Physics for Geologists, Second edition

More documents

Recommendations

Info

11 Acoustics: sound and other waves Sound Mechanical vibrations (i.e. elastic waves) with frequencies between about 50 Hz and 24 kHz can be detected by the human ear, and so constitute the audible range (much as there is a visible spectrum of colours in the range of electromagnetic radiation). The pure tones of music are very precisely related to frequencies, with middle C being 263 Hz. A blow on a bell sets the bell vibrating. The part moving out compresses the air a little, and a wave is propagated; when it moves in, the air is rarefied a little and it too is propagated. Sound in air, water and other fluids (e.g. the outer core of the Earth), consists of compression-dilation waves. When these reach your ear, sympathetic movements are induced in your eardrum with exactly the same frequencies, and you hear the note belonging to that frequency. The amplitude of the wave is not maintained, mainly because energy is dispersing over the expanding surface of a sphere (nearly), which increases in area as the square of the distance from the source as it propagates from the source. So the wave is attenuated, and the sound gets weaker with distance from the source. You can dampen the sound by touching the bell. The size of the bell determines the note emitted when it is struck. Laplace showed that the speed or velocity of sound in a gas is given by where p is the pressure, p is the mass density of the gas and y is the ratio of the specific heat capacity of the gas at constant pressure to its specific heat capacity at constant volume, cp/c,. This is strictly valid for ideal gases that obey Boyle's law (known as Mariotte's law in some countries). For gases with molecules consisting of only one type of atom, called monatomic gases, such as H2 and 0 2, y = 1.67; for diatomic gases, such as C02, y = 1.41. For polyatomic gases, the ratio is close to unity. For ideal gases, p/p = RT, where R is the gas constant and T is the absolute temperature; and the mass density is directly proportional to the pressure. So the speed of sound in a gas is independent of pressure or density but proportional to the square root of Copyright 2002 by Richard E. Chapman
Acoustics: sound and other waves 107 its absolute temperature (from Equation 11.1). The speed of sound in air at 20°C is about 343 m s-'. So a thunder clap heard 10 s after the lightning was seen will be about 3.5 km away. In water, y x 1, and the equation is usually written c = (y/~p)1/2 or c = ( ~/p)'/~ where B is the compressibility of the water (1/K, with dimensions M-'LT~, inverse pressure) and K is the bulk modulus.' The bulk modulus of water is about 2.1 GPa (lo9 pascals), and its mass density about 1000 kg/m3, so the speed of sound in fresh water is about 1450ms-', being faster in warmer water than colder because the speed is inversely proportional to the square root of the mass density. So the explosion of a mine in the sea is felt on the hull of a minesweeper before it is heard. Sound also propagates in solids, but in this case there are three types of waves: longitudinal (compression-dilation), transverse (shear) and surface waves. The compressional waves are fastest. The speed of sound - that is, the speed of the compression-dilation wave travelling longitudinally - is given by (~/p)'/~, where E is Young's modulus of elasticity for the solid (see page 88). Indeed, Young's modulus is measured in rods by timing the return of a sonic pulse. The speed of the shear wave is (~/p)'/~. The shear modulus, G, of fluids is zero: shear waves cannot be transmitted in fluids. Sound waves are reflected by solid surfaces - the echo. They travel at different speeds in different media and are therefore refracted much as light is refracted, and Snell's Law applies (see page 44). Huygens' construction of wave-fronts also applies (page 45). The Doppler effect has been noticed by all observant people. When a locomotive passes, blowing its horn, the pitch or note changes as it passes, becoming lower as the horn recedes. It would therefore be reasonable to assume that the note heard as the locomotive approached was higher than the natural note of the horn that the driver and passengers hear, and that you would hear if both you and the horn were travelling with the same velocity (in the same direction). If the horn emits sound at a frequency of n Hz at velocity c m s-' while the locomotive travels at a relative velocity V m s-' towards you, the horn emits n waves in one second, but they are contained not in a length c metres, but in (c- V) m. The pitch of the note is raised by a factor c/(c- V). Conversely, as the locomotive recedes, it is lowered by c/(c + V). A horn that gives middle C on a locomotive travelling at 25 m s-' (90 km h-') will sound more like D flat when approaching a stationary observer and B sharp when receding. These are relative velocities; the ear does not know if it is stationary or not. The effect is exactly the same if you pass a stationary horn that is blowing. The sound is transmitted at speed c in all directions, unaffected by the 1 The form c = (K/~)'/~ is also valid for ideal gases, where K is the adiabatic compressibility, corresponding to the bulk modulus in solids. (Adiabatic means that heat neither enters nor leaves the system.) Copyright 2002 by Richard E. Chapman
Page 1 and 2:
Physics for Geologists Second editi
Page 3 and 4:
Copyright 2002 by Richard E. Chapma
Page 5 and 6:
... vlii Contents Polarization 47 L
Page 7 and 8:
Figures Copyright 2002 by Richard E
Page 9 and 10:
Tables Copyright 2002 by Richard E.
Page 11 and 12:
xiv Preface waves diminishes with d
Page 13 and 14:
xvi Preface provides. This book is
Page 15 and 16:
xviii Acknowledgements to K. Whaler
Page 17 and 18:
xx Symbols mass refractive index bu
Page 19 and 20:
2 Basic concepts Table 1.1 Dimensio
Page 21 and 22:
4 Basic concepts Table 1.2 Basic SI
Page 23 and 24:
6 Basic concepts pascal (Pa) and si
Page 25 and 26:
8 Basic concepts all the relevant d
Page 27 and 28:
10 Basic concepts relating them by
Page 29 and 30:
2 Force The dimensions of force are
Page 31 and 32:
14 Force The ratio of the Moon's ac
Page 33 and 34:
16 Force Figure 2.1 The sum of the
Page 35 and 36:
18 Force When a motorcycle takes a
Page 37 and 38:
20 Force Figure 2.3 Torque is the p
Page 39 and 40:
22 Force How does momentum differ f
Page 41 and 42:
24 Force the weights - that is, the
Page 43 and 44:
26 Force Figure 2.6 Wall-sticking i
Page 45 and 46:
3 Gravity Universal gravity When di
Page 47 and 48:
30 Gravity are significant to geolo
Page 49 and 50:
32 Gravity Figure 3.2 The tractive,
Page 51 and 52:
34 Gravity Mean sea level It might
Page 53 and 54:
36 Gravity The benefits of space fl
Page 55 and 56:
38 Gravity Figure 3.6 Profile of th
Page 57 and 58:
40 Gravity Figure 3.8 The siphon at
Page 59 and 60:
4 Optics Light is an electromagneti
Page 61 and 62:
44 Optics Figure 4.2 Refraction. (a
Page 63 and 64:
46 Optics The coeficient of reflect
Page 65 and 66:
48 Optics only the light oscillatin
Page 67 and 68:
50 Optics called Iceland Spar. Two
Page 69 and 70:
52 Optics Diffraction If you shine
Page 71 and 72: 54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75 and 76: 5 Atomic structure and age-dating P
Page 77 and 78: 60 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103 and 104: Stress and strain 87 than some natu
Page 105 and 106: These three elastic constants are r
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
Page 115 and 116: Stress and strain 99 from which we
Page 117 and 118: 10 Sea waves The nature of water wa
Page 119 and 120: Sea waves 103 Figure 10.1 Wave moti
Page 121: Sea waves 105 refraction by islands
Page 125 and 126: Acoustics: sound and other waves 10
Page 127 and 128: 12 Fluids and fluid flow Introducti
Page 129 and 130: Fluids and fluid flow 1 13 Figure 1
Page 131 and 132: Fluids and fluid flow 115 Figure 22
Page 133 and 134: Fluids and fluid flow 117 and the f
Page 135 and 136: water above a vertical thickness h
Page 137 and 138: Fluids and fluid flow 121 where V i
Page 139 and 140: Fluids and fluid flow 123 ardentes,
Page 141 and 142: Fluids and fluid flow 125 Figure 12
Page 143 and 144: - 14 $ 12 E 10 K .- 3 8 r cll + 6 0
Page 145 and 146: Fluids and fluid flow 129 the liqui
Page 147 and 148: Some dangers of mathematical statis
Page 155 and 156: Appendix 139 What would happen if y
Page 157 and 158: Notes 141 and since x is very large
Page 159 and 160: References Allum, J. A. E. (1966) P
Page 161 and 162: References 145 -(1950) 'Mechanism o
Page 163: Further reading 147 Trigg, G. L. an
show all

Physics for Geologists, Second edition

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?