Two tuning forks A and B are sounded together and it results in beats with frequency of 4 beats per second . When A is loaded with wax, they again produces 4 beats per second . If frequency of A is 256 Hz, then the frequency of B is

Options

A. 252 Hz
B. 262 Hz
C. (A) and (B) both
D. None

Answer

To solve the problem, we need to determine the frequency of tuning fork B given the frequency of tuning fork A and the information about the beats produced when they are sounded together.

### Step-by-Step Solution:

1. **Understanding Beats**:
When two tuning forks are sounded together, the beat frequency is the absolute difference between their frequencies. The formula is:
\[ f_{beats} = |f_A - f_B| \]
where \( f_A \) is the frequency of tuning fork A and \( f_B \) is the frequency of tuning fork B.

2. **Given Information**:
- Frequency of tuning fork A, \( f_A = 256 \, \text{Hz} \)
- Beat frequency when both forks are sounded together, \( f_{beats} = 4 \, \text{Hz} \)

3. **Setting Up the Equation**:
From the beat frequency formula, we can write:
\[ |256 - f_B| = 4 \]

4. **Solving the Absolute Value Equation**:
This absolute value equation gives us two possible cases:
- Case 1: \( 256 - f_B = 4 \)
- Case 2: \( 256 - f_B = -4 \)

**Case 1**:
\[ 256 - f_B = 4 \implies f_B = 256 - 4 = 252 \, \text{Hz} \]

**Case 2**:
\[ 256 - f_B = -4 \implies f_B = 256 + 4 = 260 \, \text{Hz} \]

5. **Analyzing the Cases**:
- When A is loaded with wax, the frequency of A decreases. If the beat frequency remains the same (4 Hz), it means that the frequency of B must be higher than the new frequency of A after loading with wax.
- Since the beat frequency is the same (4 Hz) after loading, it indicates that before loading, tuning fork A had a higher frequency than tuning fork B.

6. **Conclusion**:
Since the frequency of A (256 Hz) is greater than the frequency of B before loading, we discard the case where \( f_B = 260 \, \text{Hz} \) because that would imply A is lower than B after loading. Thus, the frequency of tuning fork B is:
\[ f_B = 252 \, \text{Hz} \]

### Final Answer:
The frequency of tuning fork B is **252 Hz**.