Unit 14: Waves and Electromagnetic Radiation 1 Butterflies and Oil Spills
Total Page：16
File Type：pdf, Size：1020Kb
Unit 14: Waves and electromagnetic radiation 1 Butterflies and oil spills Figure 1 Thin-film interference of light waves can give spectacular colours, as seen here in the Morpho rhetenor butterfly. Figure 2 Interference seen in a thin layer of oil on a puddle. Audio 1 Introduction. Download Show transcript 2 Describing waves 2.1 What is a wave? Figure 3 Water waves travelling across the sea and breaking on a beach. Audio 2 Waves. Download Show transcript Figure 4 Energy carried by waves can cause devastation as seen from the wreckage left on the coast of Japan by the tsunami of 2011. Figure 5 Surfing is a happier demonstration of the energy carried by waves. Definition of a wave In many cases a wave can be described as a periodic, or regularly repeating, ‘disturbance’ that conveys energy from one point to another. A field is always necessary in order to have a wave, but a medium is not. 2.2 Wave properties Later, the mathematical description of waves will be considered, but first let’s look at some more qualitative ways in which the properties of waves may be described. While standing on a beach, you will have seen or heard waves break onto the shore with a fairly regular time interval between one ‘crash’ and the next. Each crash represents one wave crest breaking onto the shore and the time interval between two consecutive crashes is known as the period of the wave, usually represented by the symbol . In general, the period of a wave may be defined as the time between one part of the wave (say the crest) passing a fixed point in space and the next identical part of the wave (the next crest) passing the same fixed point. In the case of ocean waves, a convenient fixed ‘point’ is the shoreline. A quantity related to the period of a wave is its frequency. This is the rate at which waves pass a fixed point. The frequency is therefore simply the reciprocal of the period of a wave, . If the period is measured in the SI unit of seconds (s), the frequency will have the SI unit of hertz (Hz), where . As well as being periodic in time, a wave is also periodic in space. The word ‘wave’ is often used to describe a single crash onto the beach, but it really refers to the entire sequence of crests and troughs, stretching away into the distance. The form of that spatial pattern of crests and troughs at any instant of time is called the wave profile. The distance between one wave crest and the next is known as the wavelength of the wave, and is usually represented by the Greek letter lambda . In general, the wavelength of a wave is defined as the distance between one part of the wave profile, at a particular instant in time, and the next identical part of the wave profile at the same instant of time. Two adjacent crests of the wave are a convenient pair of locations to use for this definition, although any pair of equivalent points will do as long as the wave has the same ‘height’ and is changing in the same way at both points. Exercise 1 Try the following thought experiment. Imagine that you are standing on a beach and watching wave crests break on the seashore. (a) If the wavelength suddenly becomes smaller (i.e. the wave crests are closer together than before), but the wave continues travelling at the same speed, what happens to the period of the wave? What happens to the frequency? Answer If the wave crests are closer together, then, as long as the wave is travelling at the same speed as before, a shorter time interval will elapse between each crest breaking on the beach and the next. The period of the wave will therefore be shorter. Since the frequency of a wave is equal to the reciprocal of its period, the frequency of the wave will be higher. (b) If, instead, the waves suddenly begin travelling more slowly across the sea, but with the same wavelength as before, what happens to the period of the wave? What happens to the frequency? Answer If the waves are travelling more slowly across the sea, but with the wave crests the same distance apart as before, there will be a longer time interval between each crest breaking on the beach and the next. The period of the wave will therefore be longer and the frequency of the wave will be lower. You will probably have noticed that the definitions for the period and wavelength of a wave are rather similar. The period is a time interval and refers to instants separated in time; the wavelength is a distance and refers to points separated in space. The relationship between them is clearly related to the speed at which the wave is moving, and that should come as no surprise since speed is the usual way of relating distances and times. Later in this Unit the relationship between the period, wavelength and speed of a wave will be quantified. 2.3 Transverse and longitudinal waves The direction of propagation of a wave is the direction in which the energy is transported. As you have seen, the particles of the medium through which the wave propagates are not themselves permanently transposed from place to place; rather they vibrate periodically about a fixed position. In fact a wave can be thought of as the result of correlated oscillations occurring at every point along the path of the wave. It is the direction of these oscillations that determines whether a particular wave is described as transverse or longitudinal. If the individual oscillations are at right-angles to the direction of propagation of the wave itself, the wave is described as a transverse wave; an example is shown in Figure 6. Here a wave travels along a string that has been jerked up and down at one end. If one small segment of the string is marked by bright colouring, it can be seen that the marked segment simply moves up and down — it doesn’t travel along with the wave. Figure 6 A representation of a wave on a string. The coloured segment moves up and down at right-angles to the direction in which the wave travels. In contrast to this, a sound wave travelling through air is an example of a longitudinal wave. In this case the particles move back and forth in a direction that is parallel to the direction of propagation of the wave, although the mean position of the particles remains unchanged. Longitudinal waves can also be set up in a long spring (a ‘slinky’) by moving one end back and forth along its length. A sound wave travelling through air is similar to this, as shown in Figure 7. Figure 7 (a) Longitudinal waves on a View larger image spring are analogous to (b) sound waves, which are longitudinal waves in air. (c) The sound waves can be represented graphically by plotting the variation of air pressure or density against position. When the end of the spring vibrates back and forth, it generates periodic compressions and extensions of the spring, and these travel along the spring with a uniform speed. In exactly the same way, when human vocal chords vibrate back and forth, they generate periodic compressions and rarefactions in the air, and these travel away from the diaphragm with a uniform speed. In the regions of compression, the pressure and density of the air are higher than average, whereas in the regions of rarefaction the pressure and density are lower than average. These variations of pressure and density can be represented graphically in the way shown in Figure 7c; you should recognise the similarity between these graphs and the graph shown in Figure 6, which is a snapshot of a transverse wave on a string. 2.4 Examples of transverse and longitudinal waves 2.4.1 Sound waves Sound waves are longitudinal waves that can travel through a gas, liquid or solid. As a sound wave passes through air, the pressure oscillations are only of the order of which is very small when compared with normal atmospheric pressure, which is about (the pascal is the SI unit of pressure, defined as ). The range of frequencies audible to human beings is about to , although the ability to hear at the upper end of the range declines quite markedly with age. Frequencies higher than about are termed ultrasonic, and sound above this frequency is referred to as ultrasound. Animals such as dogs and bats can hear frequencies in the ultrasound region; these frequencies are also widely used in medicine (see Figures 8 and 9) and materials testing. Figure 8 Medical uses of ultrasound include monitoring foetal development in pregnancy. The foetal imaging relies on the fact that different tissue types reflect and absorb ultrasound to different extents. Figure 9 Other uses of ultrasound in medicine include shattering kidney stones. The shattering of kidney stones is a type of non-invasive surgery, which relies on the energy carried by the ultrasound wave being transferred to the kidney stone. Animals such as bats, whales and dolphins use the principle of echo location to detect objects using sound. Pulses of sound are sent out in particular directions and their reflections are detected. From the time taken for the pulses to return, the positions of intervening objects can be determined. Humans have copied this technique in a number of ways. Sonar (sound navigation and ranging) can be used to determine the depth of the sea or the location of shoals of fish, for instance.