Two tuning fork A and B are sounded together gives 5 beats per second. If frequency of B is 260 Hz and after loading B 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 these instructions:

### Step 1: Understand the concept of beats
When two tuning forks (or sound sources) of slightly different frequencies are sounded together, they produce a phenomenon called beats. The beat frequency is equal to the absolute difference between the frequencies of the two sources.

### Step 2: Identify the given information
- The beat frequency when tuning forks A and B are sounded together is 5 beats per second.
- The frequency of tuning fork B (f_B) is 260 Hz.

### Step 3: Determine the possible frequency of tuning fork A
Since the beat frequency is given by the formula:
\[ \text{Beat Frequency} = |f_A - f_B| \]
We can set up the equation:
\[ |f_A - 260| = 5 \]

This gives us two possible equations:
1. \( f_A - 260 = 5 \) → \( f_A = 265 \) Hz
2. \( 260 - f_A = 5 \) → \( f_A = 255 \) Hz

Thus, the possible frequencies for tuning fork A are 255 Hz or 265 Hz.

### Step 4: Analyze the effect of loading tuning fork B
When tuning fork B is loaded with wax, its frequency decreases. The frequency of B will be less than 260 Hz after loading. Let's denote the new frequency of B as \( f_B' \).

### Step 5: Determine the new frequency of B
Since loading B decreases its frequency, we can assume:
\[ f_B' < 260 \text{ Hz} \]

For example, let's assume \( f_B' = 259 \) Hz after loading.

### Step 6: Calculate the new beat frequency
Now we need to find the new beat frequency with the possible frequencies of A (255 Hz and 265 Hz):
1. If \( f_A = 255 \) Hz:
\[ \text{New Beat Frequency} = |255 - 259| = 4 \text{ beats per second} \]
2. If \( f_A = 265 \) Hz:
\[ \text{New Beat Frequency} = |265 - 259| = 6 \text{ beats per second} \]

### Step 7: Conclusion
Since the problem states that the beat frequency increases after loading B, the only scenario where the beat frequency increases is when \( f_A = 265 \) Hz. Therefore, the frequency of tuning fork A is:
\[ f_A = 265 \text{ Hz} \]

### Final Answer
The frequency of tuning fork A is 265 Hz.

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