Two tuning fork A and B are sounded together gives 5 beats per second. If frequency of B is 260 Hz and after loading A with was the beat frequency increases the frequency of A is

Options

A. 265 HZ
B. 255 Hz
C. 260 Hz
D. 250 Hz

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the Beat Frequency Concept
The beat frequency is the difference between the frequencies of two tuning forks. If two tuning forks A and B are sounded together and produce a beat frequency of 5 beats per second, we can express this mathematically as:
\[ |f_A - f_B| = 5 \text{ Hz} \]
where \( f_A \) is the frequency of tuning fork A and \( f_B \) is the frequency of tuning fork B.

### Step 2: Identify the Given Frequencies
We know that the frequency of tuning fork B is:
\[ f_B = 260 \text{ Hz} \]

### Step 3: Set Up the Equations for Tuning Fork A
From the beat frequency equation, we can express the frequency of tuning fork A as:
1. \( f_A = f_B + 5 \)
2. \( f_A = f_B - 5 \)

Substituting the value of \( f_B \):
1. \( f_A = 260 + 5 = 265 \text{ Hz} \)
2. \( f_A = 260 - 5 = 255 \text{ Hz} \)

Thus, the possible frequencies for tuning fork A are:
- \( f_A = 265 \text{ Hz} \)
- \( f_A = 255 \text{ Hz} \)

### Step 4: Analyze the Effect of Loading Tuning Fork A
When tuning fork A is loaded with wax, its frequency decreases. This means that the new frequency of tuning fork A will be less than either of the two frequencies we calculated (265 Hz or 255 Hz).

### Step 5: Determine the New Beat Frequency
Since the frequency of tuning fork A decreases, the new beat frequency will be calculated based on the new frequency of A:
- If \( f_A \) was initially 265 Hz, after loading it with wax, it will be less than 265 Hz, and the beat frequency with B (260 Hz) will be less than 5 Hz.
- If \( f_A \) was initially 255 Hz, after loading it with wax, it will be less than 255 Hz, and the beat frequency with B (260 Hz) will be greater than 5 Hz.

### Step 6: Conclusion
Since the problem states that the beat frequency increases after loading A with wax, the only valid scenario is when the original frequency of A was 255 Hz. Therefore, the frequency of tuning fork A is:
\[ f_A = 255 \text{ Hz} \]

### Final Answer
The frequency of tuning fork A is **255 Hz**.

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