A string of length 10.0 m and mass 1.25kg stretched with a tension of 50N. If a transverse pulse is created at one end of the string, how long does it take to reach the other end ?

Options

A. 0.5s
B. 1.0s
C. 1.5s
D. 2.0s

Explanation

To solve the problem of how long it takes for a transverse pulse to travel along a string, we can follow these steps:

### Step 1: Calculate the mass per unit length (μ) of the string
The mass per unit length (μ) is given by the formula:
\[ \mu = \frac{m}{L} \]
where \( m \) is the mass of the string and \( L \) is the length of the string.

Given:
- Mass \( m = 1.25 \, \text{kg} \)
- Length \( L = 10.0 \, \text{m} \)

Calculating:
\[ \mu = \frac{1.25 \, \text{kg}}{10.0 \, \text{m}} = 0.125 \, \text{kg/m} \]

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

Given:
- Tension \( T = 50 \, \text{N} \)

Calculating:
\[ v = \sqrt{\frac{50 \, \text{N}}{0.125 \, \text{kg/m}}} \]

Calculating the fraction:
\[ \frac{50}{0.125} = 400 \]
Now taking the square root:
\[ v = \sqrt{400} = 20 \, \text{m/s} \]

### Step 3: Calculate the time (t) taken for the pulse to travel the length of the string
The time taken for the pulse to travel the length of the string can be calculated using the formula:
\[ t = \frac{S}{v} \]
where \( S \) is the distance (length of the string) and \( v \) is the velocity.

Given:
- Distance \( S = 10.0 \, \text{m} \)
- Velocity \( v = 20 \, \text{m/s} \)

Calculating:
\[ t = \frac{10.0 \, \text{m}}{20 \, \text{m/s}} = 0.5 \, \text{s} \]

### Final Answer
The time taken for the transverse pulse to reach the other end of the string is **0.5 seconds**.

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