A string of mass 2.50kg is under a tension os 200N. The length of the stretched string is 20.0m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?

Options

A. 1s
B. `0.5` s
C. 2s
D. data given is insufficient

Explanation

To solve the problem, we need to determine how long it takes for a disturbance to travel along a string under tension. We will follow these steps:

### Step 1: Determine the linear mass density (μ)
The linear mass density (μ) is calculated using the formula:
\[ \mu = \frac{m}{L} \]
where:
- \(m\) = mass of the string = 2.50 kg
- \(L\) = length of the string = 20.0 m

Substituting the values:
\[ \mu = \frac{2.50 \, \text{kg}}{20.0 \, \text{m}} = 0.125 \, \text{kg/m} \]

### Step 2: Calculate the wave speed (v)
The speed of a wave on a string is given by the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
where:
- \(T\) = tension in the string = 200 N

Substituting the values:
\[ v = \sqrt{\frac{200 \, \text{N}}{0.125 \, \text{kg/m}}} \]

Calculating the value inside the square root:
\[ \frac{200}{0.125} = 1600 \]
Thus,
\[ v = \sqrt{1600} = 40 \, \text{m/s} \]

### Step 3: Calculate the time taken (t) for the disturbance to travel the length of the string
The time taken for the wave to travel the length of the string can be calculated using the formula:
\[ t = \frac{L}{v} \]
Substituting the values:
\[ t = \frac{20.0 \, \text{m}}{40 \, \text{m/s}} = 0.5 \, \text{s} \]

### Final Answer
The time taken for the disturbance to reach the other end of the string is \(0.5\) seconds.

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