A uniform rope of mass `m` and length `L` hangs from a celling. (a) Show that the speed of a transverse wave on the rope is a function of `y`, the distance from the lower end, and is given by `t = 2sqrt(L//g)`.

Explanation

To solve the problem step by step, we need to analyze the wave speed on a hanging rope. Here's the detailed solution:

### Step 1: Understand the Parameters
We have a uniform rope of mass \( m \) and length \( L \) hanging from the ceiling. The speed of a transverse wave on the rope depends on the tension in the rope and the mass per unit length (linear density) of the rope.

### Step 2: Define Mass per Unit Length
The mass per unit length \( \mu \) of the rope is given by:
\[
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