and analyse information by applying the mathematical model v = f λ to a range of situations. Interactive b The wavelength λ of the waves is given as 10 m. This and the frequency can now be used to calculate the wave speed v: v = f λ = = 5.0 m s 1 Module 89

13 5 Moving energy around: waves TRY THIS! FUN IN A THUNDERSTORM The next time there is thunder and lightning, notice that the flash of the lightning occurs before you hear the thunder. That s because light travels much faster than sound, so it gets to you sooner. Light has a speed of approximately m s 1, while sound travels at 344 m s 1 at an air temperature of 20 C. However, this activity needs some mental arithmetic, so we will approximate the sound speed to 350 m s 1. You can impress your friends by telling them how far the lightning is away from you. When you see the lightning flash, start counting seconds. You can use the words Oodnadatta 1, Oodnadatta 2 and so on. You then multiply the number of seconds by 350 to get the distance in metres. For example, say you saw the flash of lightning and you started counting Oodnadatta 1, Oodnadatta 2, Oodnadatta (this last count is about half a second), and then you heard the thunder. That is about 2.5 s. This gives a distance of = 875 m. That lightning is less than a kilometre away and too close for comfort! (We didn t take into account the speed of light because it acts almost instantaneously.) This calculation may be difficult to do mentally, so a very rough way to do it is to divide the number of seconds by three, which gives you the distance in kilometres. In our example, this is 25., which we can 3 see is just less than a kilometre. This is usually accurate enough for the fraternity of thunderstorm watchers. Figure Lightning strikes, but how far away is it? CHECKPOINT Increasing or reducing the tension in a rope can change the speed of a wave travelling along it. Predict how the wavelength changes for a wave on the rope if: a the frequency and speed are both halved b the speed is doubled and the period remains the same c the speed remains the same but the period is doubled. 90

14 PRACTICAL EXPERIENCES THE WORLD COMMUNICATES CHAPTER 5 This is a starting point to get you thinking about the mandatory practical experiences outlined in the syllabus. For detailed instructions and advice, use in2 Preliminary Activity Manual. ACTIVITY 5.1: EXPLORING WAVES Use the slinky springs, ropes and a ripple tank to illustrate the transmission of longitudinal and transverse waves. Equipment: slinky spring, 3 m of lightweight rope, retort stand, ring, clamp, ripple tank, signal generator, light source, screen. rope fixed at end Perform a first-hand investigation to observe and gather information about the transmission of waves in slinky springs, water surfaces and ropes. rope light beam moving wave movement of hand hand tank screen water in tank overhead projector longitudinal pulse Compression pulse A pulse produced by moving the hand to and fro in the same direction as the pulse moves along a spring. Pulse in a string A pulse produced by moving the hand from side-to-side gradually moves along a string. Ripple tank You can view water waves in a ripple tank. Figure Using a slinky, string and ripple tank to explore waves Discussion questions 1 Describe how to move the slinky spring to produce a transverse and a longitudinal (or compression) wave. 2 Explain what the lines or ripples you see on the surface of the ripple tank are. What is the name of the distance between two ripples? ACTIVITY 5.2: ANALYSING WAVES Use a frequency generator to produce sine waveforms on an oscilloscope. Equipment: signal generator, oscilloscope, BNC cable, loudspeaker, coloured pencils, calculator. Discussion questions 1 Describe what happens to the shape of the waveform when the frequency on the signal generator is increased. 2 Describe what happens to the shape of the waveform when the amplitude on the signal generator is increased. 3 Explain how you can determine the frequency of the wave from the horizontal scale of the oscilloscope. signal generator 256 Hz Figure Perform a first-hand investigation to gather information about the frequency and amplitude of waves using an oscilloscope or electronic data-logging equipment. cathode ray oscilloscope (or computer) An oscilloscope and signal generator 91

15 5 Moving energy around: waves A wave is any vibration (or oscillation) that can travel (propagate) from one place to another. Waves can be used to carry energy and information. A medium is an object or material through which the wave propagates, such as air for sound waves. All waves that require a material object as the medium are called mechanical waves. Transverse waves occur when the particles of the medium move (displace) at right angles to the direction of wave propagation, such as waves on a rope. Longitudinal (or compression) waves occur when the particles of the medium move (displace) along the same direction as the wave propagation; for example, compressing part of a slinky spring makes a longitudinal wave. The transfer of energy by a wave can take place in one, two or three dimensions, such as a rope (1-D), water surface waves (2-D) or soundwaves (3-D). Electromagnetic waves can propagate in three dimensions and do not require a medium. In a vacuum, these waves travel at the speed of light and are used in communication equipment, such as mobile phones. Chapter summary Electromagnetic waves include radio waves, microwaves, infra-red rays, visible light, ultraviolet rays, X-rays and gamma rays. Electromagnetic waves are transverse waves, where the electric and magnetic fields are at right angles to each other and to the direction of wave propagation. Mobile phone communication involves the transfer of energy between mechanical, electrical and electromagnetic energies. All waves can be described by combinations of sine waves. The maximum distance a particle oscillates from its equilibrium position (at either a peak or trough) is the amplitude. The distance between a peak (or trough) and its nearest neighbour is called wavelength (λ). The number of peaks (or troughs) that pass a point per second is called the frequency (f ). The unit of frequency is cycles per second or hertz (Hz). The time in seconds between two adjacent peaks (or troughs) is called period (T ). Frequency is the reciprocal of period: f = 1 T. Wave speed (v) is given by v = f λ. Review questions PHYSICALLY SPEAKING The items in the columns are not in their correct order. Copy the table and match each of the key physics concepts with their correct definition, symbol and units. CONCEPT DEFINITION SYMBOL UNIT Amplitude Distance between a peak and its nearest neighbour f hertz (Hz or s 1 ) Displacement Time between a peak and its nearest neighbour d joule (J) Distance The number of peaks that pass a fixed point every second s metre (m) Energy The ability to move an object v metre (m) Frequency The rate of change of distance v metre (m) Period The rate of change of displacement λ metre (m) Speed The straight-line length and direction between two points A metres per second (m s 1 ) Velocity The length of the path between two points T metres per second (m s 1 ) Wavelength The distance between a wave peak and the wave equilibrium point E second (s) 92

16 THE WORLD COMMUNICATES REVIEWING 1 The idea of frequency can be applied to any situation that repeats at regular intervals. a Given that the hands of a clock return to their starting positions at regular intervals, calculate the periods of these hands. b Calculate the frequencies of the second, minute and hour hands. 2 You can make water waves by touching and removing your finger from the surface of water at regular intervals. Describe what must happen to the frequency at which you touch the water so that you can increase the wavelength of the water waves. 3 A rope has one end tied to a wall while you hold the other end. You now wiggle the rope up and down to produce a wave that travels along the rope. Describe what happens to the wavelength on the rope if you wiggled the rope with a higher frequency. 4 What is the distance a wave travels during one period? 5 Identify the main energy types used in the communication methods listed below. a satellite b mobile phone c television d radio e fax 6 Complete the following table to summarise the transmitter, transport medium/method and receiver for each device. DEVICE TRANSMITTER TRANSPORT MEDIUM/METHOD Radio Mobile phone Landline phone RECEIVER 7 Classify each of the following as mechanical or electromagnetic (EM) waves and whether they are one-, two- or three-dimensional. TYPE OF WAVE MECHANICAL OR EM WAVE DIMENSION Sound Light Surface water wave Slinky spring y 8 a Label the wave in Figure with the features listed below in part b. b Identify which two letters best represent each of the following. D H i ii amplitude wavelength A C E G x iii rest position iv v crest trough. B Figure F 93

17 5 Moving energy around: waves Present diagrammatic information about transverse and longitudinal waves, direction of particle movement and the direction of propagation. 9 a In Figure 5.7.4, each dot represents a particle of air. For this sound wave, construct a rough graph of pressure (y-axis) versus position (x-axis). b Now construct a rough graph of pressure versus position for the same wave, half of one period later. Solve problems and analyse information by applying the mathematical model v = f λ to a range of situations. Present and analyse information from displacement time graphs for transverse wave motion. Figure wave direction SOLVING PROBLEMS 10 The hydrogen gas that fills the universe emits a radio wave frequency of 1420 MHz. Calculate its wavelength. The speed of light is m s Mobile phones use a frequency of approximately 2 GHz of EM waves. Calculate the wavelength of these waves. 12 The surf on the beach hits the shore once every 5 s. The distance between the crests of these waves is 6 m. Calculate the speed of these waves. 13 A water wave moves so that an observer sees 5 waves pass her every second. The distance between crests is noted to be 1.5 m. Calculate the speed of the wave. 14 A student throws a rock into a pond of water and counts the number of ripples coming towards the shore, the f = 10 Hz. The distance between the first and eleventh crest is 5 m. Calculate the speed of the ripple. 15 A leaf falls from a tree and swings from side to side as it falls to the ground. You notice that it swings back and forth 4 times before it lands on the ground in 2 s. Calculate the frequency of oscillation. 16 Jack and Jill are standing in the water on the beach and are 10 m apart. They bob up and down as the waves move past them. At one instant, Jill is at the crest of a wave while Jack is at the trough. See Figure a Calculate the wavelength of the waves. b Half a second later, Jill is at the trough while Jack is at the crest. Calculate the frequency of bobbing up and down. c Calculate the speed of the wave. 10 m 10 m Figure

18 THE WORLD COMMUNICATES 17 The waves generated in the Earth during an earthquake are known as seismic waves. A seismograph is an instrument that records the wave motion of the ground by tracing the changing amplitude of the wave with time, as shown on the seismogram, which is simply a graph of displacement (y-axis) versus time (x-axis). From the graph shown in Figure 5.7.6: a Estimate the maximum frequency. b Estimate the maximum amplitude Displacement (cm) Figure Time (s) 18 The vertical height aboveground of a girl on a swing can be represented approximately by a sine wave on a graph, where height (y-axis) versus time (x-axis) is plotted (see Figure 5.7.7). The lowest point of the swing is 0.5 m aboveground. a Calculate the amplitude of the wave. b Calculate the frequency of the swing Height (m) Figure Time (s) 95