A string of length L and mass M hangs freely from a fixed point . Calculate the velocity of the transverse wave along the string at any position.
(b)Calculate time taken by a transverse pulse to traverse the string.

Explanation

To solve the problem step by step, we will calculate the velocity of the transverse wave along the string at any position and then find the time taken by a transverse pulse to traverse the string.

### Step 1: Understanding the Setup
Consider a string of length \( L \) and mass \( M \) hanging freely from a fixed point. The string is under the influence of gravity, and we need to analyze the tension at any point along the string.

### Step 2: Determine the Tension at a Point
Let’s take a point at a distance \( x \) from the bottom of the string. The mass of the segment of the string below this point is given by:
\[
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