A rope of total mass m and length L is suspended vertically. Show that a transverse pulse travels the length of the rope in a time interval `Deltat=2sqrt(L//g`. Sugestion: first find an expression for the wave speed at any point a distance x from the lower end by considering the rope's tension as resulting from the weight of the segment below that point.

Explanation

To solve the problem, we need to find the time interval \( \Delta t \) for a transverse pulse to travel the length of a vertically suspended rope. We will derive the expression step by step.

### Step 1: Understanding the Tension in the Rope
The tension \( T \) in the rope at a distance \( x \) from the lower end is due to the weight of the segment of the rope below that point. The mass of the segment of the rope below point \( x \) can be expressed as:
\[ m_x = \frac{m}{L} \cdot (L - x) \]
where \( m \) is the total mass of the rope and \( L \) is its total length.
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