A cowboy ties up one end of a rope of 10.0 m and 0.200 kg to a post and pulls fr

Question

A cowboy ties up one end of a rope of 10.0 m and 0.200 kg to a post and pulls from the other end; in order to stretch the rope horizontally with a tension of 80.0 N. a) Calculate the speed of the transverse waves in the rope. b) If the cowboy moves the rope vertically one end of the rope with a frequency of 6.00 Hz, what is for the transverse waves in  the rope? c) The cowboy pulls with more strength, doubling the tension to 160.0 N. With which frequency must the free end of the rope move up and down in order to produce transverse waves with the same as in (a)?

Explanation / Answer

Length L = 10 m mass M = 0.2 kg Linear density m = M / L                         = 0.02 kg / m Tension T = 80 N (a). Speed of the transverse wave v = [ T / m]                                                        = 63.24 m / s (b). Frequency f = 6 Hz So, wavelength = v / f                           = 10.54 m (c). Tension T ' = 160 N wavelength = 10.54 m speed of the wave v = [ T ' / m ]                                = 89.44 m / s So, frequency F = v /                         = 8.486 Hz

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