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CHASE_HR17_ver1 - Chapter 17 Waves II The physics of sound...

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1 Chapter 17 The physics of sound waves is the basis of many fields of research, ranging from physiology, acoustic engineering, aviation, paleontology, military science and biology. In this chapter we introduce fundamental concepts and explore the properties of sound waves. Waves- II 17- 1
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2 In this course, a sound wave is roughly defined as any longitudinal wave (particles moving along the direction of wave propagation). Sound Waves 17- Fig. 17-2 Wavefronts : surfaces over which the the oscillations due to the sound wave have the same value, e.g, at maximum crest. Rays : directed lines perpendicular to the wavefronts, indicate direction the direction of travel of the wavefronts Spherical waves Plane waves Particle motion
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3 Speed of any mechanical wave depend on both Inertial properties of medium (to store kinetic energy) Elastic properties of medium (to store potential energy) The Speed of Sound 17- elastic property inertial property v τ μ = = In air (volume density) and (bulk modulus) B μ ρ τ change in pressure produces a fractional change in volume Material that is hard to compress large p B V V p V V B = - Speed of Sound: B v ρ =
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4 Formal Derivation of the Speed of Sound Formula 17- x t v ∆ = Fig. 17-3 ( 29 (net force) F pA p p A pA = - + ∆ = -∆ (mass) m V A x Av t ρ ρ ρ = = = (acceleration) v a t = ( 29 v F ma pA Av t t ρ = → -∆ = 2 p v v v ρ = - and V A v t v V Av t V A v t V Av t v ∆ ∆ = = ∆ ∆ = = 2 p p B v B v v v V V ρ ρ = - = - = = Pulse travels right to left move with pulse. In frame of ref where Pulse is stationary the element moves to right
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5 Demo 17.1: Lecture ( Beer ) Hall Longitudinal Wave 17- s x s t s=0 everywhere, equilibrium s(x,t=constant) s m s m s m s m s m s m s m Where is s max or min? Where is density max or min?
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6 Fig. 17-5 Traveling Sound Waves 17- Fig. 17-6 ( 29 m m p v s ρϖ =
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7 Traveling Sound Waves, Part 2 17- ( 29 ( 29 Displaceme c nt: s , o m s x t s kx t ϖ = - Fig. 17-7 ( 29 ( 29 ( 29 Pressure Amplitu s n : i de , m m m p x t p kx t p v s ϖ ρϖ = ∆ - s=0 s=0 x =
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8 17- Checkpoint 1 When the oscillating air element in Fig. 17- 7 a is moving rightward through point of zero displacement, is the pressure in the element (a) at its equilibrium value?
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