One end of a nylon rope is tied to a stationary support at the top of a vertical

Question

One end of a nylon rope is tied to a stationary support at the top of a vertical mine shaft that is 80.0 m deep. The rope is stretched taut by a box of mineral samples with mass 20.0 kg suspended from the lower end. The mass of the rope is 2.00 kg. The geologist at the bottom of the mine signals to his colleague at the top by jerking the rope sideways. What is the speed of a transverse wave on the rope at the bottom? If a point on the rope is given a transverse simple harmonic motion with a frequency of 20 Hz, what is the wavelength of the wave? How would the speed of the transverse wave on the rope at the top look like? When the tension in a cord is 75.0 N, the wave speed is 140 m/s. What is the linear mass density of the cord?

Explanation / Answer

speed of the wave = sqrt(tension / (mass / length))

speed of the wave = sqrt(20 * 9.8 / (2 / 80))

speed of the wave = 88.54 m/s

speed = wavelength * frequency

88.54 = wavelength * 20

wavelength = 4.427 m

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