Year 11 Physics Unit 2 Area of Study 1 Wave-­‐like properties of Light Chapter 7 Outcome On completion of this area of study, you should be able to describe and explain the wave model of light, compare it with the particle model of light and apply it to observed light phenomena in practical investigations. By the end of this chapter should be able to describe You will have covered the wave-­‐like properties of light including: • How scientists use models to organize and explain phenomena • The differences between transverse waves and longitudinal waves • How to represent waves • How to define waves by their amplitude, wavelength, period and frequency • The speed of travel of waves • The relationship between the speed of travel, frequency, period and wavelength of a wave. THE NATURE OF WAVES 7.1 Introducing waves Why combine the study of waves and light? For centuries there were different views on the nature of light. Some thought it was made up of waves, similar to that of water. Others thought it was made up of very small particles. In order to compare the properties of light with those of wave we must first understand the properties of waves. Once we have a good understanding of waves we will look at the behaviour of light and compare it to the wave behaviour. In science this is called modelling. If we don’t understand something (like the nature of light) we look at its properties and try to relate them to something we know or understand (the properties of waves). Waves Sometimes it is really obvious that energy is being transferred. A golf club hits a golf ball and the ball flies through the air; or the water stored in a dam is released, making a turbine spin. In all of these cases energy is transferred from one location to another. There is another manner in which energy can be transferred from one location to another. This mechanism does not involve a single body carrying the energy with it from its origin to its final location, but rather the energy is carried through the particles of a substance. A dramatic example of this is a tsunami—a huge ocean wave created when there is a movement in the Earth’s crust under the sea. The energy created at the location of the shift in the crust is passed along by the particles of the ocean water at speeds of up to 800 km h−1, and can reach the coastline in the form of a towering water wave that causes devastation. None of the water 1 particles that flow onto the shore will have been originally located near the source of the tsunami. Only the energy has been passed along. Energy being transferred from one location to another (by the passing of the energy from one particle to the next) within a substance is called a mechanical wave. The substance carrying the wave is called the medium. Mechanical waves A mechanical wave involves the passing of a vibration through an elastic medium. Energy must be present at the source of the wave and this energy is described as being carried by the wave. Overall, the medium itself is not displaced. Examples of mechanical waves include the sound waves emitted by a loudspeaker, and the disturbance that travels along a guitar string when it is plucked. A model of an elastic medium is shown in Figure 7.3. Balls joined together by springs represent the particles of an elastic medium. Each ‘particle’ occupies its own mean (average) position. An initial disturbance of the first particle to the right will result in energy being passed along from particle to particle. The particles are not all disturbed at the same time; rather the disturbance gradually passes from one particle to the next. Also note that, for example, as particle 2 pushes against particle 3, particle 3 will push back on particle 2. Hence particle 2 is returned to its mean position after it has played its role in passing on the energy. Ideally all of the energy that was present initially will be passed right through the medium. Wave pulses and continuous waves A wave pulse is a single disturbance is passed through a medium. Each particle involved in carrying the energy is displaced once as the pulse passes through, and then the particles gradually oscillate back to their mean positions. Continuous waves are created when there is a repetitive motion or oscillation at the wave source, involving more than one initial disturbance or pulse at the origin. Energy is carried away from the source in the form of a continuous wave. For example, a vibrating loudspeaker produces sound waves in air is a continuous wave. When a medium is carrying a continuous wave, the particles of the medium will vibrate about their mean position in a regular, repetitive manner. These are also called periodic waves as the motion of the particles repeats itself after a particular period of time. Please complete questions 1 – 3 on page 231 of you textbook 2 Transverse and longitudinal waves As all waves carry energy, for any wave the direction of travel of energy can be considered. There are two clearly different categories of mechanical waves. Longitudinal waves involve particles of the medium vibrating parallel to the direction of travel of the energy. An example of this is shown in Figure 7.5a. As the operator vibrates his hand in a line parallel to the axis of the spring, a longitudinal pulse is created. The particles of the medium (or the windings of the spring in this case) will vibrate in the direction shown. The vibrations are parallel to the direction of travel of the wave. Sound waves are a common example of longitudinal waves. When a speaker cone vibrates, it causes nearby air molecules to vibrate as shown in Figure 7.5b and this is parallel to the direction in which the sound energy is sent. Transverse waves are created when the direction of the vibration of the particle of the medium is 90° (perpendicular) to the direction of travel of the wave energy itself. Figure 7.4a shows an example of how this could be achieved. As the operator shakes her hand in a direction perpendicular to the axis of the spring, a transverse disturbance is created. Each particle of the medium will be moved as a pulse passes through. The particles each vibrate around their mean position, but this vibration is perpendicular to the direction in which the energy is travelling. Figure 7.5 (a) When the vibratory motion and the direction of travel of the wave energy are parallel to one another, a longitudinal wave has been created. (b) Sound waves are longitudinal waves since the molecules of the medium (air molecules) vibrate in the direction of travel of the energy. Sources of one-­‐, two-­‐ and three-­‐dimensional waves One-­‐dimensional waves occur when longitudinal or transverse waves are sent along a spring or rope. The energy travels along the length of the conducting medium. Two-­‐dimensional waves allow energy to be spread in two dimensions. Waves travelling across surfaces are two-­‐dimensional. A ripple travelling outward across the water’s surface when a stone is dropped into a pond is a familiar example of these (see Figure 7.6a). Earthquakes, produce two-­‐dimensional seismic waves that are mechanical waves travelling across the surface of the Earth. When you speak you create three-­‐dimensional waves since the sound-­‐ wave energy spreads out in all three dimensions, though obviously the majority of the energy travels directly outward from the source. Designers of particular speaker systems attempt to ensure that sound waves are spread out equally in all directions. Figure 7.6b shows a three-­‐dimensional pressure wave emitted by a bomb blast. 3 7.1 summary -­‐ Introducing waves •
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Scientists use models to link an unknown entity or observation to something that we are familiar with, in order to gain a better understanding of it. Knowledge of general wave properties will allow the possible wave nature of light to be assessed. Energy must be present at the source of any wave. All waves involve the transfer of energy without a net transfer of matter. A substance carrying a wave is called a medium. A mechanical wave is the passing of energy from one particle to the next within an elastic medium. A wave pulse occurs when a single disturbance is passed through a medium. Continuous waves are created when there is a repetitive motion or oscillation at the wave source. Energy is carried away from the source in the form of a continuous or periodic wave. Longitudinal waves occur when particles of the medium vibrate in the same direction as the direction of travel of the energy. Transverse waves are created when the direction of the vibration of the particle of the medium is perpendicular to the direction of travel of the wave energy itself Please complete questions 4 – 7 on page 231 of your textbook. 7.2 Representing wave features Displacement–distance graphs If a continuous wave was travelling across the surface of water, and we were able to freeze it instantaneously, a cross-­‐section would look something like Figure 7.8a. If the wave then continued, a brief moment later it will have moved slightly to the right and the water particles will have taken up new positions as shown in Figure 7.8b and then Figure 7.8c. The floating cork, like the particles of the medium itself, demonstrates a vertical vibratory motion. The speed of waves Rather than just examining one snapshot, a sequence of graphs can be used to represent a wave that is moving across to the right (see Figure 7.10). By tracking the progress of one crest as it moves to the right, the speed at which the wave is moving can be determined. The use of a dashed line in Figure 7.10 is just to help you keep track of the initial trough and crest that were created. Note that points P and Q and all particles of the medium simply oscillate vertically, while the crests and troughs ‘move’ steadily to the right. 4 Use the series of graphs shown to determine: a) the average speed of the wave b) the horizontal speed of particle P c) the average vertical speed of particle P between t = 0 s and t = 0.025 s. In mechanical waves the speed of the wave is largely determined by the properties of the medium and, of course, by the type of disturbance that is being carried by the medium. 5 The frequency and period of a wave Every mechanical wave must have a vibrating source. The rate at which the source vibrates directly affects the nature of the wave formed. The frequency of a source is the number of full vibrations or cycles that are completed per second. The time interval for one vibration or cycle to be completed is called the period, T, which is measured in seconds (s). EXAMPLE: A student lays a long heavy rope in a straight line across a smooth floor. She holds one end of the rope and shakes it sideways, to and fro, with a regular rhythm. This sends a transverse wave along the rope. Another student standing halfway along the rope notices that two crests and troughs travel past him each second. a) What is the frequency of the wave in the rope? b) What is the frequency of vibration of the source of the wave? c) How long does it take for the student to produce each complete wave in the rope? Displacement – time graphs 6 Wavelength and amplitude 7.1 Summary •
A mechanical wave can be represented at a particular instant by a graph of particle displacement against distance from the source. •
The frequency of a wave, f, is the number of vibrations or cycles that are completed per second, or the number of complete waves that pass a given point per second. Frequency is measured in hertz (Hz). •
The period, T, is the time interval for one vibration or cycle to be completed. •
Frequency f = 1T where f is the frequency of the wave in hertz (Hz), and T is the period of the wave in seconds (s). •
A graph of particle displacement versus time can be drawn for the particles of a medium that is carrying a continuous wave. The period of the wave can be read directly from this graph. •
Graphs of particle displacement versus distance from the source can be used to determine the wavelength of a continuous wave. •
The wavelength, λ, of a continuous wave is the distance between successive points having the same displacement and moving in the same direction; that is, the distance between points that are in phase. •
The amplitude, A, of a wave is the value of the maximum displacement of a particle from its mean position. Key Readings Section 7.2 Key Questions Section 7.2 Questions 1-­‐8, pp238-­‐239 7 7.3 Waves and wave interactions The frequency of the source and the speed of the wave in the medium determine the wavelength of a mechanical wave. • The wave equation states: v = f λ = λ/T where v = speed of the wave in metres per second (m s ) −1
f = frequency of the wave in hertz (Hz) λ = wavelength of the wave in metres (m) T = period of the wave in seconds (s). • For a wave of a given speed, λ ∝ l/f . • For a source of a given frequency, λ ∝ v. EXAMPLE: A person standing on a pier notices that every 4.0 seconds the crest of a wave travels past a certain pole that sticks out of the water. The crests are 12 metres apart. Calculate: a the frequency of the waves b the speed of the waves. 8 Waves meeting barriers Superposition: waves interfering with waves • The principle of superposition states that when two or more waves travel in a medium the resulting wave, at any moment, is the sum of the displacements associated with the individual waves. 9 Constructive interference occurs when two waves meet that have particle displacements in the same direction. Destructive interference occurs when two waves meet that have particle displacements in opposite directions. Now we can look at light!
Now that we have put together the rules describing the characteristics of waves, the question as to whether light has a wave nature can be addressed. Waves have numerous characteristics and they have been worth examining in their own right. We have been able to conclude the following: • Waves involve the transfer of energy without an overall transfer of matter. • Mechanical waves require a vibrating item at their source and a medium to carry them. • Waves can be categorised as longitudinal or transverse. • The wave equation, v = fλ, describes the relationship between the speed, frequency and wavelength of a wave. • Waves can reflect at boundaries and this will sometimes produce a change of phase. • Waves can be added according to the principle of superposition and this can result in constructive or destructive interference. Key Readings pages 240 -­‐246 Key Questions 1 to 10 page 247 In Chapter 8 we will go on to discuss whether it is appropriate to use waves as our chosen model for light. For this to be fitting, light must appear to behave largely in the same manner as waves do. That is, if a wave model for light is to be accepted, then it will need to explain the known behaviours of light. A very successful model would illustrate all of the behaviours of light. This is not likely. It is more likely that we will be able to make use of the insight that waves provide, and use this insight to further our understanding of the nature of light. 10