A string of linear density 0.2 kg/m is stretched with a force of 500 N. A transverse wave of length 4.0 m in set up along it. The speed of wave is

Options

A. 50 m/s
B. 75 m/s
C. 150 m/s
D. 200 m/s

Explanation

To find the speed of a transverse wave on a string, we can use the formula:

\[ v = \sqrt{\frac{T}{\mu}} \]

where:
- \( v \) is the speed of the wave,
- \( T \) is the tension in the string,
- \( \mu \) is the linear density of the string.

### Step-by-Step Solution:

1. **Identify the given values**:
- Linear density (\( \mu \)) = 0.2 kg/m
- Tension (\( T \)) = 500 N

2. **Substitute the values into the formula**:
\[ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{500 \, \text{N}}{0.2 \, \text{kg/m}}} \]

3. **Calculate the denominator**:
\[ \mu = 0.2 \, \text{kg/m} \]
Thus,
\[ \frac{500}{0.2} = 2500 \]

4. **Take the square root**:
\[ v = \sqrt{2500} = 50 \, \text{m/s} \]

5. **Conclusion**:
The speed of the wave on the string is \( 50 \, \text{m/s} \).

### Final Answer:
The speed of the wave is \( 50 \, \text{m/s} \).