Chapter 16 - 16 Wave Motion CHAPTER OUTLINE 16.1 16.2 16.3...

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16 CHAPTER OUTLINE 16.1 Propagation of a Disturbance 16.2 Sinusoidal Waves 16.3 The Speed of Waves on Strings 16.4 Reflection and Transmission 16.5 Rate of Energy Transfer by Sinusoidal Waves on Strings 16.6 The Linear Wave Equation Wave Motion ANSWERS TO QUESTIONS Q16.1 As the pulse moves down the string, the particles of the string itself move side to side. Since the medium—here, the string—moves perpendicular to the direction of wave propagation, the wave is transverse by definition. Q16.2 To use a slinky to create a longitudinal wave, pull a few coils back and release. For a transverse wave, jostle the end coil side to side. Q16.3 From v T = µ , we must increase the tension by a factor of 4. Q16.4 It depends on from what the wave reflects. If reflecting from a less dense string, the reflected part of the wave will be right side up. Q16.5 Yes, among other things it depends on. v A fA vA max = = = ω π π λ 2 2 . Here v is the speed of the wave. Q16.6 Since the frequency is 3 cycles per second, the period is 1 3 second = 333 ms. Q16.7 Amplitude is increased by a factor of 2 . The wave speed does not change. Q16.8 The section of rope moves up and down in SHM. Its speed is always changing. The wave continues on with constant speed in one direction, setting further sections of the rope into up-and-down motion. Q16.9 Each element of the rope must support the weight of the rope below it. The tension increases with height. (It increases linearly, if the rope does not stretch.) Then the wave speed v T = µ increases with height. Q16.10 The difference is in the direction of motion of the elements of the medium. In longitudinal waves, the medium moves back and forth parallel to the direction of wave motion. In transverse waves, the medium moves perpendicular to the direction of wave motion. 473
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474 Wave Motion Q16.11 Slower. Wave speed is inversely proportional to the square root of linear density. Q16.12 As the wave passes from the massive string to the less massive string, the wave speed will increase according to v T = µ . The frequency will remain unchanged. Since v f = λ , the wavelength must increase. Q16.13 Higher tension makes wave speed higher. Greater linear density makes the wave move more slowly. Q16.14 The wave speed is independent of the maximum particle speed. The source determines the maximum particle speed, through its frequency and amplitude. The wave speed depends instead on properties of the medium. Q16.15 Longitudinal waves depend on the compressibility of the fluid for their propagation. Transverse waves require a restoring force in response to sheer strain. Fluids do not have the underlying structure to supply such a force. A fluid cannot support static sheer. A viscous fluid can temporarily be put under sheer, but the higher its viscosity the more quickly it converts input work into internal energy. A local vibration imposed on it is strongly damped, and not a source of wave propagation.
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