A rope of length L and mass m hangs freely from the ceiling. The velocity of transverse wave as a function of position x-along the rope is proportional to

Options

A. `x^(0)`
B. `sqrt(x)`
C. `(1)/(sqrt(x))`
D. x

Explanation

To solve the problem, we need to determine how the velocity of a transverse wave in a hanging rope varies with position along the rope. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the parameters
We have a rope of length \( L \) and mass \( m \) hanging from the ceiling. The tension in the rope varies with the position \( x \) from the bottom of the rope.

### Step 2: Identify the formula for wave velocity
The velocity \( v \) of a transverse wave on a string (or rope) is given by the formula:
\[
...