LECTURE 5 TRAVELING WAVES Instructor: Kazumi Tolich
Lecture 5 2 15.1 The wave model Mechanical waves Electromagnetic and matter waves The transverse and longitudinal waves Traveling waves Waves on a string Sound waves Wave speed is a property of the medium
15.1 Mechanical waves 3 Mechanical waves are the disturbance that passes through a medium, carrying energy with it. A wave disturbance is created by a source and travels outward through the medium at the wave speed. For fun: one of the first human waves in stadiums was at Husky Stadium during a UW football game against Stanford, which was televised and made the human waves popular. https://www.youtube.com/watch?v=fy9pynco_6s
15.1 Electromagnetic and matter waves 4 Electromagnetic waves are waves of an electromagnetic field and travel through a vacuum. They include visible light, radio waves, microwaves, and x rays. Matter waves describe the wave-like characteristics of material particles such as electrons and atoms.
15.1 Transverse and longitudinal waves / Demos 5 Transverse waves are waves in which the motion of the medium is perpendicular to the direction of propagation of the disturbance. Longitudinal waves are waves in which the motion of the medium is along (parallel to) the direction of propagation of the disturbance. Demos: Bell Labs wave machine & Slinky Water waves are a combination of transverse and longitudinal waves.
Quiz: 15.1-1 (Knight P15.7) 6 An earthquake 45 km from a city produces P and S waves that travel outward at 5000 m/s and 3000 m/s, respectively. Once city residents feel the shaking of the P wave, how much time do they have before the S wave arrives in seconds?
Quiz: 15.1-1 answer 7 x = 45 km = 45000 m v + = 5000 m s v. = 3000 m s t + = 1 2 3 = 9 s t. = 1 2 5 = 15 s t. t + = 6 s
15.2 Traveling waves 8 To examine traveling waves, we can apply Newton s laws to the medium, but not wave itself.
Quiz: 15.2-1 A wave on a string is traveling to the right. At this instant, draw the direction of the velocity vector of the piece of string marked with a dot.
Quiz: 15.2-1 The wave is moving to the right, so the dot has to start moving upward in the next instant of time. If you look at the small ribbon on the Slinky, it just goes up and down. No material substance is transferred along the Slinky. A wave transfers energy, but it does not transfer any material or substance.
15.2 Waves on a string 11 Suppose a transverse wave pulse is traveling along a stretched string. The curvature of the string due to the wave leads to a net force that pulls a small segment of the string upward or downward. Each point on the string moves perpendicular to the motion of the wave, so a wave on a string is a transverse wave. An external force created the pulse, but once started, the pulse continues to move because of the internal dynamics of the medium.
15.2 Sound waves 12 When a loudspeaker cone moves forward, it compresses the air in front of it. The compression is the disturbance that travels through the air. A sound wave is a longitudinal wave. The motion of the sound wave is determined by the properties of the air.
15.2 Wave speed is a property of the medium - string/ Demo 13 The speed of a wave on a string, v 9:;<=>, is given by v 9:;<=> = T 9 μ where T 9 is the tension in the string, and μ = B is the linear density of the string, the mass-tolength ratio. C Demo: Tension dependence of wave speed v 9:;<=>
15.2 Wave speed is a property of the medium gas 14 The speed of sound in the gas is given by v 9DE=F = γk IT m = γrt M Where m is mass of an atom, γ is a constant that depends on the gas (γ = 1.67 for monatomic, γ = 1.40 for diatomic, and γ 1.3 for triatomic gasses), k I is the Boltzmann s constant, T is the absolute temperature in kelvin, R is the gas constant, and M is the molar mass. We will use 343 m/s as the default speed of sound in air.
Quiz: 15.2-2 These two wave pulses travel along the same stretched string, one after the other. Compare the wave speeds, v P and v I.
Quiz: 15.2-2 answer v P = v I The wave speed does not depend on the size and shape of the pulse, how the pulse was generated or how far it has traveled only the medium that carries the wave.
Quick: 15.2-3 A wave bounces back and forth on a guitar string; this is responsible for making the sound of the guitar. As the temperature of the string rises, the tension decreases. This the speed of the wave on the string. A. increases B. does not change C. decreases
Quick: 15.2-3 answer A wave bounces back and forth on a guitar string; this is responsible for making the sound of the guitar. As the temperature of the string rises, the tension decreases. This decreases the speed of the wave on the string. v 9:;<=> = Q R S
Quiz: 15.2-4 Suppose you pluck the thinnest guitar string, and at the same time, your friend plucks the thickest guitar string which is under the same tension as the thinnest string. Which note travels faster in the air? A. B. C. Your note Your friend s note They travel at the same speed.
Quiz: 15.2-4 answer 20 They travel at the same speed. Speed of waves relative to the medium in which they are traveling depends on the medium the air. Both notes travels in the same air. Speed of waves do not depend on the motion of the source. Otherwise you cannot enjoy music played by different instruments on a stage.
Example: 15.2-1 (Knight P15.58) 21 A spider spins a web with silk threads of density ρ = 1.3 10 V kg m V and diameter d = 3.0 10 YZ m. A typical tension in the radial threads of such a web is T 9 = 7.0 10 YV N. Suppose a fly hits this web. Which will reach the spider first: the very slight sound of the impact or the disturbance traveling along the radial thread of the web?
15.2 Wave speed is a property of the medium EM waves All electromagnetic waves travel in a vacuum at the speed of light c. c = 3.00 10 ] m s Although light travels more slowly in air than in a vacuum, this value is still a good approximation for the speed of electromagnetic waves through air.