A nylon string has mass 5.50 g andlength L 5 86.0 cm. The lower endis tied to the floor

Chapter 18, Problem 76

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A nylon string has mass 5.50 g andlength L 5 86.0 cm. The lower endis tied to the floor, and the upperend is tied to a small set of wheelsthrough a slot in a track on whichthe wheels move (Fig. P18.76). Thewheels have a mass that is negligiblecompared with that of thestring, and they roll without frictionon the track so that the upperend of the string is essentially free.At equilibrium, the string is verticaland motionless. When it is carrying a small-amplitudewave, you may assume the string is always under uniformtension 1.30 N. (a) Find the speed of transversewaves on the string. (b) The strings vibration possibilitiesare a set of standing-wave states, each witha node at the fixed bottom end and an antinode atthe free top end. Find the nodeantinode distancesfor each of the three simplest states. (c) Find the frequencyof each of these states.

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