A uniform rope of length `12m` and mass `6kg` hangs vertically from a rigid support. A block of mass `2kg` is attached to the free end of the rope. A transverse pulse of wavelength `0.06m` is produced at the lower end of the rope. What is the wavelength of the pulse whwn it reaches the top of the rope?

Explanation

To solve the problem, we need to determine the wavelength of a transverse pulse when it reaches the top of a vertically hanging rope. Let's break down the solution step by step:

### Step 1: Understand the system
We have a rope of length 12 m and mass 6 kg hanging vertically. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse with a wavelength of 0.06 m is generated at the lower end of the rope.

### Step 2: Calculate the tension at the lower end of the rope
At the lower end of the rope, the only force acting on the rope is the weight of the block attached to it. The tension (T1) at this point is given by:
\[ T_1 = m_{\text{block}} \cdot g \]
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