(II) A ski gondola is connected to the top of a hill by a...

(II) A ski gondola is connected to the top of a hill by a steel cable of length $660 \mathrm{~m}$ and diameter $1.5 \mathrm{~cm} .$ As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took $17 \mathrm{~s}$ for the pulse to return, $(a)$ What is the speed of the pulse? (b) What is the tension in the cable?

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Key Concepts

Wave Propagation in a Tensioned String

This concept explains that the speed of a transverse wave traveling along a stretched cable or string is dependent on both the tension within the string and its linear mass density. The relationship is given by the formula v = ?(T/?), indicating that higher tension or lower mass per unit length leads to faster wave propagation.

Linear Mass Density

Linear mass density is the mass per unit length of a material, which is crucial for understanding the dynamics of wave propagation. It connects the intrinsic physical properties of the cable with the behavior of waves moving through it. Calculating linear mass density involves the material's volume and density, taking into account dimensions like diameter in cylindrical objects.

Time of Flight and Round-Trip Measurement

This concept involves using the measured time it takes for a wave pulse to travel through a medium and back (round trip) to determine the speed of the wave. By knowing the total distance traveled and the time elapsed, one can calculate the wave speed, which subsequently is used in determining other properties such as the tension in the cable.

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