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CHAPTER 16 WAVES AND SOUND CONCEPTUAL QUESTIONS ____________________________________________________________________________________________ 1. REASONING AND SOLUTION As Figure 16.4 shows, in a water wave, the wave motion of the water includes both transverse and longitudinal components. The water at the surface moves on nearly circular paths. When the wave passes beneath a fishing float, the float will simultaneously bob up and down, as well as move back and forth horizontally. Thus, the float will move in a nearly circular path in the vertical plane. It is not really correct, therefore, to say that the float bobs straight "up and down." ____________________________________________________________________________________________ 2 . REASONING AND SOLUTION "Domino Toppling" is an event that consists of lining up an incredible number of dominoes and then letting them topple, one after another. As the dominoes topple, their displacements contain both vertical and horizontal components. Therefore, the disturbance that propagates along the line of dominoes has both longitudinal (horizontal) and transverse (vertical) components. ____________________________________________________________________________________________ 3 . REASONING AND SOLUTION A longitudinal wave moves along a Slinky at a speed of 5 m/s. We cannot conclude that one coil of the Slinky moves through a distance of 5 m in one second. The quantity 5 m/s is the longitudinal wave speed, v speed ; it specifies how fast the disturbance travels along the spring. The wave speed depends on the properties of the spring. Like the transverse wave speed, the longitudinal wave speed depends upon the tension F in the spring and its linear mass density m / L . As long as the tension and the linear mass density remain the same, the disturbance will travel along the spring at constant speed. The particles in the Slinky oscillate longitudinally in simple harmonic motion with the same amplitude and frequency as the source. As with all particles in simple harmonic motion, the particle speed is not constant. The particle speed is a maximum as the particle passes through its equilibrium position and reaches zero when the particle has reached its maximum displacement from the equilibrium position. The particle speed depends upon the amplitude and frequency of the particle's motion. Thus, the particle speed, and therefore the longitudinal speed of a single coil, depends upon the properties of the source that causes the disturbance. ____________________________________________________________________________________________ 4 . SSM REASONING AND SOLUTION A wave moves on a string with constant velocity. It is not correct to conclude that the particles of the string always have zero acceleration. As Conceptual Example 3 discusses, it is important to distinguish between the speed of the waves on the string, v wave , and the speed of the particles in the string, v particle . The wave speed v wave is determined by the properties of the string; namely, the tension in the string and the linear mass density of the string. These properties determine the speed with which the disturbance travels along the string. The wave speed will remain constant as long as these properties remain unchanged.
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