The tension in a stretch string fixed at both ends is changed by `2%`, the fundarmental frequency is founder to get changed by 1.5 Hz . Select the correct statement(s).

Options

A. Wave length of the string of fundamental frequency does not change
B. Velocity of propagation of wave length changes by 2%
C. Velocity of propagation of wave changes by 1%
D. Original frequency is 1500Hz

Answer

To solve the problem, we need to analyze the relationship between the tension in a stretched string and its fundamental frequency.

### Step-by-Step Solution:

1. **Understand the Relationship**: The fundamental frequency \( f \) of a stretched string is related to the tension \( T \) by the formula:
\[ f \propto \sqrt{T} \]
This means that if the tension changes, the frequency will change in proportion to the square root of the tension.

2. **Change in Tension**: We are given that the tension in the string is changed by \( 2\% \). This can be expressed mathematically as:
\[ \Delta T = \frac{2}{100} T = 0.02 T \]

3. **Change in Frequency**: The problem states that the fundamental frequency changes by \( 1.5 \, \text{Hz} \). We need to find the original frequency \( f \) before the change.

4. **Percentage Change in Frequency**: Since the frequency is proportional to the square root of the tension, the percentage change in frequency \( \Delta f \) can be related to the percentage change in tension:
\[ \frac{\Delta f}{f} = \frac{1}{2} \frac{\Delta T}{T} \]
Substituting the percentage change in tension:
\[ \frac{\Delta f}{f} = \frac{1}{2} \cdot 0.02 = 0.01 \]

5. **Expressing Change in Frequency**: We can express the change in frequency as:
\[ \Delta f = f \cdot 0.01 \]
Given that \( \Delta f = 1.5 \, \text{Hz} \), we can set up the equation:
\[ 1.5 = f \cdot 0.01 \]

6. **Solving for Original Frequency**: Rearranging the equation to find \( f \):
\[ f = \frac{1.5}{0.01} = 150 \, \text{Hz} \]

7. **Conclusion**: The original frequency \( f \) before the change in tension is \( 150 \, \text{Hz} \).