Frequency of tuning fork A is 256 Hz. It produces 4 beats/second with tuning fork B. When wax is applied at tuning fork B then 6 beats/second are heard. Frequency of B is :-

Options

A. 250 Hz
B. 260 Hz
C. 252 Hz
D. (A) & (C) both may possible

Explanation

To find the frequency of tuning fork B, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Frequency of tuning fork A (f_A) = 256 Hz
- Beats produced with tuning fork B (initially) = 4 beats/second
- Beats produced after applying wax on tuning fork B = 6 beats/second

2. **Understanding Beats:**
- The number of beats per second is given by the absolute difference in frequencies of the two tuning forks.
- Therefore, the relationship can be expressed as:
\[ |f_A - f_B| = \text{Number of beats} \]

3. **Setting Up the Equation for Initial Beats:**
- For the initial case (4 beats/second):
\[ |256 - f_B| = 4 \]
- This gives us two possible equations:
1. \(256 - f_B = 4\) → \(f_B = 256 - 4 = 252 \text{ Hz}\)
2. \(f_B - 256 = 4\) → \(f_B = 256 + 4 = 260 \text{ Hz}\)

4. **Possible Frequencies for B:**
- From the above calculations, the possible frequencies for tuning fork B are:
- \(f_B = 252 \text{ Hz}\)
- \(f_B = 260 \text{ Hz}\)

5. **Analyzing the Effect of Wax:**
- When wax is applied to tuning fork B, it increases the mass and thus decreases its frequency.
- In this case, the number of beats increases to 6 beats/second:
\[ |256 - f_B'| = 6 \]
- This gives us two new possible equations:
1. \(256 - f_B' = 6\) → \(f_B' = 256 - 6 = 250 \text{ Hz}\)
2. \(f_B' - 256 = 6\) → \(f_B' = 256 + 6 = 262 \text{ Hz}\)

6. **Conclusion on Frequency of B:**
- Since applying wax decreases the frequency of tuning fork B, we need to consider the case where the frequency of B was initially higher (260 Hz) and then decreased.
- Thus, the only feasible frequency for tuning fork B that satisfies both conditions (initially producing 4 beats and then 6 beats after applying wax) is:
\[ f_B = 252 \text{ Hz} \]

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

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